experience curves for modern low-head hydroelectric turbines · experience curves for modern ·...

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i ~ A P r.-> LA 5 1 ~ · ' ~ ··I ~ ~ l 1 Rlesearch Technical Completion Report

EXPERIENCE CURVES FOR MODERN · LOW-HEAD HYDROELECTRIC TURBINES

by C.S.K. Kpordze C.C. Warnick Civil Engineering Department

Bureau of Reclamation HYDRAULICS BRANCH

OfFICE \ -~ ~\lE COPY

'iTREN BOf'.FO\'iED RETURN PROMPTLY

for Bureau of Reclamation

United States Department of the Interior

Contract NO. 81-VOlSS

Idaho Water and Energy Resources Research Institute University of Idaho

Moscow, Idaho May, 1983

Contents of this publication do not necessarily reflect the views and policies of the U.S. Department of the Interior, nor does mention of trade names or commercial products constitute their endorsement or recommendation for use by the U.S. Government.

•

Correction:

The 11 Correlation Coefficient 11 used in this report is r 2 instead of r

which is shown on the nomographs and tables. r2 as used measures how

much variation in the dependent variable can be explained by the model. 2 r can range from 0 to 1, see page 11 .

FOREWARD

This study of the characteristics of manufactured hydroelectric

turbine equipment in the form of experience curves is presented to make

available information and experience that can be used in planning and

preliminary design of hydropower developments. It is intended to

supplement material already available for the more conventional hydrau

lic turbines and therefore concentrates on information about low-head

type turbines. In the tradition of the Idaho Water and Energy

Resources Research Institute the report has been prepared to meet a

need and desire of government agencies and practicing professional

engineers involved in hydropower engineering.

i

ACKNOWLEDGEMENTS

The authors wish to recognize the support of the Bureau of Recla

mation, U.S. Department of the Interior through Contract No. 81-V0255

and earlier support to initiate work by the Office of Water Research

and Technology. The counsel and advice of Clifford A. Pugh as techni

cal monitor of the project from the Bureau of Reclamation has been

especially helpful.

Most of the data used in this report came from a number of manu

facturers of hydroelectric equipment. To name all who contributed data

in this acknowledgement is not possible, however, a listing in the

Appendix does give the names and addresses of all the manufacturers

contacted in connection with the study. A very special thanks goes to

all the firms that contributed, especially to representatives of

several of the firms that took time to explain to the authors their

approaches to selection of turbines.

Thanks is given to the secretarial staff of the Institute and the

Civil Engineering Department for their help in typing and preparing

manuscripts, tables, and processinq needed paper work. A special

thanks is extended to Don Schutt for this work in drafting and aiding

in the preparation of all figures.

The report has been prepared under supervision of Dr. James H.

Milligan as Chairman of the Department of Civil En~ineering and Dr.

John R. Busch as Director of the Idaho Water and Energy Resources

Research Institute.

i i

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES ix

ABSTRACT xi

SUMMARY . Xi i

INTRODUCTION 1

COLLECTION AND ORGANIZATION OF DATA 5

METHODS OF ANALYSIS 8

RESULTS ...... . 15

ANALYSIS AND USE OF RESULTS 113

COMPARISONS ....... . 123

CONCLUSIONS AND RECOMMENDATIONS 134

REFERENCES 139

APPENDIX

SAMPLE CALCULATIONS FOR TURBINE CONSTANT CONVERSIONS . . . 144

SAMPLE CALCULATIONS FOR DETERMINING TURBINE DIAMETER AND TURBINE SPEED BY DIFFERENT METHODS

COMPLETE TABLE OF DATA

COMPUTER PROGRAMS . .

LIST OF TURBINE MANUFACTURERS

i i;

147

157

175

180

Figure No.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

LIST OF FIGURES

Caption Page

Schematic drawings of three types of low-head turbines of the reaction type . . . . . . . 4

Schematic drawing of cross-flow turbines of the low-head impulse type . . . . . 6

Specific speed versus rated head for bulb turbines . . . . . . . ..... .

Specific speed versus rated head for bulb turbines for different manufacturers

Specific speed versus unit power for bulb turbines ............... .

Specific speed versus unit discharge for bulb turbines . . . ........ .

Unit speed versus specific speed for bulb turbines . . . . . . . . . . . . . . . .

Unit power versus unit discharge for bulb turbines ............. .

Unit speed versus unit power for bulb turbines . . . . . . . . . . . . . .

Unit speed versus unit discharge for bulb turbines ...... .

Speed ratio versus specific speed for bulb turbines .....

Speed ratio versus unit power for bulb turbines ...... .

Turbine diameter versus speed ratio for

17

18

19

21

22

23

24

26

28

29

bulb turbines . . . . . . . . . . . 30

Turbine diameter versus P/H ratio for bulb turbines .....

Turbine diameter versus Q/N ratio for bulb turbines ..

Turbine speed, N, versus P/H for bulb turbines ............. .

iv

31

32

34

LIST OF FIGURES (continued)

Figure No. Caption Page

17. Turbine speed versus /HID ratio for bulb turbines . . . . . . . . . . . . . . . 35

18. Specific speed versus rated head for tubular turbines . . . . . . . . . . 40

19. Specific speed versus rated head for tubular turbines from different turbine manufacturers . . . . . . . . . . . . . . . . . . 41

20. Specific speed versus unit power for tubular turbines . . . . . . . . . . . . 42

21. Specific speed versus unit discharge for tubular turbines . . . . . . . . . . . . 43

22. Specific speed versus unit speed for tubular turbines . . . . . . . . . . . . . . 44

23. Unit power versus unit discharge for tubular turbines . . . . . . . . . . . . . . 45

24. Unit speed versus unit power for tubular turbines . . . . . . . . . . . . . . . . . . 47

25. Unit speed versus unit discharge for tubular turbines . . . . . . . . . . . 48

26. Speed ratio versus specific speed for tubular turbines . . . . . . 49

27. Speed ratio versus unit power for tubular turbines . .. . . . . . 50

28. Turbine diameter versus speed ratio for tubular turbines . . . . . . . . . 51

29. Turbine diameter versus P/H ratio for tubular turbines . . . . . . 52

30. Turbine diameter versus Q/N ratio for tubular turbines . . . . . . 53

31. Turbine speed versus P/H ratio for tubular turbines . . . . . . . . . . . . . . 57

32. Turbine speed versus IH/o ratio for tubular turbines . . . . . . . . . . . . 58

v


Figure No. Caption Page

33. Specific speed versus rated head for cross-flow turbines . . .... 59

34. Specific speed versus unit power for cross-flow turbines . . . . . . . . . . . . . 61

35. Specific speed versus unit discharge for cross-flow turbines . . . . . . . . . . . . . 62

36. Specific speed versus unit speed for cross-flow turbines . . . . . . . . . . . . . . . 63

37. Unit power versus unit discharge for cross-flow turbines . . . . . . . . . . . . . 64

38. Unit speed versus unit power for cross-flow turbines . . . . . . . . . . . . . 65

39. Unit speed versus unit discharqe for cross-flow turbines . . . . . . . . . . 66

40. Speed ratio versus specific speed for cross-flow turbines . . . . . . . . 68

41. Speed ratio versus unit power for cross-flow turbines . . . . . . . . . 69

42. Turbine diameter versus speed ratio for cross-flow turbines . . . . . . . . . . 70

43. Turbine diameter versus P/H ratio for cross-flow turbines . . . . . . . . 71

44. Turbine diameter versus Q/N ratio for cross-flow turbines . . . . . . 72

45. Definition diagram for suction head and draft head for different types of turbines . . . . 76

46. Stratification of relation between plant sigma and specific speed for different manufacturers. . 78

47. Specific speed versus cavitation coefficient for tubular turbines . . . . . . . . . . .82

48. Simplified dimensioning sketch for water passages of bulb turbines . . . . . . . . . . . . 85

vi

Figure No.

49

50.

51.


Caption

Distance from turbine entrance to draft tube outlet versus rated power output for bulb turbines . . . . . . . . . . . ....

Distance from turbine entrance to draft tube outlet versus turbine diameter for bulb turbines .... · ..... .

Length of bulb versus rated power for bulb turbines ....

52. Length of bulb turbine versus turbine

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

diameter

Turbine entrance area versus rated power output for bulb turbines ..... .

Turbine entrance area versus turbine diameter for bulb turbines .....

Bulb diameter versus rated power for bulb turbines ........... .

Bulb diameter versus turbine diameter

Draft tube exit area versus rated power for bulb turbines ........ .

Draft tube exit area versus turbine diameter for bulb turbines

K/Ae ratio versus rated power output for bulb turbines . . . ....

Turbine entrance velocity versus rated power for bulb turbines ....... .

Turbine entrance velocity versus turbine diameter for bulb turbines ...... .

Turbine entrance area versus rated turbine discharge for bulb turbines ....

Draft tube exit area versus rated turbine discharge for bulb turbines ....

Dimensioning recommendations for low-head reaction turbines ........... .

vii

Page

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98

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101

102

103

106

Figure No.

65.

66.

67.

68.

69.'

70.

71.

72.

73.

74.

75.

76.

77.


Caption

Schematic drawing defining dimensions used in study of standard tubular turbines

Turbine entrance area versus turbine diameter for standard tubular turbines ....... .

Draft tube exit area versus turbine diameter for standard tubular turbines ....... .

Length from runner blade centerline to turbine entrance versus turbine diameter for tubular turbines ............. .

Length from runner blade centerline to draft tube exit versus turbine diameter for standard tubular turbines . . • . . . . ...•

Reproduction of KMW nomograph for selection of turbine diameter and turbine speed for bulb turbines . . . . . . . . . . . . . . .

Nomograph for estimating turbine diameter from rated head and rated power output for bulb turbines ................. .

Nomograph for estimating turbine diameter from rated head and rated power output for tubular turbines . . . . . . . . . . . . . . . . . .

Nomograph for estimating turbine diameter from rated head and rated power output for cross-flow turbines ........... .

Comparison of experience curves of specific speed versus rated head for different types of low-head turbines ............ .

Comparison of experience curves of speed ratio versus specific speed for different types of axial-flow turbines . . . . . . . . . ...

Comparative of experience curves of plant sigma versus specific speed for different low-head turbines ...... .

Comparison of experience curves of plant sigma versus unit discharge for different low-head turbines . . . . . . . . . . . . . . . . . . . .

viii

Page

109

110

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120

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126

128

130

Table No.

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2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

LIST OF TABLES

Caption

Comparison of turbine constants in different systems of units and forms of equations

Summary listing of regression information and equations relating turbine characteristics to various turbine constants for bulb turbines ................ .

Summary listing of regression information and equations relating turbine characteristics to various turbine constants for tubular turbines ............ .

Summary listing of regression information and equations relating turbine characteristics to various turbine constants for cross-flow turbine ............... .

Summary listing of regression information relating to turbine setting for bulb and tubular turbines ............ .

Summary listing of regressionn information and equations relating to water passage dimensions for bulb turbines ..

Reference information and source for standard tubular turbine water passage dimensions .

Summary listing of regression information and equations relating to water passage dimensions for standard tubular turbines .

Summary listing of regression information and equations for special case of manufactured KMW bulb turbines ........... .

Comparison information of regression equations for Ns versus H for different types of low-head type turbines ............. .

Comparison of draft tube exit velocity with Purdy•s recommended limit for manufactured bulb turbines . . . . . . . . . . . . . . . .

Comparative results of different methods of estimating turbine diameter and turbine speed

ix

Page

13

36

55

74

80

104

108

115

117

125

132

133

Table No.

13.

14.

LIST OF TABLES

Caption Page

Comparison of value of correlation coefficients for the important regression equations . . . . . 135

Summary listing of regression information and equations relating turbine specific speed to rated head for bulb and tubular turbines from different turbine manufacturers . . . . . . . . . . . . . 141

X

ABSTRACT

This report contains the research findings of an extensive inves-

tigation of characteristics of over 300 low-head hydraulic turbines

that have been manufactured all over the world. These results are

presented in the form of experience curves and regression equations

relating the traditional turbines constants of specific speed, speed

ratio, unit power, and cavitation coefficient to such parameters as

rated head, rated discharge, rated power output, runner speed, and

runner diameter. Additional information on the characteristic dimen-

sion of the water passages is also presented. Traditional methods of

estimating turbine diameter and turbine speed have been checked with

actual practice and new simplified methods for estimating turbine dia-

meter and turbine speed have been proposed and verified.

A comparison has been made as to how well the draft tube exit

velocities on manufactured units are complying with recommended limits.

Rather limited success was obtained in characterizing the turbine

setting parameter and its relation to the specific speed. Excellent

comparisons were possible with published regression relations and

experience curves of conventional reaction turbines.

KEY WORDS

BT -Hydraulic Turbines, Power Plants, Turbines, Turbine Runners NT - Axial Flow Turbines, Bulb Turbines, Tube Turbines, Impulse

Turbines (cross-flow) RT - Draft Tubes, Hydroelectric Plants

xi

SUMMARY

This report presents information on experience curves and empiri

cal relations useful in the preliminary planning of hydroelectric

power plants and their components based on actual manufactured and

operating units. The objectives of the study were to develop up-to

date relations for low-head hydropower turbines giving (1) relations of

specific speed to design head, (2) relations of turbine runner diameter

to design head, rotational speed, and velocity ratio, (3) draft head

relations to specific speed and cavitation coefficient and (4) empiri

cal relations of physical dimenions of flow passage dimensions of in

take and draft tube areas to the turbine runner diameter.

Data for making the study were obtained by personal contact of the

authors in visits to over twelve manufacturers of turbines, by careful

review of existing technical literature, and by extensive correspon

dence with over thirty manufacturers of hydroelectric turbines. A

careful assessment was also made of the literature on simulitude laws

and turbine constants that have been extensively used in the hydraulic

machinery field. Much reference and comparison have been made to the

U.S. Bureau of Reclamation Monograph No. 20 which has wide acceptance

and use in the planning and feasibility field by both public agency

engineers and by consulting engineers. Contact with over 200 different

consulting engineers by Professor Warnick has likewise been used as a

basis for judging and determining the approaches that are currently

used in professional practice. The ultimate goal of the study has been

to present useful procedures that can be authoritatively accepted by

the engineering profession and provide for a more uniform and

consistent preliminary selection of hydraulic turbines.

xii

The basic approach of the analytical portion of the study has been

to make regression analyses of the data collected on various turbine

characteristics used in hydropower planning. The regression approach

used was that of relating one independent parameter to a dependent

parameter, or to two parameters expressed as a single ratio. The curve

fitting utilized a logarithmic eqyation of the form:

log y = log A + m Log X.

Sets of data were analysed on a computer system known as Statistical

Analysis System (SAS).

The study centered on three types of turbines, (1) the bulb type

units, (2) the tubular type units, and (3) the cross-flow units (See

Figures 1 and 2). The results are presented in four distinct contribu

tions: (1) Experience curves and regression equations were developed

for relating specific speed to rated head and similar regression equa

tions were developed between the various standard turbine constants .

(see Tables 2, 3 and 4), (2) Relations were developed for determining a

cavitation coefficient that is used in choosing the turbine setting

(see Table 5), (3) Experience curves were developed for estimating

water passage dimensions and referencing those dimensions to the nomin

al diameter of the turbine (see Figures 48 to 69), and (4) speed and

diameter selection procedures were assessed and compared with published

information on propeller turbines and new procedures developed for

making speed and diameter selection at the feasibility staqe of

planning.

The new selection procedures are presented in the form of noma

graphs and comparative experience curves beginning with Figure 71 and

continuing to Figure 77. Sample calculations on how to apply the

xiii

experience curves are presented in Appendix 2. The conclusion is made

that these procedures are simpler and more direct than conventional

procedures now in use and appear to offer more consistent results. The

compilation of data on manufactured low-head turbines should offer an

excellent reference in itself for designers and planners to use in

preliminary design and feasibility studies.

Because this study applied to only low-head turbines and also

because new data on manufactured units are now available on convention

al Kaplan, Francis and Pelton type turbines, it is recommended that the

new methodology developed on this study be used to update experience

curves and selection procedures for those types of turbines used in

higher head applications.

xiv

INTRODUCTION

In planning and design of hydroelectric plants much advantage is

gained by utilizing the experience gained from the various installa

tions that have already been made. Publications like Engineering Mono

graph No. 20 of the U.S. Bureau of Reclamation (1976) entitled,

"Selecting Hydraulic Reaction Turbines" have been developed for this

purpose. Records of experience have been analysed and various exper

ience curves and empirical equations developed that provide a conven

ient way to proceed in plannin9 for new hydropower developments.

Experience curves provide a way of making visual comparison easily and

with engineering judgement help the engineer in proceeding through the

complex task of planning and designing a hydropower development. These

do not substitute for the design selection that a turbine manufacturer

must make to proceed to final design. Experience curves however, do

provide the planning engineer with useful information to proceed with

feasibility and preliminary design studies.

Modern low-head hydroelectric turbines such as tubular turbines,

bulb type installations, and cross-flow turbines have now been in

production long enough to provide enough operating units from which

experience curves can be generated. The work of de Siervo and de Leva

(1976 and 1977) and de Siervo and Lugaresi (1978) treating conventional

Francis turbines, vertical Kaplan turbines, and Pelton turbines did not

consider the more modern low-head type turbines, neither did the

Engineering Monograph No. 20.

OBJECTIVE

The objective of this report is to provide experience curves and

practical empirical equations useful in planning and preliminary design

1

of hydroelectric developments for modern low-head type turbines. Spec

ifically, to provide information on bulb type turbines, tubular type

turbines, and cross-flow turbines that have been manufactured in the

past thirty years. Particular relationships to be developed would

provide information on the following:

1. Specific speed relation to design head.

2. Turbine runner diameter relation to design head, rotational

speed, and velocity ratio.

3. Draft head relation to specific speed and cavitation coeffi

cient.

4. Physical dimensions of flow passages (intake and draft tube)

relations to turbine runner diameter.

EXPERIENCE CURVES AND TURBINE CONSTANTS

Historically a series of turbine constants have been developed by

using similarity laws of hydraulics and fundamental hydraulic equations

to characterize the performance of hydraulic turbines. Mathematical

development of the various constants is covered in texts by Barrows

{1927), Doland (1954), Csanady {1964), Warnick (in press), and in an

M.S. thesis by Kpordze (1982). A worthwhile discussion on different

expressions for turbine constants is presented by Barr {1966). Recent

ly international manufacturers have suggested an approach that reports

the various constants in dimensionless form (Allis Chalmers, no date).

Table 1 presents expressions for different forms of the various turbine

constants in use and the new dimensionless system of expressing the

turbine constants. This table contains a list of terms used in the

report along with appropriate units in which the terms are expressed.

The American system reports the constants in units of power output as

2

horsepower, diameter of runner in inches, turbine discharge in

ft3fsec, head in feet, and rotational speed in rpm. The European

system reports the constants in units of power output in kilowatts,

diameter of runner in millimeters, turbine discharge in cubic meters

per second, head in meters, and rotational speed in rpm. The European

system has been used throughout this report because so much of the

manufacturer's literature and experience curves that have been reported

have been published in the European system. Conversions and relation

ships between the different forms of the turbine constants are provided

in Table 1 and in an example in the Appendix demonstrating the use of

the conversions.

Manufacturers who have worked with these constants and model tests

have further utilized the' constants to develop multiparameter relations

termed ''Hill Curves." These hill curves are proprietary information

and therefore are not available to practicing engineers for use in

selection and design. In practice many engineering firms develop their

own experience curves and once developed the curves are made proprie

tary information of the firm. In this effort the experience curves and

empirical equations are being proposed as a way to achieve more consis

tency in the planning studies and to provide a better and more uniform

base for proceeding with engineering design. In a sense it does pro

vide a check as to the recommendations and quotations of performance

that are put forth by the manufacturers who may be asked to bid on and

supply hydraulic turbines.

The types of turbines studied are of two general types, reaction

turbines and impulse turbines. Three reaction type turbines were

studied: bulb type units, tubular type units and rim-generator units.

Typical representation of these units are shown in Figure 1. The

3

Rim-generator turbine

Tubular turbine

ILWATER

Bulb turbine

Figure 1. Schematic drawings of three types of low-head turbines of the reaction type.

4

impulse turbine studied was a cross-flow turbine. Figure 2 is a line

drawing representation of the cross-flow type turbine.

COLLECTION AND ORGANIZATION OF DATA

DATA COLLECTION

Collection of data was initiated first on this project when one of

the authors, Professor Warnick, contacted numerous turbine manufactur

ers in connection with preparation of a new textbook on hydropower

engineering. This included reference lists and characteristics of tur

bines manufactured by various turbine manufacturers. These personal

contacts have continued since that time and during the course of the

present research contract, several manufacturers were visited. A table

in the Appendix gives the list of manufacturers visited, a contact

name, and the address and the then active telephone number. On these

visits company literature particularly concerned with selection of tur

bines was collected. A complete set of this manufacturer's information

has been assembled for the Bureau of Reclamation as a reference docu

ment. Much of this document includes nomographs published by the com

panies for use in selecting turbines and for providing preliminary data

on dimensions of standard turbines and water passages of the civil

works portion of hydropower installations.

The technical literature was searched for data on turbines and

representative of this is the technical articles like that of de Siervo

and de Leva (1977 and 1978) and also a listing of information prepared

by Cottillon (1977, 1979, and 1981).

Subsequent to the literature search and the initial personal

visits of Professor Warnick, considerable correspondence was carried on

to complete the collection of data. In some cases there were no

5

,

--Flow control

runner

Turbine runner-·--

Horizontal entrance Vertica I entrance

Figure 2. Schematic drawing of cross-flow turbine of the low-head impulse turbine type.

6

replies but in general good response was obtained in acquiring missing .

data and clarifying information that was obtained in personal contacts

or from published reference lists.

ORGANIZATION OF DATA

All information that was received was first checked to verify con-

sistency and identify appropriate measurement units. Transformation of

all units were made to make all units compatible with the European sys-

tern of reporting turbine constants. Data were then entered in a com-

puter file that would permit easy access for analysis. This informa-

tion included type of turbine, name of manufacturer, name of power sta-

tion, date of commissioning, rated head, rated flow, rate capacity per

unit, runner diameter, unit rotational or running speed and specific

water passage dimensions designated by letters of identification. A

complete list of all the data used or obtained during the study is

reproduced as tabular material in the Appendix 3.

Once a standardized file of the various data was prepared then

computer programs were developed to extract the data in various strati-

fications as to a particular type of turbine, a particular manufactur-

er, or a particular year of commissioning. These computer programs are

filed in the Appendix 4 to permit future researchers to proceed with

analyses of additional data.

7

METHODS OF ANALYSIS

The study basically entailed classifying and analysing different

sets of data from various manufacturers and data reported by the numer

ous companies. Different statistical procedures were used in proceed

ing with the analysis. One such statistical procedure is cluster

analysis.

The cluster analysis is a means of classifying observation (in

this case turbine characteristics) on the basis of similarity

(Anderberg, 1973). Cluster analysis in this research was used to group

the turbine data into periods of similar turbine design characteris

tics. This method was considered a valid statistical technique for

classifying the turbine data into periods of similar turbine design

characteristics. In this study, the type of cluster analysis technique

used is similar to the weighted pair-group method used by Davis (Davis,

1973). The data base of four turbine characteristics on 221 bulb tur

bines manufactured all over the world, was treated as a 4 x 221 matrix.

The four turbine characteristics used were: specific speed, rated

head, unit discharge and unit power. Using a computer, the 4 x 221

matrix was partitioned into a 4 x n1 and 4 x n2 submatrices based

on the date of commissioning of the turbines. Where n1 denotes num

ber of bulb turbines put into service during the periods of time under

consideration and n2 denotes 221 - n1. The only restriction placed

on the value of n1 was that n1 be greater than 15 (n1 > 15}. The

analysis procedure was started from the earliest date among the turbine

commissioning dates, 1953 to the next date, say, 196a such that n1

was greater than 15. Then linear regression analysis was performed on

the resulting 4 x n1 and 4 x n2 matrices and the corresponding

8

correlation coefficients noted for each of the four groups of charac

teristics. The value of n1 was then increased by increasing the per

iod of analysis and the correlation coefficients recomputed and compar

ed with the previously computed values. This process was repeated

until the resulting correlation coefficients were less than the nearest

previously computed values. Then the first period of analysis was

taken as the sample period corresponding to the highest value of corre

lation coefficient. The procedure was repeated to determine the next

period of turbine design characteristics. The second trial period was

selected to include one year after the first period up to the year such

that n1 for the second time interval exceeded 15 turbine characteris

tics. Two such periods identified for the 221 bulb turbines were:

1953 to 1965, constituting the first sample period, and 1966 to 1984,

the second sample period. The two above mentioned periods were then

used to group all the turbine characteristics throughout the rest of

the analysis to determine experience curves for low-head hydroelectric

tu-rbines. The only modifications made were in the cases where the

characteristics curves resulting from the regression analysis for the

two periods were so close as to justify representation by a single

regression curve or the number of turbine characteristics in each time

period were too few to justify the group classification. In all such

cases the period of analysis was taken to include 1953 to 1984.

STATISTICAL METHOD OF DATA ANALYSIS

The data used in developing the experience curves resulted from

the measurement of a number of variables and came from different

sources and were collected under a variety of conditions. In order to

describe the relationship existing between such variables, the standard

9

procedure is to formulate a statistical hypothesis setting forth the

explicit mathematical form of the relationship between the variables.

A common assumption is that the relationship between two variables, for

example, X and Y or the transformations of X and Y is linear. Having

assumed linearity, our objective then is to specify a rule by which the

11 best 11 straight line fitting X andY is to be determined. The 11 line of

best fit 11 is said to be that which minimizes the sum of the squared

deviations of the points of the graph from the points of the straight

line (with distances measured vertically). The general method of find

ing equations for approximating curves which fit given sets of data

points plotted on a rectangular coordinate is known as curve fitting.

One of the main purposes of curve fitting is regression which is the

process of estimating the variable Y (dependent variable) from the

variable X (independent variable). If Y is to be estimated from X by

means of some equation, the equation is called the regression curve of

Yon X. The degree of relationship between variables is known as

correlation. When only two variables are involved, the relationship is

called simple regression and simple correlation. When more than two

variables are involved, the relationship is known as multiple regres

sion and multiple correlation (Spiegel, 1961) and (Pindyck and

Rubinfeld 1981). Sometimes it helps to plot the scatter diagrams in

terms of transformed variables. For example if Log Y leads to a

straight line, log Y = a + bX will be used as an equation for the

approximation curve. The type of equations used in this study are:

Linear regression: y = a + bX

Exponential curve fit: y = aebx

Power curve fit: y = axb

10

',

Logarithmic curve fit: Y = a + log X 10

Where a, b and e are constants.

The degree to which numerical data tend to spread about an average

value is called the variation or dispersion of the data. One of the

most common measures of dispersion is the standard deviation, s. The

standard deviation of a set of N numbers x1, x2,

by the expression:

s = ( ~ (x - x)2 I N)0.50 j=l j

• • • • • • • X j is defined

which is the root square mean deviation and x is the arithmetic mean.

In the graphical representation of the curve, if parallel lines to the

regression line of Y on X are constructed at respective vertical dis-

tances s, 2s, and 3s from the regression line, statistical theory

states that there would be included between these lines 68%, 95% and

99.7% of the sample points, respectively. This is true only if the

numbers of data points, N, is large enough. The symbols with the s,

2s, and 3s lines are referred to as one-, two-, and three standard

deviations respectively.

The measure of how well a straight line explains the relationship

between two variables X and Y is the correlation coefficient, r and it

is expressed as the square root of the ratio of the explained variation

to the total variation. ( E(Y - Y) 2 I L: (Y - Y) 2 )0·50 where Y is the

estimated value of Y from the regression equation and Y is the

arithemetic mean value. Values of r = 1 or r = -1 denote perfect

correlation. The above defined statistical concepts have been used in

the data analysis and were embodied in the computer system used in the

studies and plotting the resulting experience curves.

11

The data used in the analysis were screened to include only tur

bines having complete information; those having incomplete information

or unusual operating characteristics were eliminated. The resulting

sets of data were analyzed using a computer system known as .. Statis

tical Analysis System .. (SAS), developed by SAS Institute, Inc. of North

Carolina, USA. The above named group of programs was run on IBM

Virtual Machine Facility/370 (CMS). The SAS computer system is set up

to perform linear regression analysis, to plot data values and to print

out any desired input or computed values. In order to use the trans

formed variable models, the data must be transformed and arranged in

the appropriate linear model form. The selection of turbine constants

used in the linear regression models was based on the turbine constants

currently used in practice and the type of information needed for pre

liminary investigation or feasibility studies of hydroelectric pro

jects.

Traditionally the turbine constants specific speed, Ns, and the

speed ratio, 0, are used to select the appropriate type of turbine and

with developed empirical equations estimates are made of turbine runner

diameter and turbine speed. These turbine constant terms of Ns and

0 are defined mathematically in Table 1 and procedures for using the

constants in preliminary design and feasibility studies are illustrated

in sample calculations in Appendix 2. Among the procedures illustrated

in the sample calculations is the method used in the U.S.B.R. Monograph

No. 20 for estimating turbine runner diameter and turbine speed. Other

turbine constants such as unit speed, unit power, and unit discharge,

that are used to report turbine test data were also calculated for the

manufactured units and analyses were made to develop regression

12

Table 1. Comparison of turbine constants In different systems of units and forms of equations American system European system Dimensionless

Parameter hp,lnch,CFS,ft,rpm kW, m,:m3/sec,rpm system

Designation Formula Designation Formula Designation Formula

Speed ratio

Unit speed

Unit discharge

Discharge coefficient

Unit torque

Torque coefficient

Energy coeflclent

UnIt power

Power coefficient

SpecIfIc speed

ConversIon term

dn

<P ·----

n1

n 5

n • 0.262 N

43.368(h) 0"5

dn

q q., __ _

1 d2 ho.s

p

p ·---1

0.5 n p

n •---s N s

N .. 166. Ul s s s s

WO k

u

0 N 3

ku • wad

60C2gH)0.50

(1) • ---ad

CgH>o.s

ON =--

Q

p

p ·-11

N •---

0.5 T)

s

(1)0

(.\)ad.--

(gH)o.s

Q

Qed Qed .. ----

02Cgh)o.s

Q

~d ~d.

TUld

T • ad

T

3 pO gH

T

T •----Uld pw2 o'

gH

p

p p • Uld

Uls ·----(gH)0.75

n s

(1) • ----s

H • net head, m of water; h "' net head, ft of water; d • runner diameter In Inches, 0 .. runner diameter In m; q .. discharge In cfs, ft3/sec; Q • discharge In m3/sec; Ul z angular velocity, rad/sec; T • torque kgm; g • acceleration due to gravity, m/sec2; p =mass of density of ~ter, kg/m3 n "'efficiency. 13

relations between the different constants and the basic parameters of

rated head, rated power output, rated discharge, turbine speed, and

turbine diameter.

In this study emphasis was directed toward relations of specific

speed to rated head, speed ratio to specific speed, and the relation of

these constants to actual runner diameter and actual runner speed the

same as was used in the approach defined in the U.S.S.R. Monograph No.

20.

14

RESULTS

The results are presented in three main classifications and fur

ther subdivided into subclassifications. The first classification pre

sents results relating to characteristics of the turbines and the tur

bine diameter in relation to parameters of rated head, rated discharge,

rated output, and rotational speed of the turbine. This treats rela

tionships and interelationships concerned with the turbine constants,

specific speed, unit speed, unit power, velocity ratio, unit discharge,

and some new alternative ratios as parameters.

The second classification presents information on draft head,

suction head, specific speed, and cavitation coefficient. The third

classification is concerned with turbine constants and the characteris

tic dimensions of the water passages of the civil works portions of the

hydropower installations. This includes relating dimensions of the

entrance works leading up to the turbine and dimensions of the draft

tube to the turbine constants.

Under each of these classifications subclassification information

is presented on the three different types of turbines: {l} bulb type

units, {2) tubular type units, and (3) cross-flow type units. Infor

mation on rim-generator type units was insufficient to make any mean

ingful analyses.

TURBINES CHARACTERISTICS

The most common experience curve is obtained by relating the spec

ific speed, Ns, to the rated head, H. Cluster analyses was performed

and the data stratified according to the time of commissioning.

15

Bulb Turbines

For bulb type turbines the

3, where three different curves

iods of manufacturing are given

N = 1155.937 H-0· 346 s

Ns = 964.130 H-0· 1631

Ns = 1520.256 H-0· 2837

N P0.5 where N = s H1.25

N = rotational speed in rpm

P = rated power output in KW

H = rated head in m.

Ns vs H relation is shown in Figure

representing three different time per-

by the following regression equations:

(1953-1960) Eq. ( 1)

(1961-1970) Eq. (2}

(1971-1984) Eq. (3~

Eq. (4)

A further stratification of the Ns vs H relationship showing the

variation of the relation for various turbine manufacturers is

presented in Figure 4 for all bulb turbines for which data were

obtained. Summaries of the data from individual manufacturers is

presented in Appendix 3 along with the specific regression equations.

Figure 5 presents the relation between specific speed, Ns, and

unit power, P11, for all bulb turbines for which data were obtained

where the regression equation is given as:

p where P 11 = ---

02Hl. 5

and 0 = turbine runner diameter in m.

16

Eq. ( 5)

Eq. ( 6)

2000

1600 "'0 Q) Q) 0..

"'0 1200 Q) ll)

Q) u 0.. .,.... ll) 4-

u 1000 .,.... u .,.... Q)

4- 0.. .,.... 800 u ll)

Q) .. 0.. (/)

ll) z .. 4-...... (/) 0 ........ z 600 0 .--

Ol 0

....J

400

320

3.3

3.2

S. I

3.0

2.9

2.8

2.7

2.6

2.5 1'''''''''1''

0.0 0.2

• ro_,-- ds = 1520.256H-0· 2837 (1971-1984)

r = 0.40 S = 118.24

~ No. of units = 119

~AI/A •

A • A

= 1155.937H-0.2797

r = 0.37 (1953-1960)

s = 216.06

No. of units = 32

0.4 0.8 0.8 1.0 Log 10 of H, Rated Head in Meters

Ns 964.130H-o ·6131 ~ (1961-1970) "" \

0.26 S = 104.24- I

units = 67

• • A

1.2 1.4

I I I I' I' I I I' I' I 1. 0 1. 5 2 5 10 16 20 24

H, Rated Head in Meters

Figure 3. Specific speed versus rated head for bulb turbines.

2000 -

1800 j 1600 -o

QJ QJ Cl..

1400 Vl -o QJ u QJ .,... Cl.. 4-Vl 1200

.,... u

u QJ .,... Cl.. 4- Vl r-

u 1000 "' QJ Vl Cl.. :z:: Vl

4-"' 0 Vl

:z:: 800 0 .--

Ol 0

....J

......

600 1 co

400 -l

3.3

3.2

3. 1

3.0

2.9

2.8

2.7

2.6

2.5

1 = K~1W 2 = Tampella 3 = Vevey-Charmilles 4 = Voist-Alpine 5 = Voith 6 = Neyrpic 7 = Escher-\~yss 8 = Kvaerner Brug 9 = Fuji

',-,·-·~·-·I I I I I I I I I I I' I I I I I I I I I I I I I' I I I I I' I I I I I I I I I I I I iII 1

0.0 0.2 0.4 0.6 0.8 1 . 0 1 . 2 1 . 4 Log 10 of H, Rated Head in Meters

l r- ---~ 2 r-- - r 4 5 -l ~ 16 I I r I 2 b ~ 2 I


Figure 4. Specific speed versus rated head for bulb turbines for different manufacturers.

...... w

-o Q) Q) c..

V')

u .,.... 4-.,.... u Q) c..

V')

ft

Ul z

2000

1800

1600

1400

1200

1000

800

600

400

3.3

3.2

-o Q)

~ 3.1 V')

u .,.... 4-. ,.... u ~ 3.0

V')

ft

Ul z

6 2.9 0 r-

O'l 0

_J

2.8

2.7

• •

•

• •

•

~/ . ,/• / . ~ . /.-. ··/../..- .

• . /r::,:i../7 .. .,/' J.•'~ . /~ .~ •. •

.~.·!'·~~~ :_;:: •" '.~~,_ N • • s

• r =

= 62.021P11 °·8361

(1953-1984) 0.87 s = 63.41

No. of units = 213

• 2 • 6'i I I I 1.-; : I I ~I I (I~ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 I 1 1 I 1 1 I I I I I I I I I I I I 1 I I 1 I I I I I

0.9 1.0 I . I I . 2 I . 3 t . 4 1 . 5 1 . 6 Log 10 of P11 , Unit Power

r-·-r --,r -- ,-- a- T ~r- ,- ,1 I ,'a I 2b I I I I I I I I 13b I I I I I I I I 46

P11 , Unit Power

Figure 5 . Specific speed versus unit power for bulb turbines.


unit discharge 011 for all bulb units for which data were obtained

where the regression equations are given as:

N = 383.117 On 0.8045 (1953-1965) Eq. (7) s

Ns 390.591 o11 0.8206 (1966-1984) Eq. ( 8) =

0 where 011 = Eq. ( 9)

D2H0.5

and 0 = rated discharge in m3Jsec.


unit speed, N11, for all bulb units for which data were obtained

where the regression equations are given as:

Nll = 4.565 Ns0.5478

Nll = 7.987 Ns0.4605

NO where N11 = --

H0.5

(1953-1965)

(1966-1984)

Eq. (10)

Eq. ( 11)

Eq. (12)

Figure 8 presents the relation between unit power, P11, and

unit discharge, 011, for bulb turbines studied and the resulting

regression equations are:

pll = 9.027 0110.9347

pll = 9.345 0110.9445

(1953-1965) Eq. (13)

(1966-1984) Eq. (14)

Figure 9 presents the relation between unit speed, N11, and

unit power, P11, for bulb turbines studied and the resultinq

regression equation is:

20

~ --2000 --, 3.3 I

N = 390.591Q11 °·82~?-11966-1984) • s ';.-,

3.21-r = 0.81 S = 69.07 1600 -l

-o No. of units = 144 (1) (1)

3. I 1200 0.. (/)

-o (1) u (1) .... ~ 1000 4- 3.0 ....

u i A u (1) ....

800 0.. 4- (/) .- 2.9 u "' (1) V')

0.. z (/)

4-"' 0 V') 600 -z 0

? 7j • A ,......

0.8045 01 ~-.,A-.• a-

Ns ~ 383. 117Q11 (1953-1965) J _3 .. I') _,.. ......

r = 0.75 s = 78.30 400 ~ 2.6~ A ~

No. of units = 62

0.0 0. I 0.2 0.3 0.4 0.5 0.6 0.7

Log 10 of Qll, Unit Discharge

I I -,

1 1.5 2 3 4 5

Q11 , Unit Discharge

Figure 6. Specific speed versus unit discharge for bulb turbines.

2000

1600 __ N = ].987N °· 4605 (1966-1984) 11 S~:--:---------__

---- -------r = 0. 86 S = 6. 99 -- -~

"'0 Q)

No. of units = 150 Q) Cl.

(,/') "'0 Q) Q)

u .,.... Cl. 4-

(,/') .,.... u

u Q) .,.... 4- 800 Cl.

.,.... (,/') 2. u Q)

~

Cl. Vl

(,/') z:

~ 600 4-

Vl 0

:z: 0 r-

r::n

• N11 = 4.565Ns 0· 5478 (1953-1965) A

r = 0.83 s = 9.55 •

No. of units = 63 N N

40J 0

...J

~ ~rA 2.

•

2.05 2. 10 2. 15 2.20 2.25 2.30 2.35 2.40 2.45

Log10 of N11 , Unit Speed

I I I -~-

120 140 160 180 200 220 240 260

N11 , Unit Speed

Figure 7. Unit speed versus specific speed for bulb turbines.

·.-

40--, 1.6-l p = 9 345Q 0·9445 (1966-1984) (11. 11 d

r = 0.84 S = 2.17 30 -I t.Si ( 11

s.. No. of units = 144 Q)

3: 0 1.41 \ A 11

~ 201

0...

+> •r- A c: ::J 1.3 .. r-r-

0...

r-

l 4- 1.2 r- 0

0... 0 r-

1.1 en 0

1.0j .,/' A 0. 9347 I'.'

lOJ ...J

, ......... ~ pll = 9.027Qll (1953-1965) w ,........: - .

~, ~- 0.93 s = 1.18

8-4 0.9 I No. of units = 62

6

0.0 0. I 0.2 0.3 0.4 0.5 0.6 0.7 Log10 of Q11 , Unit Discharge

---- -~---------T I I I I I

1 1.25 1.5 2 3 4 5


Figure 8. Unit power versus unit discharge for bulb turbines.

2.5 /__,_. N

11 = 62.021Pll0.3361 (1953-1984)

r = 0.52 S = 13.80 +

2.4 No. of units = 213 -o (lJ (lJ Q_ (/)

-o

2001 (lJ +> (lJ •r-Q_ c (/) ::::>

+> . ....... ..-c ..-

::::> z 4-0 ..- I z 0 ..-

Ol 0

1\.J I _J

~

. + ~ _.---· + +~ ~ ...

+ + + ++~~- + + .................. --·

+ ~-- fl_.+.£. .. --t ~ ._,. ............. +

~~~< .. + ~t~~. ~..}+~ ;:::-~-v-------\ + ~--- ;'.A-+~~/ . ~ ----- ----~ + ij: +~ ;..:.---

... ----- ++ t ........ + .... -tf-........ ,.. .. ':Jo + .... ----~--- -- __..---:t /

+

+

100 2.~

~.9 1.~ 1.1 1.3 1.4 1.5 I .6

Log1 0 of P 11 , Unit Power

I I I I I I I I I I ' I I I I I I I I I I I I I I I I I I I If I I I II I

7.5 8 10 12 16 20 24 28 32 36 40

P11 , Unit Power

Figure 9. Unit speed versus unit power for bulb turbines.

0.3361 N11 = 62.021 P11

(1953-1984) Eq. (15)


unit discharge Qll for bulb turbines studied and the resulting


(1953-1984) Eq. (16)

In many engineering offices and in some manufacturer's compari-

sons, the speed ratio or velocity ratio is used instead of the term

unit speed, N11' by practice and mathematically speed ratio is:

0 ~ N -3 0 = = 11.82086 x 10 Nll * Eq. (17) 60 ffgH

where g = acceleration of gravity in m/sec2

0 = turbine diameter in m.

Using the speed ratio, 0, as a characteristic turbine parameter rela-

tions were developed for manufactured bulb type turbines as follows:

0 = 0.0540 Ns 0· 5478 (1953-1965) Eq.

0 = 0.0944 Ns 0· 4605 (1966-1984) Eq.

0 = 0.1232 pll 0.9615 (1953-1965) Eq.

0 = 0.3518 pll 0.5772 (1966-1984) Eq.

0 = 1. 554 00.7640 (1953-1965) Eq.

0 = 1. 393 01.4780 (1966-1984) Eq.

* Sometimes the speed ratio is expressed in the American system of units and the 0 is expressed in inches and the H in feet.

25

(18)

(19)

(20)

(21)

(22)

(23)

N C'l

-o (l) (l) 0.

(/')

300

250

+> 200 I::

:::J

...

...-z:

150

-o (l) (l) 0.

(/')

+-' ...... I::

:::J

.-z:

_I 4-o

0 .-

en 0 _l

2.5

2. I

+

_,---

. j~ . -------""" / + ""'" -~ +- + + ~ + -- .------------\;(,{ t*~ ~j;lj\~.t*~~+-:+ -------

~ + ~ Pc T ~#oF '1:"'...(+ .1i --------- ~,..~ ~1;.it4Ht . + _:..-..-- ~

....................... ~ .... :t+"'~ \..t_ .j++ \J--..----......... * +++ ~ ,-...Y + N -

....---- 11- 127.119Q 0.3513 - + + r = 0. 53 11 ( 1953-1984)

+

s = 13.23

~ No. of units = 207 ,..

. iII I I I I I I I I I Iii I I I I I 1 00 _j 2 , 0--:J I I I I I I I I I I 1 1 1 1 1 1 1 1 1 I 1 1 I I I I I I I I I I I I I • ' ' ' I I I I' I IiI I I I

0.0 0. I 0.2 0.3 0.4 0.5 0.6 0.7

Log10 of 011 , Unit Discharge

r --- --,----~--~---, ---.-------,---,-- --T

1 1.25 1.5 1.75 2 2.5 3 3.5 4 4.5 5

011 , Unit Discharge

Figure 10. Unit speed versus unit discharge for bulb turbines.

The graphical relations for these three regression equations are shown

in Figures 11, 12, and 13. In seeking a simplification for use of

experience curves it was recognized that relating diameter to the basic

well known parameters of rated head and rated power would be most use

ful because in preliminary planning the parameters of rated head and

rated power are most generally estimated early in the planning of pro

jects based on the physical elevation situation of the water and the

power available from the estimated flows. On this basis a new regres

sion analysis was made relating turbine diameter to the ratio of P/H

where P is the rated power output and H is the design head or rated

head. Figure 14 presents for manufactured bulb type turbines the rela-

. tion between turbine diameter and the ratio of rated power to rated

head and the resulting regression equations are:

D = 0.2119(P/H)0· 4374

0 = 0.1826(P/H) 0· 4462

(1953-1965)

(1966-1984)

Eq. (24)

Eq. (25)

A similar new relation was developed relating turbine diameter to the

ratio of rated discharge, Q, to the operating speed, N. This relation

ship is shown in Figure 15 and the resulting regression equation is:

D = 4.181 (Q/N) 0· 3175 Eq. (26)

This again recogniz~s that in early planning stages the rated discharge

is known from the hydrologic analysis of power or energy potential at a

site and the choices of operating speeds are rather limited because

there are a limited number of available synchronous speeds at which

bulb turbines can operate if directly connected to the generator.

27

3.4

3.0

2.5

0 .,.... +-'

~ 2.0 "'0

~ 1.8 0.

(./)

N .. 1.6 co -e-

1.4

1.2

1.0

.,..~· ~' e .5-I ,,. ,,. ,., ,.,. ,.,

,.,.' ,.,. ,., ,.,. ,, 0 + • ,Y .,.... e.4 ~,, +-'

~,. • ¢ = 0.0944 Ns0·4605 {1966-1984) 10 0:: + "'0 <LI <LI {]; 0.3

.. -e-4-0

0.2 0 r-t

en 0

---I

0. I ,,,''

+~, /''-

<Z__{_,•'' + ,

,~,,' <P =

A •

0.0540 N °· 5478 {1953 - 1984) . s r = 0.83 s = 0.11 No. of units = 63

r = 0.86 No. of units = 150

B .ia_.~,i~•~•,•~•~•,•~•~•~•~i,'~'rTo~o~•~•~•~•~•ii~•~•~orTo~•~•~•~•~•Ti~•~•~•~orT~~~rl~~~~.-~~~~~ .. ~.-~~~~~ .. ~~~~~~~--~--~.-•ir 2.5 2.6 2.7 2.8 2.9 3.e 3.1 3.2 3.3

Log 10 of Ns' Specific Speed

I I I I I I I I I I I I I I I I I I I I I I I I I J I I I I I -r--.--,-nl 1 325 400 500 600 700 800 900 1000 1 50 0 2000

N5

, Specific Speed

Figure 11. Speed ratio versus specific speed for bulb turbines.

s = 0.08

-

3. 2-, 0.5~ - 0.5772

¢ - 0.3518P 11 ------ ___ (1_966-1984) • --

r = 0.57 S = 0.14 \ 2.8--l j

No. of units = 1 50 '"'---- ~",, • A ,

2.4 J .~ --~I A 4~ ,

A +->

0 AA~ 0 l1:l • 0::: 11 • 4 4 A4 4

•r-+-> -o

• A A\ ~~ 44 4 AA l1:l (!) 0::: (!)

2.0 0. -o V) (!)

~ 4 (!) ~

0. -& 4 V)

4-~ 0

-&

1.6 0 no ,_j -~ ~· ~,

r- . Ol 0

_J

N J ~ a""-\ • ~

¢ = O.l232P11 °· 9651 (1953-1965)

1.21 0.11 r = 0.37 s = 0.20

No. of Units = 63 I ~

1.0 ..., I I I I I I' I I I I I I I I I I I I I I I

0.9 1.0 t.t 1.2 t.3 1.4 t.S t . 6

Log 10 of P11 , Unit Power

I IIIITI IITTll lllfl

8 9 10 15 20 25 30 40

P 11 , Unit Power

Figure 12. Speed ratio versus unit power for bulb turbines.

10 I 1 . 00"'1 ~D = 1.554·0·7640 (1953-1965)

8-l

0.7J (/) 1 r = 0. 05 S = 1 . 26 s.... ( QJ

No. of units = 63 .j..) (/) QJ s.... ::E: QJ

.j..) 1:::

~ 4 ......

s.... 1::: QJ ...... .j..)

0.50 QJ s.... E QJ ro

~ ~-'-, 4: ~~~-- -~0 = 1. 393¢1. 4780 ( 1966-1984) .j..) ...... QJ 0 E ro QJ

;; 2 1::: ~ "- /..~'t r = 0.07 s = 1.77 ......

.0 0.25 QJ s.... 1::: ::I 1 - ~*'- No. of units = 150 ...... 1- ,.. .a. .0 s.... ~

::I 0 1-

4-w ~ 0 0 0 1 0 0.00

r-en 0

.....J

0.6 -0 • 25 I I I I I I I I f I I I I t j I i I I I I I I I I I I i I I I I t I l"f-y....,..-rooy·r-rrrrrr i i I I t I I I t I I I t I • • • •

1.2 1.6 z.0 2.4 2.8 3.2 3.6

Log10 of ¢• Speed Ratio

---r- I

16 20 40 60 100 200 500 1000 2000 4000

<P• Speed Ratio

Figure 13. Turbine diameter versus speed ratio for bulb turbines.

'"\

- - - -

1 O• 1.00

8 I

V')

s.... ClJ

6 .j..J V') ClJ 0.75 s.... :a: ClJ

.j..J c::

jo = 0.2119(P/H) 0~74 (1953-1965) ClJ .,....

:a: 4 s....

c:: ClJ .,.... .j..J

0. 50j r = 0. 92 ClJ s = 0.64 "" • • s.... E ClJ 1'0

.j..J .,.... lNo. of units = 63 ClJ a

E 1'0 ClJ .,.... c:: a 2 .,....

..0 ClJ s.... 0.25 c:: :::::1 .,.... I-

..0

3 n;,r.· · /D = o.l826(P/H) 0·4462 (1966-1984) s.... .. :::::1 a I-

4-w .. 0 ...... a

0 0. 00 -1 /,'f ~"< ~ r = 0.98 s = 0.60 ,......

Ol :i / .,, 0 _ _,, J. No. of units = 150

_J

0.6 -0 • 25 I I I I I I I I I I I I I I I I I I I 1 1 1 1 1 1 1 I I I I I I I I I I I I T'"T"'rY"T"T""rrr-y--r"T" i I IiI 1 iiI iII i • i

1.2 1.6 2.0 2.4 2.8 3.2 3.6

Log10 of {P/H), Rated Power over Rated Head

,-,-, 16 20 40 60 100 200 500 1000 2000 4000

{P/H), Rated Power over Rated Head

Figure 14. Turbine diameter versus {P/H) ratio for bulb turbines.

10 __, '. 00--i

8 -l Vl s... aJ

Vl - .j..l ~ 6- ~ / " ~ / . j 4 i . //~/;;~· ·- " / p i 2 " _- + ~r-~lt __ ; //Jj~+/

kl : // _i' ~ ~ // ..._ ._JJ!: ~ / D ~4 (.181 (Q/N)0.3175

"' +-.-'11- ~ / 1953 1 1 -j .3 0.00 ~,l!J"l: / r = 0.99 - 984) /. A(+ /

5 = o.8o

/ + ./ // No. of u . / /" + / m ts = 206

.--"' ,,,,,'+/""/' ,"'

-0.25~ ///'+ I I ~ I .--"' I I I i I I -3 I I I I I I

I i I I -2 I 1--,~~~~~~--l ' ' og10 of (Q/N) -1 . ' ' ' '

' Rated Dischar e 0 g over Turb· lne Speed

~~----~~~--~--~--~~--~--~--------~--~-.-..--.

0.001 0.005 0.01 0.05 0.10 0.5 1 5 8

(Q/N), Rated Discharge over Turbine Speed

Figure 15. Turbine diameter versus (Q/N) ratio for bulb turbines.

An additional regression was developed between the turbine speed

and the ratio of rated power to rated head and the resulting regression

equations are

N = 1810.648 (P/H)-0.4176 (1953 1965) Eq. (27)

N = 2152.857 (P/H)-0.4062 (1966 1984) Eq. (28)

Figure 16 presents the graphical representation of N vs P/H.

As a result of inspection of an Escher Wyss nomograph for standard

tubular turbines a regression relation ~as developed between turbine

speed and the ratio, /H7D. The regression equations for bulb turbines

for that relation between turbine speed, N, and the ratio /HID are as

follows:

N = 162.103 ( /ff/0) 0·8912

N = 169.119 ( IH/0)0· 9260

(1953-1965)

(1966-1984)

Figure 17 presents the graphical representation of N vs IH?D.

Eq. (29)

Eq. (30)

Table 2 summarizes all the regression relations that were devel

oped for manufactured bulb type turbines. In the table are shown all

the equations that were developed, the regression correlation coeffi

cient for each particular regression, the corresponding standard devia

tion, the sample period and the number of different units used in

developing a particular relation.

In the Appendix an example is given showing how these turbine con

stants and regression equations can be used to make a diameter selec

tion utilizing the analysis system used in Monograph No. 20 of the U.S.

Bureau of Reclamation and parallel calculations show selection of tur

bine diameter using newly developed experience curves involving dir

ectly a P/H ratio and a Q/N ratio and the resulting regression equa-

tions. 33

w ~

"'0 QJ QJ 0.

(./)

QJ s::: .,.... .0

s.... :::J 1-

~

z

1ooo -1 3. 00

500

50()

00

300

260

200

160

100

80

60

36

"'0 QJ

~ 2. 75 (./)

0"> s::: .,.... s::: s::: :::J

0::: 2.50 QJ s::: .,.... .0 s.... :::J

1-~

:z: 2.25 ~ 0

0 r-

0"> 0 _J

2.00

1. 75

....

•

....... ....... ...... ...... ... , ..... .....

•

•

' ... + .....

+

......

•

I • + + + • • +

.......... + ........ ....

• ........ '+--1+ i' ........

N = 2,152.857 (P/H)- 0·4062 (1966-1~34)

y = 0.85 s = 109.11

No. of units = 152

+ •

+ ...... • .... .JL

......... "1r ._L • • • ... + +

N = 1810.648(P/H)-0. 4176 +

y = 0.59 s = 97.24 (1953-1965)

+ No. of units = 67

"', • T

...... ++ + +-...... _t.. • . .. ..... ,... • • + .................... ,

+ ................ . +

• • • •• ......

........ . .. . +. '+- ............ + . .... .. • .... ..~ .... . ~ ......... .

+ ...... -. .. .. + ++

+ ...... ......

1 . 2 I .6 2.0 2.4 2.8 3.2 3.6 Log

10 of (P/H), Rated Power to Rated Head Ratio

I I I I I I I I I I I I I I t I ,,---T-- I 1 I I I ----.---.----.-- • I I I ' I

16 24 30 40 60 100 0 200 300 500 1000 2000 3000 4000

P/H, Rated Power to Rated Head Ratio

Figure 16. Turbine speed N, versus P/H ratio for bulb turbines.

1000 3.00

800

.L.75 ~ N = 169.119(1j)0.9260 E 0.. s.. 600 s:: r = 0.97 s = 22.65 .,.... "'0

Q) "'0 Q)

::1 No. of Units = 150 Q) 400 0.. Q) V) 0..

V) Q)

Q) s:: 2.50 .,....

s:: ..0 .,.... s.. ..0 :::::5 s.. I-:::::5 I- 200 ..

.. ~2.251 +~N = 162.103(~) 0 · 8912 z: (1953-1965) w 1..3 U"i . r = 0.95 s = 22.95

100 ~ 2.00 ...:J .~..:" .liiEI.i..,. No. of Units = 63

60 1 . 75

-0.5 -0.3 -0.1 0.1 0.3 0.5 0.7

Log10 of ~' Square root of Rated Head over Turbine Diameter

r------r----.----y---,-----,r-..-----r---,----y---r--,--___,....--.-----.----, I J

0.5 1.0 2.0 3 4 5

~' Square root of Rated Head over Turbine Diameter

Figure 17. Turbine speed versus ~ratio for bulb turbines.

Equation Number

1

w 0"'1

2

3

5

7

8

10

11

TABLE 2

SUMMARY LISTING OF REGRESSION INFORMATION AND EQlJATIONS RELATING TURBINE

CHARACTERISTICS TO VARIOUS TURBINE CONSTANTS FOR BULB TURBINES

Dependent Regression Correlation Standard Sample Parameter Equation Coefficient Deviation Period

Ns N = 1155.937 H-0•2797 s 0. 37 216.06 1953-1960

Ns N = s 964.130 H- 0•1631 0.26 104.24 1961-1970

Ns N = 1520.256 H-0•2837 s 0.40 118.24 1971-1984

Ns N = s 62.021 p1~.8361 0.87 63.41 1953-1984

Ns N = s 383.117 0~i8045 0.75 78.30 1953-1965

Ns N = s 390.591 0~i 8206 0.81 69.07 1966-1984

N11 Nll = 4 565 N0.5478 • s 0.83 9.55 1953-1965

Nll Nll = 7 987 N0.4605 • s O.R6 6.99 1966-1984

Number of Units

32

67

119

213

62

144

63

150

TABLE 2 CONTINUED

Equation Dependent Regression Correlation Standard Sample Number Number Parameter Equation Coefficient Deviation Period of Units

13 p11 p11 = 9.027 0~i9347 0.93 1.18 1953-1965 62

14 p11 p11 = 9.345 0~i9445 0.84 2.17 1966-1984 144

15 N11 Nll = 62.021 Pii3361 0.52 13.80 1953-1984 213

w -.....!

N = 127 119 o0•3513 16 N11 0.53 13.23 1953-1984 207 11 • 11

18 ' ~ = 0.0540 N~· 5478 0.83 0.11 1953-1965 63

19 t • = 0.0944 N°· 4605 0.86 0.08 1966-1984 150 s

20 ~ t = 0.1232 P0.9615 11

0.37 0.20 1953-1965 63

21 t ~ = 0.3518 p 0.5772 11 0.57 0.14 1966-1984 150

22 n D = 1.554 ~0.7640 0.05 1.26 1953-1965 63

23 n 0 = 1.393 ~1.4780 0.07 1.77 1966-1984 150

24 f) D = 0.2119{P/H) 0•4374 0.92 0.64 1953-1965 63

TABLE 2 CONTINUED


25 D D = 0.1826(P/H) 0•4462 0.98 0.60 1966-1984 150

26 0 D = 4.181(Q/N) 0•3175 0.99 0.80 1953-1984 20fi

27 N N = 1810.648(P/H)-0•4176 0.59 97.24 1953-1965 67

w 28 N N = 2152.857(P/H)-0•4062 0.85 109.11 1966-1984 152 00

29 N N = 162.103({H) 0•8912 0.95 22.95 1953-1965 63 0

30 N N = 169.119(~) 0 • 9260 0.97 22.65 1966-1984 150 0

Tubular Turbines

For tubular type turbines the Ns vs H relation is shown in Figure

18 and the regression relation is given as:

N = 1107 303 H- 0· 2998 s . Eq. (31)

Stratification of the Ns vs H relationship showin~ the variation

of the relation for various turbine manufacturers is presented in

Figure 19. A summary of the data for individual manufacturers is pre-

sented in Appendix 3 along with the specific regression equations.


unit power, P11 , for tubular turbines and the resulting regression

equation is given as:

Ns = 52.96 p 110.8882 Eq. (32)


unit discharge, o11 , for all tubular turbines and the resulting

regression equation is given as:

Ns = 357.294 0110.9029 Eq. (33)


unit speed, N11 , for tubular type turbines for which data were obtained

where the regression equation is given as:

Ns = 0.497 N11 1.4080 Eq. (34)

Figure 23 presents the relation between unit power, P11 , and unit

discharge, 011 , for tubular type turbines studied and the resulting


pll = 10.133 Q1~.7315 Eq. (35)

39

1000

900

BOO

"'0 700 <V <V 0..

(./')

u .,... 600 '+-. ,...

u <V 0..

(./')

500 Ill

z

~ 0

400

3.8

~ 2.9 <V 0..

(./')

u .,... '+-.,... u <V 0..

(./')

Ill z '+-0

0 ....-

C'l 0 _J

2.8

2.7

2.6

= ll07.303H-0.2998

r = 0 62 5

(1957-1984) • = 92.71

No. of units = 54

• •

- • •

-~~

......

~ 2,!) ~·~i~!~l~!,l~l~l~!~l,!,i,l~l~l~l~i~l~l~!,l,i,l,!,l,l,l,l,!,i,i·i·I·!·I·I·I·I•J•I•I•I•I•J•J•J•J•I•J•J•I•I•J•J•I•I•I•J•J•J•t•l•l,!,l~l~l~l~!~l,l~i~l~l~i~!~i~l~!~l~!~i~!~I~I~!~I~!~I~I~!~IMI~!MIM!M!M!M!MIM!Mi~

0.s 9.6 0.1 0.8 . 8.9 1.0 1.1 1.2 1.3 1.4 l.!i

Log10 of H, Rated Head in Meters

I I I I -, I ' I I ~ -,- I I I .-- I I I I I I I I I I I I I I I I I' I

4 5 6 7 8 9 10 15 20 25 30


Figure 18. Specific speed versus rated head for tubular turbines.

"'0 Q) Q) 0.

(./)

u .,... 4-.,... u Q) 0.

(./)

" (/) z

~ ......

1000

900

800

700

600

500

400

320

"'0 Q) Q) 0.

(./)

u •r-4-•r-u Q) 0.

(./)

(/)

z 4-0

0 r-

01 0

_J

3.0

2.9

2.8

2.7

2.6

.............. ~#2 .... .... .... .... .... .......... .... ...... ...... .... .... .... .... ..... .... ..... ..... ..... .... ..... .... ...... .....

1 - Tar.~pell a 2 -· Vevey-Charmi 11 es 3 - Allis Chalmers 4 - Kvaerner Brug

..... ..... ...... .... ...... ...... .... ......

~ ~~4''~,, ..........

" ....... " ...... ..... .. .. ..... .... ...... ..... "-.... -........,,........_

~~~ '"-..,,........_,,,

2 • 5J f I I J iII I I I I I I I I I I I I IiI I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I;) I I I I I I I I I I I I I I I I I I I I I ,,,,,,,,,,,,,,,,, 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Log 10 ·of H, Rated Head in Meters

I I ' J

4 5 6 7 8 9 10 15 20 30


Figure 19. Specific speed versus rated head for tubular turbines from different turbine manufactures.

1000 --1 3.0

900

800 j 2) • -a

700 QJ QJ 0.

-a (./) i Ns = 52.96P11 °· 8882 (1957-1984)

• QJ QJ u 0. ...... 2.8

(./) 4-600 ...... r = 0.71 S = 55.91 u u ...... QJ

4- 0. ...... (./) ~ No. of unit = 41 u QJ ~

0. 500 .::...(/') 2.7 (./)

4-(/') J 0

z 0 ......-

en ~

400 -i 0 2.6 I'.) _J

/ /

300 2 • s 11 I U I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I" I I I I (a I I I IiI I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I IiI IiI I I I

0.5 0.6 0.7 0.8 0.9 t.0 t.l t.2 1.3 1.4


I I I I I I I I I I I I I I I I I I I I -.-,---,TT I 1 I I 4 5 6 7 8 9 10 15 20 25

P11 , Unit Power

Figure 20. Specific speed versus unit power for tubular turbines.

1000

8001 "'0 Q) Q)

0-

f 600~ (/} .hf u

N s = 357.294Q 0.9029 •r-

(1957-1984)-... '+-

11 •r-u 2.8 r = 0.70 s = 59.37

~ Q) c..

•

(/} :1 No. of units = 37 u Q)

l c.. 111

(/} z , \ • '+- 2.7

111 I 0

z 0 r-

O'l 0

~ I __J

w 400 -I 2.6

325 2 · 5.,~Tj~i~i~i~i~i~i~i~i~i~jTI~I~i~i~i~i~ITI~ilj~l~i~i~ITI~i~i~i~i,j~tt-ri~i~i~ITi~l~i~i,j~l~iTi~I~ITI~I~i~l,j~l~i~l~i~iTI~i~irTI-rj

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

Log10 of 011 , Unit Discharge

...----r---r-----r-----r---,.---y---T I -- I I 0.2 0.3 0.4 0.5 1.0 2.0 2.5


Figure 21. Specific speed versus unit discharge for tubular turbines.

1000 l 3.0

Ns = 0.497N 11 1·4080 (1957-1984)

..

~ r = 0.85 s = 44.20

"'0 2.9 800 -j (1)

No. of units = 41 . .,.,..... ~ (1) c..

(./) "'0 (1) u (1) .... c.. 4-

(./) .... u

u 600 (1) .... c.. 4- (./) .... u "' (1) (/)

• c.. :z:: (./)

4-~ ~ ' "' 0 2. 7-:I .... ~

(/)

:z:: 0 ....--

C'l 0

~

400 ~ _J

~

2.6

325 2.5 '• '

I I I I ' I I I I I I I I I I I f ' ' I I I ' I I I ' I ' I ' I ' I I I I ' • ' I I ' • I I I ' I I ' I ' ' I I I I I I ' I I I '

2.02 2.06 2.10 2. 14 2.18 2.22 2.26

Log10 , of N11 , Unit Speed

' r 11 0 120 130 140 150 160 170 180

N11 , Unit Speed

Figure 22. Specific speed versus unit speed for tubular turbines.

-

20-; 1.3

18 j i p = 10 133Q 0.7315 16 t.2 11 . 11

14 r = 0.89 s = 1 .30

(1957-1984) •

~

1 · 1 ·~ No. of units = 39 12 ~ ~ ~

10 i ClJ 3 0

0...

+-' •r-s::: 8 ::> I ,.....

0...

4-,..... 6 j

0 0...

0 ,..... 01 / 0 _I

.+::> (.]1

4

-0.8 "':"0.6 -0.4 -0.2 0.0 0.2 0.4

Log 10 of 011 , Unit Discharge

.---,-~r·-.- -.-----.---, -·, J---,--·,--,--,··m·r---·----.---~ ~·r-·~

0.2 0.4 0.6 1.0 1.5 2.0 2.5


Figure 23. Unit power versus unit discharge for tubular turbines.

Figure 24 presents the relation between unit speed, N11 , and unit

power, r11 , for tubular type turbines studied and the resulting regres-

sion equation is:

N = 52 96 p 0.3882 11 . 11 Eq. {36)


unit discharge, 011, for tubular type turbines studied and the

resulting regression equation is:

N = 120 144 Q 0· 4210 11 . 11 Eq. {37)

Using the speed ratio, 0 as the dependent term of characteristic

turbine parameter, empirical relations were developed for manufactured

tubular type turbines as follows:

0 0.0389 Ns 0· 6013

Eq. {38)

0 = 0.626 pll 0.3882 Eq. ( 39)

With the turbine diameter, D, as the dependent term of the empirical

relations for manufactured tubular type turbines the following regres-

sian equation was developed:

D = 1.5424 0 0.5767 Eq. (40)

The graphical relations involving the speed ratio, 0 , and the specific

speed, Ns, unit power, P11, and tubular turbine diameter, D, are

presented in Figures 26, 27 and 28.

The graphical relations relating the tubular turbine diameter, D,

to the P/H ratio is presented in Figure 29 and the relation between

tubular turbine diameter, D, and Q/N ratio is presented in Figure 30.

46

-+'> ........

\j Q) Q)

200

180

~ 160 ~ .,... c::

::>

r-

£140

120

115

\j Q) Q) c..

(,/')

::>

rr-

z:

0 r-

01 0

....J

2.30

2.25 N = 50 g6p 0.3882 11 Lo 11

r = 0.32 s = 14.93

No. of units = 41

0.s 0.6 0.7

(1957-1984)

•

• /

• ./ •/

/. /

//:/// • ~··/ /-..

./ /•

//· ... m-TT] 1 1 1 1 • • • 1 1 1 w 1 1 1 1 • • .-.I 1 1 1 1 1 1 1 • 'I-. • 1 1 1 1 • 1 • 1-.----rrT·m..--..--T

0.8 0.9 1.0 t . I t.2 1.3 1.4

Log10 of P11 , Unit Power

1 -- 1 --. r I 1 I 1 I 1 • 1 I 1 • • • I 1

I I I I 1

I I I I 1

4 5 6 7 8 9 10 15 20 25

P11 , Unit Power

Figure 24. Unit speed versus unit power for tubular turbines.

+::> (X)

200-., 2. 30

"'0 Q)

130

~ 160 (/")

.j-) .,... s::

:::>

r-

£ 140

120

115

"'0 2. 25 Q) Q) c..

(/")

.j-) .,... s::

:::> 2.20

r-z 4-0

0 2.15 r-

O'l 0 _j

2. 10

• N = 120 144Q 0·4210(1957-1984) 11 . 11

r = 0.35 s = 15.28

No. of units = 37

2 . 05 I I I I I I I I I I I I I i I I I I ( I I I I {I I I i I I I 1.1 I I I I I I I I I I I' I I I I I''' I I •• ' ••••

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 Log10 of Q11 , Unit Discharge

----~--~--~~~~~~--~~~~.-~~~~~~~~T~

0.2 0.3 0.4 0.6 0.8 1.0 2.0 2.5


Figure 25 . Unit speed versus unit discharge for tubu1 ar turbines.

• • • • .. - - .....

0.35 2. 2-, ... • 2.1

2.0 J 0.30

1. 9 0 j • .,....

+'

1.8 ~ 0::

0 0.251 / •r- -o +' Q) ••/ ~ Q)

0:: 1.7 0.. (/)

-o Q) ~

Q) -& 0..

0.20-:f / •/ (/) 1.6 4- r = 0.85 s = o.os 0 /

-& 1. 5 I ~ :1 / / /.• No. of units = 41 Ol

/A

0 _l

..j:>. 1.4_1 0. t5 \.0

1.3

0 • t0 1 ~~~~~;-r;-r;-r;~~~i~l~i_,i_,l-,l~l~i-TI~i-rl-rt-rl~i~l~i~f~l_,l_,i_,i~i~f-,1-TI-rt-ri-ri-fr-l~f~ir<ir<lr;i~l_,i_,i_,i_,i_,i_,-1

2.55 2.6t 2.67 2.73 2.79 2.85 2.91 2.97 3.03

Log 10 of Ns, Specific Speed

-.--r--~ -- - r- ----. ----.-- ---, I ' I ' I

400 500 600 700 800 900 1000

Ns, Specific Speed

Figure 26. Speed ratio versus specific speed for tubular turbines.

•

(Jl

0

•

2.2

2.0

0 ·r-

~ 1.8 0:::

""0 (!) (!)

0.. (/}

_; 1.6

1.4

..

0.35

0 0.30 •r-....... tO

0:::

""0 (!) (!)

~ 0.25

" -€7-

4-0

0 r-

0) 0

...J

0.5

....! ___ .A

Q = 0.626P 0.3882 11

r = 0.32 s = 0.18

(1957-1984) \

\

. / )//

. . //· .. ··~ / No. of units = 41

/

0.6 0.7 0.8 0.9

. . /. /1 ·/ •

/ " . . . /

Y/o ••

• •

•

t.0 t.t 1.2


t.3 t.4

1 I - -.-~, - I 1 I 1 1 1 1 --. 1 1 1 1 r 1 1

4 5 6 7 10 15 20 25

P11 , Unit Po\'/er

Figure 27. Speed ratio versus unit power for tubular turbines .

-

• • • • • .. - ..

1~3 t.ee (/)

s... <lJ

• I -1-l (/)

6 <lJ 0.75

s... :E: <lJ

-1-l c

• ,9:! .,_ ""'- 4 .. s... c

<lJ .,.... -1-l <lJ s... E <lJ ro +..>

• • •• • • • • • • •

.,_

•

<lJ a •

-~ • E

• • •

ro 2 <lJ • • •

.,.... s:::: 0.25

• • • • • •

Cl . ,_

• • ..0

• • •

<lJ s...

• c

:::J . ,.... I-..0

s... 1.0 .. :::J a I-

• • ---~ 0 = 1 .5424¢0· 5767

0.8 If-01 .. 0

•

....... Cl

0 0.6 -l ......

r = 0.03 s = 1.45 ~ -0.25 -I

0.4 j No. of units = 41

0. 19 e. t 4 0.18 0.22 9.26 0.30 9.34 Log10 of ¢, Speed Ratio

I ' I ' I ' I ' I ' I ' I ' I ' I ' 1 ' 1.4 1.5 1.6 1.7 1.8 )_q ? " • 2

¢, Speed Ratio

Figure 28. Turbine diamater versus speed ratio for tubular turbines.

1 0 -=1 1.00

~ /

Vl / s... / /. / <lJ /

;...> /

Vl <lJ 0.75 s... ~-

<lJ 5 ..,_

;...> s:: ~

.,..... s...

s:: <lJ .,..... ;...> <lJ s... E

<lJ tU ;...> .,..... <lJ 2 0 E tU <lJ .,..... s::

0 .,..... ..c

~ / _/-.~o = 0.1433(if)V.;.JII;) (1957-1984) <lJ s... s:: ::::::1 .,..... 1-..c

Clll CIIICIII_] _/. / r = 0.94 s = 0. 91 s... 1

~ / ::::::1 0

1-4-

1// / / No. of units = 45 U1 ~ 0 1'\.) 0

0 /

0.5 ~ - /

1.0 1.4 1.8 2.2 2.6 3.0 3.4

Log10 of P/H, Rated Power over Rated Head

10 20 50 100 500 1000 2000

P/H, Rated Power over Rated Head

Figure 29. Turbine diameter versus P/H ratio for tubular turbines .

• • a ... -

• • • • • - - .._

10 1.00 Vl

8 s... Q) +J

Vl 6 .$ s... ..,__ 0.75 Q)

+J s:: Q) .,....

:::::: 4 s...

s:: Q) .,.... +J Q) 0.50 s... E

Q) ro +J .,.... Q) Cl E

~D = 4.511 (Q/N)0.3393 ro 2 Q) .,.... s:: Cl .,.... 0.25 ..0

(1957-1984) Q) s... s:: ::I .,.... 1- r = 0.99 s = 0.46 ..0 s... .. ::I 1 Cl

0.00 No. of Units = 37 1-4--

U'1 .. 0

w Cl 0 .---

en 0

......1

0.5

-.-, ......... , ......... , ..... .....----.-----., ... . -2.0 -1.5 -1.0 -0.5 0.0 0.5

Log1 0 of Q/N, 'Rated Discharge over Turbine Speed

r • • • ' • • • 1 1 • 1 • 1 • r '1 • r • 1 ' 1

0.01 .05 .1 .2 .4 .6 .8 1 2 3 4

Q/N, Rated Discharge over Turbine Speed

Figure 30. Turbine dia~eter versus Q/N ratio for tubular turbines.

The empirical relation as a regression -equation relating tubular tur

bine diameter D, to the P/H ratio is given as:

D = 0.1433 {P/H) 0· 5115 Eq. (41)

The corresponding empirical relation as a regression equation relating

tubular turbine diameter, D, to the Q/N ratio is given as:

D = 4.511 {Q/N) 0· 3393 Eq. ( 42)

The additional new relation relating turbine speed, N, to the ratio of

rated power output, P, to the rated head, H, is given by the following

regression equation:

N = 2044.395 {P/H)-0·4329 Eq. ( 43)

This relation is shown graphically in Figure 31.

The regression equation for tubular turbines relating turbine

speed to the ratio /[/D is given as:

N = 156.193 ( IH/0) 0· 8895 Eo. ( 44)

This relation is shown graphically in Figure 32.

Table 3 summaries all the regression relations that were developed

for manufactured tubular type turbines. In the table are shown all the

equations that were developed, the regression correlation coefficient

for each particular regression, the corresponding standard deviation,

the sample period and the number of different manufactured units used

in developing a particular relation.

Cross-Flow Turbines

For cross-flow type turbines the specific speed, Ns, vs rated

head, H, relation is shown in Figure 33 and the resulting regression

equation is given as:

N = 513 846 H-0· 5047 s . Eq. ( 45)

54

•

•

• •

Equation Number

31

(.]1 (.]1

32

33

34

35

36

37

38

• • • ... - .....

TABLE 3

SUMMARY LISTING OF REGRESSION INFORMATION AND EQUATIONS RELATING TURBINE

CHARACTERISTICS TO VARIOUS TURBINE CONSTANTS FOR TUBULAR TURBINES


Ns Ns = 1107.303 H -0•2998 0.62 92.71 1957-1984

Ns N = 52 96 p 0.8882 s • 11 0.71 55.91 1957-1984

Ns Ns = 357.294 Q~i 9029 0.70 59.37 1957-1984

Ns N = 0 497 N1•4080 s • 11 0.85 44.20 1957-1984

pll p = 10 133 00.7315 11 • 11 0.89 1.30 1957-1984

N11 N = 52 96 P 0.3882 11 • 11 0. 32 14.93 1957-1984

N11 N = 120 144 q0•4210 11 • 11 0.35 15.28 1957-1984

~ ~ = 0.0389 N~· 6013 0.85 0.09 1957-1984

Number of Units

54

41

37

41

39

41

37

41

TABLE 3 CONTINUED


39 t $ = O.n26 P~i3882 0.32 0.18 1957-1984 41

40 [) 0 = 1.5424 ~ 0 • 5767 0.03 1.45 1957-1984 41

41 D [) = 0.1433(~)0.5115 0.94 0.91 1957-1984 45 H

<J'1 0 = 4.511(0/N)0.3393 C) 42 D 0.99 0.46 1957-1984 37

43 N N = 2044.395(P/H)-0•4329 0.69 114.60 1957-1984 54

44 N N = 15n.193({1H) 0•8895 0.95 29.47 1957-1g84 41 f)

• • - - -

• • • • .. -1000 -1 3.00

N = 2044.395 (P/H)-0· 4329 (1957 -1984)

r = 0.69 s = 114.60

500 -IE 2. 75 1, -~~ No. of Units = 54

c.. s...

~ ~ ~ ~. •

E c c.. .,.... ' '-s... ' '"0

..._ ' c Q) 2.50 .,.... Q) c..

'"0 (/)

2.25 J ~

.... ,_ . ........_ • Q) Q) Q)

' c.. c ..._. (/) 200 .,.... , .

..0

~ ·~. ......._

Q) s... • c ::::::1 • ' .,.... 1-..0 s... "' ::::::1 z: 1-

4-"' 0

z: 100 0 2.00 (.,., ....---.....1 c;

0 _J

60 ~ t. 75 i . ........._ • 1111 t a 111 a 1 at t 1 t a 1 a 'I at r; a; at; 11 a a 1; t t; a 1 a 111 at u 1 a

1.0 1.4 t.8 2.2 2.6 3.0 3.4

Log10 of P/H, Rated Power over Rated Head

-, 10 20 50 100 500 1000 2000

P/H, Rated Power over Rated Head

Figure 31. Turbine Speed versus P/H ratio for tubular turbines.

500 -1 1

400 "-1 2.751

E

N " 1

56.193(,11)0.88S5 //

0.

E

~

0. s:::

r" 0.95 D (1957-1984) ~/ / ~

......

s:::

s "29.47 //

......

No. of Units " 41 ~ /:/ "0 (l) (l) 0.

2.25 (/)

. ~

(l)

d~·/ s::: .....

/ ;;;;} . ..0 ~ ::::1 100

1- 2.00 4-

en

z:

l~ co 0

...J t . 75 -t ',_/ //

32 -1 t . 50

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Log 10 of ~' Square root of Rated Head over Turbine Diameter

I I ---.- ---,- -r r ,- --,- ----,- ----.--.---- r ---, -- 1- 1- T-------, I I I 0.2 0.5 1 .o 2 3 4

~, Square root of Rated Head over Turbine Diameter

Figure 32. Turbine speed versus ~ratio for tubular turbines .

• A - ----~ ... - ....

• • • • • • - ....

300--, 2.50-:j '-~ Ns = 513.846H-0· 5047 (1965-1982)

-~r = 0.79 S = 36.89

2.25 ...... - :~·of units= 17

·~ "0 Q) ..... Q) ..... ...... 0. ......

~ :.~ V) "0 Q) u ~ 100 ·..- .....

4- 2.00 ..... • ..... V) ·..-

~ • u

u Q) .,..- 80 0. 4- V) ...... ·..- ........ u .. Q) Ill 0. 60 :z:

V) 1. 76 4-0

~ ~ :z: 0

(.]"1 40 f 1.0

1.501 ...... .....

30~ ...............

• 201 '.25~ I' I I I I I I I I I I' I I I I I I I I I I I IiI I' I I I

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Log10 of H, Rated Head in Meters

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ------T - 1 - 1

4 5 10 15 20 30 40 60 80 100 140


Figure 33. Specific speed versus rated head for cross-flow turbines.

Here again· only one manufacturer's equipment was studied and no

stratification of experience data was attempted for the modern units

that have been manufactured. Figure 34 presents the relation between

specific speed, Ns, and unit power, P11, for cross-flow turbines

studied and the resultant regression equation is given as:

Eq. ( 46)


unit discharge, 011, for cross-flow turbines studied and the

resultant regression equation is given as:

Ns = 120.605 0110.4958 Eq. {47)


unit speed, N11, for cross-flow turbines studied and the resultant


N = 1 249 N 1· 2379 s . 11 Eq. { 48)

Figure 37 presents the relation between unit power, P11, and

unit discharge, 011, for cross-flow turbines studied and the


pll = 8.0743 0110.9905 Eq. {49)


unit power, P11, for cross-flow turbines studied and the resultant


Nll = 41.989 p110.0049 Eq. (50)


unit discharge, 011, for cross-flow turbines studfed and the


Nll = 42.444 Q110.0005 Eq. (51)

60

•

•

•

• • •

300

200

I -o Q) Q)

u 0. 100 (./')

u .,.... u .,....

80 Q) 4--.,.... 0. u (./') Q) 0. ..

Vl (./')

60 z: " Vl 4--

z: 0

0 40 ..-0"1 ._. 01 0

...J

20

2.50

2.25

2.00

1. 75

1.50

• • •

//

~ / // ~/ /

• ..

/ /

', N = 41 .989P 0· 5049 (1965-1982) .... ,____. s 11

r = 0.96 s = 26.91

No. of Units = 17

t · 25 I 1 I , a a a 1 r ; r r 1 r a 1 1 a a 1 1 1 1 t 1 r 1 a 1 a 1 1 a a 1 t a 1 1 a t

-0.6 -0.3 0.0 0.3 0.6 0.9 1.2


I I I I I I I I I I I I I I I I I I I I I I I I I I 0.25 0.3 0.5 1.0 2.0 3.0 5.0 10 12 15

P11 , Unit Power

Figure 34. Specific speed versus unit power for cross-flow turbines.

300 2.50

200 I

"0 (l.J (l.J

0.. "0 (./)

(l.J (l.J u 0.. ......

(./) 100 4-.,.... 2.00 u u .,.... (l.J j / / /.Nc = l20.605Q,,v.'+:?:Jo (1965-1982) 4- 0.. ..... 80 (./) u (l.J .. 0.. Vl

(./) 60 z '

i;o I. 751 //,, / No. of units = 17 Vl z

...... 01

O'l 40 ~ .3 N

1.50

20

-1.5 -1.0 -0.5 0.0 0.5

Log1 0 of 011 , Unit Discharge

J -- -- - - ~- -, "0 ., -.-. --- -T- T T T I I I ,-----l

0.03 0.05 0.1 0.2 1.0 1.5 2.0 3.0


Figure 35. Specific speed versus unit discharge for cross-flow turbines.

• • • -~·.~, . ... ...

- ..

"'0 Q) Q) 0.. Vl

u •r-'+-•r-u Q) 0.. Vl

~

Vl z

0'\ w

30

100

80

60

40

20

..

"'0 Q) Q) 0.. Vl

u •r-

rVl

z

0 ,_. 0'\ 0 _J

2.se

1.56

- -

------------• ~·:-.a---------

------------• ------- N = 1 249N 1· 2379 (1965-1982) s . 11

r = 0.06 s = 56.96 •

No. of units = 17

•

1.60 1.64 1.68 1. 72 t. 76 1.80

Log 10 of N11 , Unit Speed

..--~--r---,- -----.---,---.---------.- T .-----I f I I ' I I I I I I I I I I

38 40 45 50 55 60 63

N11 , Unit Speed

Figure 36. Specific speed versus unit speed for cross-flow turbines.

30-, t . 5 J

20-1 i

10 --1 s.... t . 0

~

<lJ

s.... 3

d;P 0

<lJ c...

3: 0

+J

c... .,....

+J

s:::::

,.... ::::>

. p s:::::

-~

::::> ,...... ,...... df_

2 c...

c... 4-

_j 0

0 ,......

/~ 11 - 8.074301 0.9905 (1965-19

m Ol

+=-0 0.0 I_J

g./ r=0. 98 1 82)

0.5 J

s = 0.60

1

p/ No. of units = 17

o. 32-l -0.5- -

I I I I I I I I I

- t 5 . I I I I • I I I

-t .0 -0.5 Log of Q 0.0

10 11' Unit o· 0.5

1scharge

I I I I I I II I I I I I I I I 'I ,-,-, . 032 . 04 . 05 0.10 0. 2 0. 4 1 . 0 1 . 5 2. 0 3. 0


Figure 37.. Unit power versus unit discharge for cross-flow turbines .

- .-.

• •

63 --1

60

j

55~ "'0 Q) Q) 0.

"'0

50i i Q) Q) 0.

(/)

~ •r-c

::::>

451 ~ ,..... ,..... z:

0 ,..... O'l

0'\ r3 (J1

40 -l

35.

- - -1.ae

1. 75

1. 70

1.65

I .60---, •

-0.6 -0.3 0.0

0.25.3 0.4 0.5 l.O

-

• N = 41 989P· 0 · 0049 (1965-1982) 11 . 11

r = 0.002 s = 5.71

No. of units = 17

•

• •

• • • ..! •

• • •• • •

• •

0.3 0.6 0.9 1.2


2.0 3.0 4.0 8 10 12 16 20

P11 , Unit Power

Figure 38. Unit speed versus unit power for cross-flow turbines.

... - -

-1.5 -1.0

= 42.444011 °· 0005 (1965-1982)

0.00003 s = 5.71

of units = 17

•

• •

• • • •

•

-0.5 0.0 Log1 0 of 011 , Unit Discharge

•

• •

• •• •

• _ _. __

0.5

I , , ' ,-T--rT•T~ I"''T'"II'"II""' I I I I I ' I --~---~

0.04 0.10 0.15 0.2 0.3 0.4 0.5 1.0 2.0 3.0


Figure 39-. Unit speed versus unit discharge for cross-flow turbines .

~ =-..-.

•

•

•

Using the speed ratio, 0, as a dependent term of characteristic

turbine parameters empirical relations were developed for cross-flow

type turbines studied as follows:

0 = 0 3977 N 0.0478 . s

0 = 0.4963 p110.005

Eq. (52}

Eq. (53}

The reqression equation relating the cross-flow turbine diameter D, to

the speed ratio, 0, is given as:

D = 1.2151 0°· 6254 Eq. (54}

The graphical relations involving the speed ratio, 0 and the specific

speed, Ns, unit power, P11 and cross-flow turbine diameter, D,

are presented in Figure 40, 41 and 42.

The graphical relations relating the cross-flow turbine diameter,

D, to the P/H ratio is presented in Figure 43 and the relation between

cross-flow turbine diameter, D, and the Q/N ratio is presented in

Figure 44. The empirical relation as a regression equation relating

cross-flow turbine diameter, D, to the P/H ratio is given as:

D = 0.354 (P/H} 0· 2571 Eq. (55}

The corresponding empirical relation as a regression equation relating

cross-flow turbine diameter, D, to the Q/N ratio is given as:

D = 1.5848 (Q/N} 0· 1615 Eq. (56}

The additional empirical relation as a regression equation

relating cross-flow turbine speed, N, to the P/H ratio is given as:

N = 1126.25 (P/H}- 0· 5367 Eq. (57}

The regression equation for cross-flow turbines relating turbine speed,

N, to the ratio IH/D, is given as:

N = 42.866( IH/0} 0· 9939 Eq. (58}

67

• A

o. 8 --i -e . t e

/-o / r

= 0.3977N °· 0478 (1965-1982) s = 0.06 s = 0.06

I II

No. of units = 17

I •

----------------- ••

• •

----· •

••• •

•

•

-

-0.35j • I I I I I I I i I I I I I I I I I I I I I I I I I I I I I I I I I' I I I ' I I I I i I I I ' I t I I I I I 'I I I I I I I I '

1.2 1.4 1.6 1.8 2.0 2.2 2.4 Log10 of Ns, Specific Speed

~ --,---- ~--, -,-,--~-~----,-- T I -,

1~ 20 30 40 50 60 80 100 200 250

Ns, Specific Speed

Figure 40. Speed ratio versus specific speed for cross-flow turbines .

- - -

• • • • • ... -

¢ = 0.469P 11 °· 005 (1965-1982)

r = 0.002 s = 0.07 •

No. of u~its = 17

• -----

• • •

• • • • • • ••

• • • •

0.0 0.3 0.6 0.9 t • 2 Log10 of P11 , Unit Power

.......----....,..----r---r--r---:r-r---r-.---r--,.-,~-.-....,..--,-,....,.-,--r-r--r--T - I

0.25 0.5 1.0 2.0 3.0 4 3 10 12 16 20

P11 , Unit Power

Figure 41. Speed ratio versus unit power for cross-flow turbines.

9.11 • 7. Vl

s.... <lJ

V) ~

• • • • • t <lJ s.. E <lJ

0. -a. 1 ~

~

c

• • •

<lJ ...... E s.. c <lJ .,.. ~ s.. <lJ E <lJ tO ~

<lJ ...... E q

• • \

-a. s-j tO

<lJ ,.. c q ......

.a <lJ c s....

'D : 1 .215¢0

·6254 (1965-1982)

0. ::J ..... 1-- -a.4

• r : 0.04 s ; 0.24

.a s.. "' ::J

q 1--'-1

4-0

"' 0 -a.s q

0.3- a ,_

No. of units : 17 • O'J 0

0. 25-/-J .... -

-9.38 -9.34

-9.39 -9.26 -e. 22~

-e. 1a -9. f 4 0.4

0.45 Log 10 of ¢, Speed Ratio

o.s 0.55

0.6 0.65

Figure 42. Turbine diameter versus speed ratio for cross-flow turbines .

¢, ·Speed Ratio 0.7

• • • ; ... .... -

.. - -

1.2 Vl s....

1.0 Q) ....., Vl Q) s.... E Q)

/'

/' ........

....., s::: Q)

0.8 -.,....

E • s.... s::: Q) .,.... ....., / Q)

s.... 0.6 E

Q) ttl ....., .,.... /'

Q) Cl E ttl Q) .,.... s:::

Cl .,.... ...-..0

Q) s.... s::: 0.4 ::J .,.... I-..0 s.... ::J

j~ I--.....! .. .....

Cl

/ D = 0.354(P/H) 0· 2571 (1965-1982)

r = .0.89 5=0.10

No .. of units= 17 0 .--

01

0.25--i _g -0.

-0.6 -0.2 0~2 0.6 1.0 1.4 1.8 Log 10 of (P/H), Rated Power over Rated Head

1-T-.------r-,---,-.--, T---. 'T-,--,--.--.,---,- T ,- r -,- 1 -,-I

.25 .3 0.5 1.0 2.0 4.0 10 20 40 60 80

(P/H), Rated Power over Rated Head

Figure 43. Turbine diameter versus (P/H) ratio for cross-flow turbines.

1.2 ~ ~.'

1.0 Vl ~-~ !-

/. /

Cl)

+-' Vl Cl) !- 0.8 E Cl)

s::: -~.' +-' Cl) .,.... E

!-s::: Cl) .,....

't:: -~.2 !- 0.6 E Cl) "' +-' .,.... Cl) Cl E

Cl) -~.3 "' .,.... s::: Cl .,....

..0 = 1.5848 (Q/N) 0· 1615 (1965-1982)

Cl) !- ~ ~ ~ ..,.,.

s::: 0.4 ::I ... .- I- -~.4 ..0

r = 0.84 S = 0.15 !- ~

::I Cl I-

60 -~.51 / / -....s ~ / N Cl ./ 0.3 •

No. of units = 17

0.25

-4.5 -4.0 -3.5 -3.0 -2.5 -2.B -t.5 -1 .B Log 10 of (Q/N), Rated Discharge over Turbine Speed

l - 1 1 1 TTTr- , l ---------r 1 I 1 l 1 1 I 1 1 1 1 1 1 1 I 1 1-r---. I 1 I - r -.---I 0. 03 0.1 0. 2 0. 4 . 6 . 8 1 . 0 2 5 10 20 40 lOO

(Q/N), Rated Discharge over Turbine Speed (Xlo3)

Figure 44. Turbine diameter versus (Q/N) ratio for cross-flow turbines.

''-

•

•

Table 4 summarizes all the regression relations that were

developed for manufactured cross-flow type turbines. In the table are

shown all the equations that were developed, the regressions

correlation coefficient for each particular regression, the particular

standard deviation, and the number of different manufactured units used

in developing a particular relation.

TURBINE SETTING CHARACTERISTICS

It is common practice to relate a turbine constant known as the

cavitation coefficient or plant sigma to the specific speed for exper-

ience curves. The equation ·for the plant sigma is given as follows:

H - H - H a v s o=------ Eq. (59} H

where o = plant sigma, dimensionless

Ha = atmospheric pressure head in ft or meters

Hv = vupor pressure head at temperature of water issuing from

turbine in ft or meters

Hs = difference in elevation between m)nimum tailwater level

and the cavitation reference point at the outflow from the

turbine in ft or meters

H = net effective head in feet or meters

The term, Hs, is referred to as suction head and it has slightly

different designation depending on the type of turbine, the location of

the tailwater and the orientation of the turbine and turbine shaft. A

related term is, z, the draft head the difference in elevation between

the tailwater level and the centerline of the distributor or the cen-

terline of the turbine runner. Figure 45 shows diagramatically what

these two terms are for different types of reaction turbines having

73

Equation Number

45

""-J ~

46

47

48

49

50

51

52

- -

TABLE 4

SUMMARY LISTING OF REGRESSION INFORMATION AND EQUATIONS RELATING

TURRINE CHARACTERISTICS TO VARIOUS TURBINE CONSTANTS FOR CROSS-FLOW TURBINE


Ns N = 513.846 H-0•5047 s 0.79 36.89 1965-1982

Ns Ns = 41.989 P1i.5049 0.96 26.91 1965-1982

Ns Ns = 120.605 o~i 4958 0.93 27.42 1965-1982

Ns N = 1 249 N1•2379 s • 11 0.06 56.96 1965-1982

p11 p = R 0743 00.9905 11 • 11 0.98 0.60 1965-1982

N11 N = 41 989 P0•0049 11 • 11 0.002 5.71 1965-1982

N11 N = 42 444 00.0005 11 • 11 0.00003 5. 71 1965-1982

~ $ = 0.3977 Ns0.0478 0.06 0.06 1965-1982

. - ~· """

Number of Units

17

17

17

17

17

17

17

17

• - ... - -

TABLE 4 CONTINUED


53 ~ ~ = 0.4963 p1~· 005 0.002 0.07 1965-1982 17

54 [) D = 1.2151 ~0 • 6254 0.04 0.24 1965-1982 17

55 D D = 0.354 (P/H) 0•2571 0.89 0.10 1965-1982 17

'-.1 56 D D = 1.5848(Q/N) 0"1615 0.84 0.15 1965-1982 17

c.n

57 N N = 1126.25(P/H)-0•5367 0.79 213.95 1965-1982 17

58 N N = 42.866(~) 0 • 9939 0.98 31.5S 1965-1982 17 0

HW

Francis Turbine

Inclined Tubular Turbine

Vertical Tubular Turbine

Bulb 8 Horizontal Tubular Turbine

Figure 45. Definition diagram for suction head, Hs and draft head, Z, for different types of turbines.

76

different shaft orientations. Sometimes difficulty is experienced in

relating the plant sigma to other turbine characteristics because the

cavitation reference point is not always consistently defined. In this

study for the axial flow units which includes bulb type units, the

tubular type units, and the rim-generator units the cavitation refer-

ence point was taken as the highest point on the propeller blade above

the tailwater level. In the case of cross-flow turbines the pressure

in the runner zone is essentially atmospheric pressure and is therefore

not subject to cavitation. No turbine setting and plant sigma analysis

was done on the cross-flow turbines.

Bulb Turbines

Figure 46 presents stratification of the relation between the

plant sigma, a, and the specific speed, Ns, for six different tur

bine companies• manufactured bulb type turbines. It is interesting to

note that the correlation coefficient for different companies varies

quite markedly. The empirical equations for the relation between plant

sigma, a, and specific speed, Ns, for the respective manufacturer•s

units are indicated below: Source

a = 4 549 10-6N 1· 908 • X S * KMW Eq. (60)

a = 313.332 X 10-6N 1· 274 s * NO-KMW Eq. (61)

0.097 x 10-6 N 2·479 * a = TAMP Eq. (62) s

a = 111.435 X 10-6 N 1· 423 * s VOITH Eq. (63)

a = 80 774 10-6 N 1· 491 • X S * VEVEY Eq. ( 64)

a = 1541 62 10-6 N 1•015 * • X S VOEST ALPINE Eq. (65)

*The values of a are based on the definition of plant sigma used in this study.

77

'o

0 E ~

en

-c: 0

a..

I 0.0 -r---:-----,.---r--,----,---.-----------------,

8 .0 ~--+--+----+---+-----"r---1

4 .0 +---+---+--+--+-----,.---4

2.0

1.0

0.8

'

a= 80.774 x 10-6 Ns 1·491 Mfg. No. 5

a = 313.332 x 10-6 N 1·274 Mfg. No. 2 s

7.625 X 10-5 N 1·4850 s

0.097 x 10-6 N 2·479 Mfg. No. 3 s

111.435 x 10-6 N 1·423 Mfg. No. 4 s

a = 4.549 x 10-6 Ns 1· 908 Mfg. No. 1

a = 1541.62 x 10-6 N 1·015 Mfg. No. 6 s

500 600 800 1000

Specific Speed, N5

Figure 46. Stratification of relation between plant sigma and specific speed for different manufacturers.

78

•

Figure 46 also presents a composite experience curve of the

relation between plant sigma, a, and specific speed, Ns, for all

manufactured bulb turbines for which turbine setting data were

obtained. The regression equation for this composite experience curve

is given by the following regression equation.

a = 7 625 10-5 N 1. 485 • X S Eq. ( 66)

The correlation coefficient for this regression is not very high and it

shows that such an experience curve is not expected to be very reli-

able. Using a regression relation suggested by Khanna and Bansal

(1979) a relation was developed between plant sigma, a, and unit dis

charge, Q. The regression equation developed for bulb turbines studied

on this project is:

a = 0. 5750 Q 1. 1937 11 Eq. (67)

Table 5 summarizes all the regression information on turbine

setting for manufactured bulb-type turbines that was obtained and gives

the respective correlation coefficients and the number of units used in

each regression relation that was developed. The information source or

manufacturer is also indicated in Table 5.

Tubular Turbines

Figure 47 presents the relation between plant sigma, a , and the

specific speed, N5 , for all manufactured tubular turbines studied.

The empirical equation for the relation between the plant sigma, a ,

and specific speed, Ns, for the manufactured tubular turbines is

indicated below:

a = 3.987 X l0-5N 1· 579 s Eq. {68)

79

Equation Number

60

00 0 61

62

63

64

65

66

67

-

TABLE 5

SUMMARY LISTING OF REGRESSION INFORMATION RELATING TO TURBINE

SETTING FOR BULB ANO TUBULAR TURBINES


() ()= 4.549 X 10-6N 1•9080 o. 58 0.84 1953-1984 s

o- = 313.332 X 10-6N 1•2740 () 0.92 0.11 1953-1984 s

() ~ = 0.097 X 10- 6 N~" 4790 0.92 0.15 1953-1984

tT ~ = 111.435 X 10-6N1•4230 0.47 0.47 1953-1984 s

cr ~= 80.774 X 10-0N1"4910 0.44 1.02 1953-1984 s

cr ~ = 1541.62 X 10-6N1•1050 0.84 0.20 1953-1984 s

o- () = 7.625 X I0- 5N I. 4850 0.53 0.64 1953-1984 s

() () = o. 575 011 1.1937 0.43 0.68 1953-1984

•• l....._

Number Type of of Units Turbine

12 Bulb

10 Bulb

4 Bulb

15 Bulb

11 Bulb

3 Bulb

61 Bulb

61 Bulb

00 to-'

TABLE 5

Equation Number

68

69

CONTINUED

Dependent Parameter

cr

cr

Regression Equation

cr = 3.987 x 10-5N 1•579 s

o- = 0. 3074 Qll 2.066

Correlation Standard Sample Number Type of Coefficient Deviation Period of Units Turbine

0.53 0.33 1957-1984 31 Tubular·

o. 77 0. 24 1957-1984 31 Tubular

00 N

1000--, 3. 0

"'0 Q) Q) 0..

(/)

u

800

~ 600 .,..... u Q) 0.. (/)

Vl z

400

"'0 Q) Q) 0.. (/)

u .,..... 4-.,.....

2.9

u ~ 2.8

(/)

Vl z 4-0

0 r-

O'l 0

_J

2.7

2.6

-•

-----...-

• ~ • •

- ----.~. ·~ __:-:--__-a = 3~987 X l0-5N 1.579 s (1957-1984)

• r = 0.53 s = 0.33

No. of units = 31

2. 5 -'--..., I I I I ' • • .--.--.--.-....-.-i'"~--i~•-r ...... "I ....,.... I i""'"l I I ' I i I ' T

-0.4 -0.2 0.0 0.2

Log 10 of a, Cavitation Coefficient (Plant Sigma)

1 ~--..-----, ~ ,~

0.4 1.0 1.5 2

a, Cavitation Coefficient (Plant Sigma)

Figure 47. Specific speed versus cavitation coefficient for tubular turbines.

As for bulb turbines the correlation coefficient for this composite

regression for tubular turbines is not very high and it shows that such

an experience curve is not expected to be very reliable.

The relation between sigma, a, and unit discharge, Qn, for

tubular turbines is given by the regression equation:

a = 0.3074 Q112•066 Eq. ( 69)

The summary of regression information on turbine setting characteris-

tics for tubular turbines is presented along with regression informa-

tion on bulb turbines in Table 5.

WATER PASSAGE CHARACTERISTICS

The water passages of low-head turbines are quite different from

conventional Francis and vertical shaft Kaplan propeller turbines and

as such the dimensioning of the water passages is different for differ-

ent types. Significant in feasibility and preliminary design are the

entrance dimensions, the draft tube outlet dimensions or area, the

maximum diameter of the water passage surrounding the turbine, the

total length from entrance to draft tube outlet, and the length from

the centerline of the turbine to entrance. These data are useful in

layout design of the civil works and power house arrangement planning

as well as helpful in cost estimating. In this study it was possible

to obtain only enough different sets of data on manufactured bulb type

units to make regression analyses and develop experience curves.

In seeking the water passage information it was found that most

turbine manufacturers prefer to consider the various dimensions pro-

prietary information so that this phase of the research had to be

scaled to what could be collected under public disclosure allowances.

83

In the manufacturer contacts it was possible in several cases to

get recommended dimensions related back to a common turbine parameter

such as turbine runner diameter. This information has been grouped and

organized to be useful for design and also compared with different

manufacturers performance data to provide representative dimensions

that can be related to plant capacities.

During the study several companies provided standardized selection

information that gives considerable detail on different sized units.

These water passage dimensions have been analysed and comparisons

between different company's unit made and where possible regression

studies were conducted. In general there was insufficient information

on the possible standardized units to develop experience curves.

Following the earlier pattern the specific information on water passage

dimensions is presented systematically according to different turbine

types, beginning with bulb type turbines.

Bulb Turbines

To present the water passage information it is necessary to show

schematically the various water passage dimensions that were analysed.

Figure 48 shows a simplified dimensioning sketch with dimensions label

ed with letters that were used in the regression analyses and the com

parisons. All dimensions have been related back to the desi9n diameter

of the turbine runner as obtained from the manufacturer. Since the

rated power is frequently an estimated value that is obtained early in

the feasibility study, water passage dimensions were also related to

rated power, P, and in some cases relations were sought with the rated

discharge, Q. In certain cases like the entrance to the turbine and

the exit from the draft tube the dimensions actually represent areas.

84

F G H.W. sz ~ ',,, r--~ K

T. w. --

' 1 __ 0 Ao ~c L\JI- I~ ~ co

J U'1

~ c

Figure 48. simplified dimensioning sketch for water passages of bulb turbines.

These areas are sometimes circular, square, or rectangular in cross

section.

Figure 49 presents the relation of the distance from turbine

entrance to the exit of the draft tube outlet (F + G), to the rated

power and the resulting regression equation for bulb turbines is given

as:

(F + G) = 0.6744 P0·4188 Eq. (70)

Figure 50 presents the relation of the distance from the turbine

entrance to the exit of the draft tube outlet, (F + G) to the runner

diameter, 0, and the resulting regression equation for bulb turbines is

given as:

(F + G) = 8.2075 o0· 9801 Eq. (71)

Figure 51 presents the relation of the length of the bulb, K,

including the turbine runner to the rated power, P, and resulting

regression equation for bulb turbines is given as:

K = 0.580 P0.3268 Eq. (72)

Figure 52 presents the relation of the length of the bulb includ-

ing the turbine runner to the turbine diameter, 0, and the resulting

regression equation for bulb turbines is given as:

K = 3.1994 o0·8744 Eq. (73)

Figure 53 presents the relation of the entrance area. Ae, to

the rated power, P, and the resulting regression equation for bulb tur-

bines is given as:

A = 0.1465 p0· 6503 e Eq. (74)

Figure 54 presents the relation of the entrance area, Ae, to the

turbine diameter, 0, and the resulting regression equation for bulb

86

(X) '-1

+.l 4-~

~ 50 0

.f-)

Q) 40 u s:: ~ s... .f-)

~ 30 Q) s:: ......

..0 s... ::I 1-

Vl E s... e ~ 2o 4-CV

E Q) us:: S::•r~

t: t 15 ........... Cl .f-)

::I "0

c..!)Q) +..o LL. ::I ..__.I- 1 0

Q) u s:: ~ s... +.l s::

UJ

Q) s:: ......

..0 s... ::I 1-

Vl E s... 0 Q) s... .f-) 4- Q)

E Q)

u s:: s:: ...... ~

+.l .f-) Vl Q) ...... ..... Cl +.l

::I .. 0

(..!) Q)

+ ..0 LL. ::I

1-

4- +.l 0 4-

~ OS.. ..... Cl

01 0 0

.-1 .f-)

/ /

1.7i

Lei / / ,.

,/ / ,,'

/ ,,++ / ,, ,, ,,

1.1

2.2

/ /

,,

,,~ / ,, /

,.//\/' // ,,' // ,, ,, + // r = 0 ( 1953-1984)

,/ • 82 s = 11. 80 /

/ ,, ,, ,, No. of units = 5 // ,.,

,, ,, ,, ;/

,

2.6 3.9 3.4 3.8 4.2 4.6 Log10 of P, Rated Power in KW

~~--~-r-.-.,ro.------,--,-,-,,.-,.,,---~~-.~-.1'1~

.16 0.2 1.0 10 20 30 40 50

P, Rated Power in MW

Figure 49. Distance from turbine entrance to draft tube outlet versus rated power output for bulb turbines.

0 .._, .._,

50 ~ QJ u

ro c s... ro Cl s... .._, 0 40 .._, c

LJ.J

QJ QJ u c c ...... ro .0 s... 30 .._, s...

:::::! c

l.J..J 1-

QJ E 0

c s... ...... ~ .0 s... QJ :::::! u

1- 20 lll E s...

c ro .._,

QQ.) lll s,....._, ...... ~QJ

E Cl

QJ . uc ......... C•r- L!J ro .._, .._, +

l.J...

CX> l/lQJ ...... .--CX> Cl .._,

.........

~ :::::!

~a 0

.--.. L!JQ.) +.O 10 l.J...:J

........ I-

1.7

c

~ 1.1 :::::!

1-

-0.4 -0.2

~/ / / /

;// ,,'' //

, ,'

,' .... , /

// ,,"'Z_ , r = 0 ( 1965-1982)

.95 s = ..., ~;/// (F+G) = 8.2075D0.980l

+ / / / 3.o7

A/// / No. of units = 4

,' ,' , /+

,/ / ,,

/ ,'

0.0 0.2 0.4 0.6 0.8 Log 10 of D, Turbine Diameter in meters

I I

0.4 0.5 1 .o 2.0 3 4 5 6 7

D, Turbine Diameter in meters

Figure 50. Distance from turbine entrance to draft tube outlet versus turbine diameter for bulb turbines.

~ .. - .... ~/~ 1 .251 ~ fi-:: 16 J /·y/-

" ...... 12 -1

,, + + ...... , .... + .... 10

1 00 ;%. --- / + . .... .. Vl

~~):J/ s.. Q) +l 8 Q)

E

c 6 - + .,,'"f+ .....

.,...

0.75 / --;/ ~

;= ~-------- + '-.. K = O. 580po. 3268 ( 1953.1984)

+l 01 c

::li , ., .. Q)

"' / ----- /_.-· =081 5=2.47

_J 4

~ ,.. r . ..0

~ .... ~ ,...... ::::::1

':; 0.50 --- No. of units = 53

co ~

0 ..... + ~ .... ,...... c:> 01 +

1.0

0

2 -I_J 0.25

0.00d ~j-rl,irTI-i~i-ri,irTI-ri,jrTI~irTI-ri,irTI~irTI-ri,jrTI~irTI-ri,i-ri,irTI-i~j-ri~irTI-ri,irTI~irTI-ri~j~i-rl,lrTI~i~i-rl~lrTI-rj~irTI-rl-1~1-rl~l~l-rl~j~l-rl-1~1~

2.2 2.6 3.0 3.4 3.8 4.2 4.6 Log10 of P, Rated Power in KW

~-,--T

. 16 . 20 1 2 1 0 40 60


Figure 51. Length of bulb versus rated power for bulb turbines.

18 :1 1.25 16

12 -=1 r Cli

+.J

t. ee 1 + Vl 10 Cli l- E Cli

+.J I:: Cli 8 .,.... -i + . ../ ... - / + E

_ ... .0

I:: .-.,.... :::::s

6 co .0 0.75 .- 4-

:::::s 0 co

..s::

~ // ~K = 3. 199400.8744 (1953-1984) 4- +.J 0 C"l

4 I:: + ..s:: Cli / .... +.J _J / .... r = 0.80 s = 1 .80 01 / _.... -I:: .. 0.50 Cli ~

_J

~// No. of Units = 53 4-1.0 .. 0 + 0 ~ / ,,'

0 ...... + .- _ ..... 2 ~ Ol

0 _J 0.25

1

-0.2 0.0 0.2 0.4 0.6 0.8 Log 10 of D, Turbine Diameter in meters

~· I -, ,- 1- ---. - -, ------~ --.-- T--- ,---, ---.-,---.--1' .6 .7 1.0 2.0 3.0 4.0 5.0 6.0 7.0


Figure 52. Length of bulb turbine versus turbine diameter.

Vl Q)

l.(') 1:: l.(')

..0

co s... ::1

+ 0 +-' \ + ~ '<.T

\ ,-... ..0

\ \ o:::T 0 .-\ 00 (V') ::1 \ + 0"1 ..0 \

\ .-~+ + I s...

\ \ (V') 0 0 \ +.P, l.(') N '+-

\ \ 0"1 0"1 (\1 't .- (V') +-' +'

~ ::1

\ 0 0. \ (V') N +-' +\ 0 .- ::1

\ l.(') II (V') 0 \ ~

-k V) II 3 0 s... \ 0 :::.2 .- Q)

a... Vl 3 \ l.(') -+-' 1:: 0 \ \ \ ~ ..... CIO 3 0. \ o:::T 1:: . ::£: \

\ 0"1 ::1 s... -o \

~ \ ,...... Q) 1:: Q) \ \ 0 '+- 3 l.(') •r- +-'

\ 0 0 0 ItS + \ II a... s... s... \ + II Q)

+ ' 0 -o 3 Vl +\ s... z: Q) 0 ::1

\ -+-' a... Vl

~ ItS s...

+ \ + 0:::: -o Q) \ Q) > \

~ +-' \ a... ItS ItS \ ~ N 0:::: Q)

\ \ '+- s... 0 ItS

+\ a... 0 Q) \ .- u \

\ \ + en 1:: +\ (5) 0 ItS

\ ....J s... . .- +-' \ ~ 1:: + \

\ Q) \ \

Q) \ \ 1:: \

' •r-

\ \ 0 ..0

\ s... \ ::1 \ \ \ \ co o:::T 1-

\\<\+ (\1 0

(V') l.(')

Q) s...

N ::1 O'l

\ (\1 ~ LJ...

\ \ ' .-\ \ ' (\1

CIO 1J) (\1 0) . N - - (5) C5i)

w UL ea;. 'rJ a:> u e;. + u3 au~q.J.nl 'a'r.f .J.O 0 L5ol 6

Iiiii 11 II I' I I I I I I I I I I I I

0 0 0 0 0 0 l.(') N 0 CX) ~ o:::T N .-.-

6w u~ ea.J.\:.f a:>UT!J.lU] au~q.J.nl ,a\:.f

91

N E

s::: •r-

ttl ClJ s...

c::!

ClJ u s::: ttl s... 4-> s::: w

ClJ s:::

•r-..0 s... ;:::, I-

0..0 N

c::!(l)

100 80

60

40

20

10

8

6

4

2

2. I

-0.4

/ ,.

,' / ,,, , ,"' ,,

~,,'~ , , ,

,, , ,,' + ,, , ,.

-0.2 0.0

/~, / + .... ' ·~ t~~

*'t-,

+ ,,

,,+ ,,

(/

/ ,,,,,y/

~ , , ,,+ ,'

+ ¥/'',,¥ , , / ,, ,, ,, ,,

,, ,, /

,,,, / +

A = 4.3951D1· 7827 (1953-1984) e

r = 0.93 s = 8.33

No. of units = 31

0.2 0.4 0.6 0.8 Log10 of D, Turbine Diameter in meters

~~~~~~~~~----~~--~~--~--~~~--~~~----1

0.4 1 2 3 4 5 6 7


Figure 54. Turbine entrance area versus turbine diameter for bulb turbines.

turbines is given as:

A = 4 3951 o1· 7827 e . Eq. (75)

Figure 55 presents the relation of the bulb diameter, B, to the

rated power, P, and the resulting regression equation for bulb turbines

is given as:

B = 0.1887 P0· 3526 Eq. (76)

Figure 56 presents the relation of the bulb diameter, B, to the

turbine diameter, 0, and the resulting regression equation for bulb


B = 1.1745 o0· 9546 Eq. (77)

Figure 57 presents the relation of the draft tube exit area, A0 ,

to the rated power, P, and the resulting regression equation for bulb


A0

= 0.0978 P0•6846 Eq. (78)


to the turbine diameter, 0, and the resulting regression equation for

bulb turbines is given as:

A = 2 8686 o2·0047 0 • Eq. (79)

Figure 59 presents the relation of the ratio, K/Ae, to the rated

power, P, and the resulting regression equation for bulb turbines is

given as:

K/Ae = 4.335 p-0.3278 Eq. {80)

Figure 60 presents the relation of the velocity at turbine

entrance, Ve, to the rated power, P, and the resulting regression

equation for bulb turbines is given as:

v = 0 2690 p0.2254 e . Eq. {81)

93

10 1 I .00

8 V'l s... (1)

+> 6 (1)

V'l E s... (1) c: +> ..... (1)

4 E s... (1)

~ + ++-c: +-> ..... (1)

s... E co + (1) .....

+> Cl (1)

E .0 co ..... .... 2 :::::l

Cl OJ

.0 .. ..... OJ :::::l

OJ 4-

+ B = 0.1887P0·3526 (1953-1984)

0 \D ..

0.0~/: ..j:::> OJ - 0 .....

Ol 0

..-l

r = 0.76 s = 1.25'

No. of units = 54

2.~ 2.5 3.0 3.5 4.~ 4.5

Log 10 of P, Rated Power in kw

I-~---,---------,---- -----,- -~-.-----~ ,---, ---,-,--,-, l

0. 1 0 1 . 0 1 0 50


Figure 55. Bulb diameter versus rated power for bulb turbines.

(/)

s... Q)

+-' Q)

E

s::: .,... s... Q)

+-' Q)

E ttl .,... Cl

..0

...-::I co

.. co

~ (.]'1

10

8

6

4

2

(/)

s... Q)

+-' Q)

E

s::: .,...

s... Q)

+-' Q)

E ttl .,... Cl

..0

...-::I co

.. co 4-0

0 ...-

C'l 0 _J

1.00

0.75

0.00

/. .. · .Aj)r+_;>/

~~~/+ ,""'t"· /

+ + ' ..., / ,,..... / +

d +-'"' ./ +

~, .. ..+ t"' /+ /.//__..-+ ///

/ ......;:.---:Y- B = 1.174500.9546 (1953-1984)

/ ,..... / -+

/ _____ ,,-· / r - 0.81 S = 0. 71

// .......... // // .... / + +

No. of units = 54

.... .... ....

--" • ~!) :.~.~~~·~•~•~•~•~•~•~•~•-,1-y;-y;-r•~•~•~•~•~•~•~•~•~•~•~•~•-y•~•~•~•-r•-r•-r;-r;-;r-;r-;r-;r-;r-;r-;~;r-;r-;r-;r-r;-r;-;r-;r-;r-;~;r-ar-ra~c -0.2 0.0 0.2 9.4 0.6 9.8

Log10 of D, Turb1ne Diameter in meters

,--1 ·-r

0.6 1 2 3 4 5 6 7


Figure 56. Bulb diameter versus turbine diameter.

100 C'J

80- E

C'J s:: E .,.... s:: 60- tO .,.... Q)

s-tO 40 Q)

<:(

s- +J c:x:: .,....

X +J L.L.J .,.... X Q)

w 20 ..0

::::::1 Q) t-

..0 ::::::1 +J t- 4-

tO ;....> s-4-

10 tO s-

Cl

~

Cl

~

0 0. c:x::

0 \.0 c:x:: 0\ 4-0

5 0 ....-

Ol 0

_J

2-

/ /

/

+ ~--~ ,·

+ ,.,~~ / , .. +.... t, .. + /

+ + / + _..,-·+++

/

+ ~~+ + ......

,, .,.,

,~ ,,

.,.," /

.,"/++ / + . + ,.," +

/

/ + ,~'' + .,.,"' .....+ + + ,., /

~,/' + .," + / ,, ,, / ++,,,:V' + A = 0.0978P0 · 6846 (1953-1984)

, / 0

r = 0.71 s = 33.49 ""/.,.,.,' / ,, ,,,'"' +

No. of units = 53 ...... ,.,' + .y..... + ,, / .-¥--/ >"

2.2 2.6 3.0 3.4 3.8 .4.2 4.6

Log10 of P, Rated power in kw

r---r----r------r----r--,---.--r-r....----.------r--r---r--r- ,- .--.--,- T .. T I

.16 0.2 1.0 10 40


Figure 57. Draft tube exit area versus rated power for bulb turbine.

100-120 _j 2. I 100

N E s::

•r-N

E ro Q)

s:: s.. •r- c(

ro -+J Q) •r-s.. X c( LLJ

+-' Q) •r-X 20 .D

::I LLJ t-Q) +-' .D 4-::I ro t- s..

Cl +-' 4- 10 .. ro 0 s.. c(

Cl

\.0 -.....J

.. 4-

c(o

0

0 r-

C'l

4--l 0 _J

2

-0.4

, ,

-0.2

,' ,, ,,

,,

,

/ + //

k +tf¥'/ ++' + ~,~y

/ + + , .. -/ " + + 7/ / /

~ ~,,' + ,' ,' +

. /.,'' / / ,' / ++~/ + ,' /

,' ,,

,,' /

1'' +

,,'' / , _,¥~Ao = 2.868602.0047 ./+ ,,''_ //+ - (1953-1984)

/ r - 0.88 s = 19.92

,, ,' ,' ,'

0.0

+

0.2

No. of units = 53

0.4 0.6 0.8 Log10 of D, Turbine Diameter in meters

I I 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7


Figure 58. Draft tube exit area versus turbine diameter for bulb turbine.

1J) N

I

co ........ N (V)

0 I 0... L() (V) ('')

o:::t

II

0

II

(/)

0

II

II

.,....

4-0

0 z:

+.

/ I

·' I

//

,ll

I , I

I l I / + I

/. ....... ?' I ,'*:t

/ .. i·: I +,'

I I

I

+ / I

/+ l!t.-

1 +l

I I

.j.

I ...,

I /

I I ,

/ /

l/ , /

I

/ 1J) N

~ I

I I

I

I

~ 1J)

(S)

+

I sJa:).aw u~

1J) ,.... (S) I I

ea;v aJueJ1U3 au~qJnl JaAo qln~-j.O 4+6ua1 ,aV/>l j.O OL6ol I I I I I I I I I I I' I I I I I

1.0 NO CO 1.0 o:::t . . 0 0 0

N

0 0

98

.,.... SQ)

3: 0

0...

1J) -o (/') 2

IJ)

(\1

(S) . N

10 a::

0...

4-0

0 r-

Ol 0 --'

0 0 0 0 L()

0 0 0 0 N

0 0 0 0

0 0 0

0 0 .--

.,.... SQ)

3: 0

0...

-o Q) +J 10 a::

0...

(/)

Q) s:: .,....

..0 S:::s +l

..0 r-:::s

..0

So 4-

+-l :::s 0.. +l :::s 0

SQ) :;;: 0 c. -o Q) +l 10 S-

(/)

:::s (/)

SQ)

> 0

+l 10

• S-

Q)

c:l: -:::.::: (J) L()

Q) S:::s 0)

LL...

u Cll Vl

........ E 3

u Cll s:: Vl .,....

........ E >,

+-> s:: .,.... .,.... u

0

~ ,..... Cll 2 .,.... > u

0 Cll ,..... -· u Cll s:: > ttl

s... Cll +-> u s:: s:: LJ..J ttl s... Cll

+-> s:: s:: .,....

LJ..J ..Cl s...

Cll :::l s:: f-.,....

..Cl .. 1.0 s... Cll 1.0 :::l

f-> '+-.. 0

Cll > 0

0.5

0.5

0.4

0. I

-0. I , ....

2.2

~-..... .. .. /' .,..-'

~ + + ...... --~ it.--.. ~

+

~ .... ~ / + , .. ;§.+ "" .... _,.....

~----- ;:.--~--.... + ...... + \ + / ..... _,.....

~ ........ ~ ... ~----+

?' ,... + ....

~----- --------- --..... .,., ....... --~ ......

......... ,............ + ,.. ./ ,, , + ,.... _,......... ,.. ~

~

+

2.6 3.0 3.4 3.8

Ve = 0.2690P0.2254

(1953-1984)

r = 0.48 s = 0.50

No. of units = 31

4.2 4.6 Log 10 of P, Rated Power in kw

-r---r---....------,.----,----,--,-.,...-,-----,----,--.----r---r- ,.--,-, -.--,--"

.16 20.2 1 10 20 40 50


Figure 60. Turbine entrance velocity versus rated power for bulb turbines.

Fiqure 61 presents the relation of the velocity at turbine

entrance, Ve, to the turbine diameter, D and the resulting regression


ve = 1.0133 o0· 5043 Eq. (82)

Figure 62 presents the relation of the turbine entrance area,

Ae, to the rated turbine discharge, Q, and the resulting regression


A = 1 01 Q0.848 e . Eq. (83)


to the rated turbine discharge, Q, and the resulting regression


A = 0 5045 q0· 9743 0 . Eq. (84)

Table 6 summarizes all the regression relations that were develop-

ed for water passage dimensions of manufactured bulb turbines. In the

table are shown the equations that were developed, the regression cor-

relation coefficient, for each dependent parameter studied, the corres-

ponding standard deviation, the period of analysis for which the manu

factured turbines were designated for commissioning, and the number of

different units used in developing a particular relation.

Tubular Turbines

Insufficient manufacturer•s data on actual manufactured turbines

were obtained to develop a useful regression equation for tubular

turbines water passage dimension. However, information was obtained

from certain manufacturers that gave recommended relations between the

sizes of certain water passage locations and the diameters of the

propeller runners. Figure 64 gives the recommendations for preliminary

100

....... 0 .......

u Q) Ill

......... E

c: .,....

3.4

3

~ 2 .,.... g 1.8 '; 1. 6 >

~ 1.4 c: tO ~

.j-l c:

LLJ

Q) c: .,....

..0 ~ ::I 1-..

Q)

>

1.2

0.5

u Q) Ill

......... E

c: .,....

>, .j-l .,.... u 0 r-Q)

> Q) u c: tO ~

.j-l c:

LLJ

Q) c: .,....

..0 ~ ::I 1-..

Q)

> 4-0

0 r-

01 0 _l

0.5

0.4

0.3

0.2

0. I

-0. I

+ y /

/+

~ ++ ... + o&. ........ "'+ ....

/ ,,'~ / .......... /

/

,..,-¥ .... +

...... / .... .....

/

+ . ............... ' .. ~ .... -ft...... / ...... + .... .......

.......... '~+ / .... / +

/ ...... /

/ ..................... /.. ..... ve = l.Ol33D0

·5043

(1953-1984)

/ .... .... ........ r = 0. 38 s = 0. 55 ........ ..... +

.. .. .... , ..

-0.2

/ .... /

+ No. of Units = 31

+

0.0 0.2 0.4 0.6 0.8 Log

10 of D, Turbine Diameter in meters.

r-1 I 1 ~- I'

0.6 1 2 3 4 5 6


Figure 61. Turbine entrance velocity versus turbine diameter for bulb turbines.

1000 ----d 3.0 u Q) Vl -u 400 (V)

Q) E Vl 2.5 - c

(Y) .,... E

Q) c en .,... s...

ttl Q) ..s::: en 100 u 2.0 s... Vl ttl .,...

..s::: 60 0 u Vl Q) .,... 40 c

0 .,... ..CJ 1.5 Q) s...

c :::::! .,... 20 1-

..CJ s... -o :::::! Q) I- +-'

10 ttl 1.0 -o 0:: ..... Q)

0 +-' .. N ttl 0'

0:: 4-.. 0

0' 0 0.5 ....-

en 0

_J

0.0

Q = 0.9888A 1.1792 e

~t-~ / ~ .. 7 ;' * .,........ /

/ + .................. + ,.., / _ ...... /' + ......

,..-"" .. ...,. .. ~ ..... '"++ ...... ..... /

"1." ./ .............. ,. /

/--~ +_,----------~ + / // ... ,, .,.,, A = 1.01q0·8480 (1953-1984)

.,., ~, e / + ....

/ .......... r = 0.89 s = 20.20 ,.. /

.,., /........ / .,., .. " .... .... .... .... , .. ...... ./

No. of Units = 31

, /

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Log10 of Ae' Turbine Entrance Area in m2

1 - 1 I 1 --1 • 1 • 1 I 1 I 1 I 1 ~--.-· I 1 · · · · 1 I 1 I r·-T--T' T'l 1 5 10 20 40 60 80 100

Ae, Turbine Entrance Area in m2

Figure 62. Turbine entrance area versus rated turbine discharge for bulb turbines.

~

C> w

. u Q) Vl -C0 E

s:: •r-

Q) Ol s-10

..!:: u Vl .,....

Cl

Q) s::

•r-.0 s:::3

1-

'"0 Q)

+> 10

0:: .. c:r

1000 800

600 400

3.0

s:: 2.5 .,.... 200 _J Q)

Ol s-10

lOOi ~ 2.0 80 .,.... 60~ Cl

40

20

10

Q) s::

•r-.0 s:::3

1-

'"0 Q)

+> 10

0:: .. c:r 4-0

1.5

1.0

0 0.5 ,..... Ol 0 _J

0.0

........................

Q = 2.0183A

0

1.0264 + -~ ~: + ·;f;.-

~~ +""' ___ .. -!f.

~ . ____ .----+.f. __ i¥ +: ~

.... ¥ .........

~......... .. .............. ~ ......... _I_ .... + ~ .... ...

- ----=!=" .,. "" ..... ~ ...... + '* ............ ~ ...... .......

+ ------ ++ A _ __...---+ ..r o = o. so45Qo. 97 43

~ --; - (1953-1984)

r - 0.87 s = 23.39

No. of U . m ts = 53

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2. I

Log 10 of A0

, Draft Tube Exit Area in m2

'I I r T r'l1 I T rrl-- I T-----.- I I r-Ill I

4 6 8 1 0 20 50 1 00

A0

, Draft Tube Exit Area in m2

Figure 63. Draft tube exit area versus rated turbine discharge for bulb turbines.

Equation Dependent Number Parameter

70 (F + G)

...... 0 71 (F + G) .+::>

72 K

73 K

74 A e

75 A e

76 B

77 B

78 A 0

TABLE 6

SUMMARY LISTING OF REGRESSION INFORMATION AND EQUATIONS

RELATING TO WATER PASSAGE DIMENSIONS FOR BULB TURBINES

Regression Correlation Standard Sample Equation Coeffi c1 ent Deviation Period

(F + G) = 0.6744 p0•4188 0.82 11.80 1953-1984

(F + G) = 8.2075 o0•9801 0.95 3.31 1953-1984

K = 0.580 P0•3268 0.81 2.47 1953-1984

K = 3.1994 n°· 8744 O.RO 1.80 1953-1984

A = 0 1465 P0•6503 e • 0.79 20.39 1953-1984

A = 4.3951 0 1•7827 e 0.93 8.33 1953-1984

B = 0.1887 P0•3526 0.76 1.25 1953-1984

B = 1.1745 D0•9546 0.81 0. 71 1953-1984

A = 0.0978 P0•6846 0

0. 71 33.49 1953-1984

Number of Units

5

4

53

53

31

31

54

54

53

TABLE 6 CONTINUED

Equation Dependent Regression Correlation Standard Samp 1 e Number Number Parameter Equation Coefficient Oeviation Period of Units

79 A A0

= 2.8686 D2•0047 0.88 19.92 1953-1984 53 0

80 K/ A e

K/A = 4•335 p-0.3278 e 0.66 0.19 1953-1984 31

81 ve V = 0.2690 P0•2254 e 0.48 0.50 1953-1984 31

....... 0

ve = 1.0133 D0•5043 (.]1 82 ve 0.38 0.55 1953-1984 31

83 A Ae = 1.01 00.8480 0.89 20.20 1953-1984 31 e

84 A 0

Ao = 0.5045 00.9743 0.87 23.39 1953-1984 53

l 2.0 D

20 sq __ _j

STRA FL 0 Turbine

Draft Tube

' ' --

30 X*,'---~,',,/' __ _ 20Wide ~/C-

L ," --~"-

2.08 D Bulb Intake 8 Case

Bulb Turbine

2.0 D ' I. 4 D --ll---~- ---=----/ j_ _...JL__--L._/ __

Tubular Intake a Case

Tubular Turbine

Escher Wyss Turbines Allis-Chalmer Turbines

Figure 64. Dimensioning recommendations for low-head reaction turbines.

106

sizing of tubular turbines as suggested by Allis-Chalmers Corporation.

Figure 64 also gives similar recommendations for preliminary sizing of

tubular turbines as suggested by Escher-Wyss of Switzerland.

A few of the manufacturers have developed recommended dimensions

for standard tubular turbines and published these data. Copies of the

information was furnished to the U.S. Bureau of Reclamation. Table 7

gives the standard tubular recommendation information and the source

from which the data were taken. These respective tables of recommended

dimensions were used to develop experience curves relating water pass-

age dimensions for tubular turbines to the propeller diameter. The

information presented in each company's tubular material apparently was

developed by the companies from their own model tests. The water pass-

age dimensions Ae, Ao, L1, and M used in the regression equations

are defined on Figure 65.

Figure 66 presents the relation between turbine entrance area,

Ae, and the turbine diameter, 0, and the resulting regression equa-

tion for tubular turbines is given as:

A = 2.345 o1· 1067 e Eq. (85)

Figure 67 presents the relation between draft tube exit area,

A0 , and the turbine diameter, 0, and the resulting regression equa

tion for tubular turbines is given as:

Ao = 3.330 01.5605 Eq. (86)

Figure 68 presents the relation between the distance, L1, from

the runner blade centerline to the turbine entrance where, Ae, is

measured and the turbine diameter, 0, and the resulting regression

equation for tubular turbines is given as:

L1= 2.5408 o0· 1522 Eq. (87)

107

~

Table 7. REFERENCE INFORMATION AND SOURCE FOR STANDARD TUBULAR TURBINE WATER PASSAGE DIMENSIONS

Company Address Publication Title Publication Code No. Page Allis-Chalmers Hydro-Turbine Div. 11 Stnadardized Hydroelectric 54Bl241-03 6

Tampella-Leffel

Neyri pic

Kvaerner Moss

York, PA Generating Units ..

426 East Street 11 Standard Tubular Turbines .. Springfield, OH

Box 3834 969 High Ridge Rd. Stamford, CT

800 Third Ave. New York, NY

11 Standardized Hydroelectic Turbine for Low Heads ..

11 Mini Hydro Turbines 11

S~rumsand Verstsad A/S N-1920 S~rumsand, Norway

None

None

None

Other Standard Turbine Literature with Dimensioning but not Used in the Study.

None

None

8

~ Barber Hydraulic Barber Point, 11 Standard Turbine Arrangement SHOB No. 5 No. 511 Single Horizontal Box 346, Port -

Colborne, Ontario Canada, L3K 5Wl

Open Bulkhead

This is not a true tubular turbine, it has spiral casing for entrance.

Bell Engineering Escher Wyss

KMW

Sulzer Bros. Inc. 11 Standard S-turbines .. Western District

Office 1255 Post St. Suite 911 San Francisco

Fach S-68101 11 KMW Miniturbines 11

Kristinehamn, Sweden

1978

None None

Tl78-E

...... 0 1.0

H.W =

..... ·:-:··: ;·;:..~;

~~~

~.!I .:-:J.' . .,.';::; v T.W .

. -t

1- L1 M,,··:.

· .. ;: ........ ..I • c. • _.........._

~----- L--

Fi~ure 65. Schematic drawing defining dimensions used in study of standard tubular turbines.

----. I I I I I I I I T

0.3 0.4 0.6 0.8 1 2 3

0, Turbine Diameter in Meter

Figure 66. Turbine entrance area versus turbine diameter for standard tubular turbines.

• •

60

40 N

E

s:: .,.... ~ 20 (I) ~

<:::(

+-' .,.... 10 X UJ

(I) 8 ..0 ::I I- 6 +-> 4-~ 4 ~

Cl ~ ~ ~

" .:::(0

2

1

0.5

•

N E

s:: .,....

~ (I) ~

<:::(

+-' .,.... X

UJ

t.8

t.S

t.2

(I) ..0 ::I I-+' 8.9 4-~ ~ Cl

0 <:::(

4-0

0 ,..... C'l 0 _l

..

-8.5

...

• /

/

-8.3

-

/ /

/. •

•

// /

-8.'

~-

/. • ///:· •

/ /

•

/ /

// . / ..... . ~~A_ = 3.330D1 ·5605 (1953-1984)

0

r = 0. 51 s = 7.97

No. of Units = 34

0. 1 8.3 e.s Log10 of D, Turbine Diameter in Meters

r---r---r----r---r---r--..----.r-r-,.....,..--r--.r-r-----,----~-----.---,--- r

0.4 0.6 0.8 1 2 3

D, Turbine Diameter in Meters

Figure 67. Draft tube exit area versus turbine diameter for standard tubular turbines.

8 (!)

0 s:: -1-l .,.....

..0 (!) s... s:: ;:;;, ,_ .... ,_ s... 0 (!) -1-l 5 -1-l

s:: (!) (!) s:: u ,_

,.._ • (!) s... 4 "0 (!) lt1 -1-l • ,_ s:: co (!) • u s...

(!) (!) ':> s:: "0 '"' s:: lt1 ;;:s ,.._ ~ co

• • • _...,. -..-.

E s... 0 <ZJ s... ....... s:: If.-....... s:: 1'\) ;;:s V) 2 .J:: ~ s... -1-l

(!) 0) E ..., s:: (!) 0 .s! (!) u s... -J s:: 4- .....

.J:: s:: .. ~8.2 . ,..... ,.._ ...., -1-l -./ s:: 0) (!)

4.1 s:: u 4-(!) s:: 0 (1)8 ' -./ lt1 o.~ • s... .. ...., ,.._..0 -s:: 0) s... -J 4.1 0 ;:;;,

-J ,_8 8 ·..,_,

• • • •

• • •

• •

• • ••• • • •

• • •

• • • • . ..___.. • • • •

•

LJ ~ 2.S4Joo. 1s22 •

r ~ 0.06 s ~ 1. 02

-e.s -8.3 -e.'

8. t 8.3

e.s 0.3 0.4

Log10

of D, Turbine Diameter in Meters.

0.6 0.8 7.o


Figure 68. LeniJth from runner blade centerline to turbine entrance versus turb1ne dJameter for tubular turbines .

2 3

• .. .... ,.... . ._ -

•

•

•

•

•

•

•

•

'

Figure 69 presents the relation between the distance, M, from the

runner blade centerline to the draft tube exit where A0 is measured,

and the turbine diameter, 0, and the resulting regression equation for

tubular turbines is given as:

M = 5.939 o0· 5560 Eq. (88)

Table 8 summarizes the regression information and equations devel-

oped for relating water passage dimensions to the turbine diameter for

standard tubular turbines .

The actual data used in this regression analysis of standard tubu

lar turbines is presented in the Appendix 3.

Cross-Flow Turbines

No information was obtained on sizes of water passage dimensions

for cross-flow turbines .

ANALYSIS AND USE OF RESULTS

The basic purpose of the research was to present simplified

methods for making preliminary selection of diameter and speed of low

head turbines. A review of the work of Lindestrom (no date) of the

Swedish firm KMW presented a simplified nomograph for making that

selection. Figure 70 is a reproduction of the nomograph from

Lindestron (no date) for bulb turbines. Because the basic parameters

used were the same as those involved in the regression developed as

Eqs. (24) and {25) that is D = F {P/H), it was simple to construct a

similar nomograph from the regression equations developed on this pro-

ject. To check the validity of the KMW nomograph, the basic data for

bulb turbines manufactured by only KMW were subjected to a seperate

regression analysis the same as with all the bulb units. Table 9

113

16 ~ 4- 14 <0 s...

Cl

0 12 ~

(l) 10 s:: ·.--..- 9 s... (l) ~ 8 s:: (l)

u 7 (l)

"0 <0 6 ..-

co s... 5 (l) S::Vl s::s... ::I (l)

0::: ~ (l) 4

t-' E~ .... ~ 0 ~ s... s::

4- ·.--

..c ~ ~ ·.--c:nx 3 s:: w.J (l) _,J(l)

..0 .. ::I

~~--

s... (l) s:: s:: ::I

0:::

..c ~ c:n s:: (l)

_,J

.. .."'-

4-0

Ill s... (l)

~ (l)

~

s:: ..... ~ ..... X

w.J

(l) ..0 ::I

1-

0~ ..- 4-

c:n <0 0 s...

_,J 0

1.2

1.1

1.0

9.9

0.7 //

-e.s -0.3

• //

/ .//. /

/

M- 5.J

• / / .

• • ••

(1953-1984) /~ - 039D0.5560

r = 0.54 s = 2.35

No. of Units = 35

-e. 1 e. 1 0.3 e.s

Log10 of D, Turbine Diameter in Meters ~--,- -,--.-T-.--,-T -1-r 1-, T 'T-- ---~-- ----.--~~-,

0.3 0.4 0.5 0.6 .7 .8 .9 1 2 3


/

Figure 69. Length from runner blade centerline to draft tube exit versus turbine diameter for standard tubular turbines.

- • •

Equation Number

85

......

...... 86 <.Tl

87

88

TABLE 8


RELATING TO WATER PASSAGE DIMENSIONS FOR STANOARO TUBULAR TURBINES

Dependent Regression Correlation Standard Samp 1 e Parameter Equation Coefficient Deviation Period

A A = 2.345 o1•1067 0.24 7.81 e e

A - 3 330 D1•5605 A 0.51 7.97 0 0- 0

L1 L1 = 2.5408 D0•1522 0.06 1.02

M M = 5.939 D0•5560 0.54 2.35

- - -

Number of Units

45

34

45

35

E c ·-"0 0 Q) L;

"0 Q)

0 a::

25~------~--------~------~--------,--------.-------~

20

15

10

10 20 30 40 50

Rated power output in M W

Fi0ure 70. Reorod1.·ction of KtivJ nomot;Jraph for selection of turbine dia~eter and turbine speed. for bulb turbines.

116

Equation Dependent Number Parameter

Ns ...... ...... -....1

• ~

D

D

D

N

N

CT

rr

TABLE 9


FOR SPECIAL CASE OF MANUFACTURED KMW BULB TURBINES

Regression Correlation Standard Equation Coefficient Deviation

N = 1553.445 H-0•2918 s 0.50 112.23

~ = 0.1660 N°· 3728 s 0.86 0.07

~ = 0.9205 p1~.2522 0.65 0.10

D = 0.2917 ~3 • 8367 0.52 1.00

D = 0.1763 (P/H) 0•4489 0.97 0.48

D = 4.1604 (Q/N) 0•3064 0.99 0.64

N = 3583.987 (P/H)-0•4833 0.78 104.66

N = 164.706 (JH/0) 0•8876 0.99 5.58

~= 1.786 X 10-5 N 1•7023 s 0.60 0.61

CT = o.422 o11 1.5486

0.64 0.64

Samp 1 e Number Period of Units

1959-1984 25

1959-1984 25

1959-1984 25

1959-1984 26

1959-1984 25

1959-1984 26

1959-1984 25

1959-1984 26

1959-1984 24

1959-1984 24

presents the summary of the results of that special regression analysis

of KMW manufactured bulb units, giving the empirical equation, correla-

tion coefficient, standard deviation, sample period and the number of

units involved. A check of using the regression from the authors

special study confirmed the individual curves of the nomograph that had

been presented in Lindestrom (no date).

Figure 71 gives a nomograph for estimating bulb turbine diameters

based on rated head and rated power output. This nomograph was devel

oped by using the regression equation, Eq. 25. A similar nomograph for

tubular turbines is presented in Figure 72 which utilizes regression

equation, Eq. 41. The corresponding nomograph for cross-flow turbines

is presented in Figure 73 which utilizes regression equation, Eq. 57.

An estimation of turbine speed can be made in several ways. One

way is to use the same parameters of rated head and rated power output

as used for bulb turbines the regression equation, Eq. 27. Another

method is to use the estimated diameter as found from the nomograph

Figure 71 or Eq. 25 and substitute that in regression equation, Eq.

26. An additional approach is to take the estimated diameter as found

from nomograph Figure 71 or Eq. 25 and substitute that value of dia-

meter into the regression equation, Eq. 30.

The more conventional approach for estimating turbine diameter and

speed has been that explained in U.S.B.R. Monograph No. 20 and is to

first find a trial value of specific speed, Ns, from a curve like

Figure 3. Then proceed to find a trial speed, N', from the specific

speed equation.

Ns = Nrp

From Eq. (4) H 1.25

118

-E -0 <t LLJ :I:

...... ...... \0

30------~----~----~----~------r-----~~~

251 I I I I ~ - ~ ·- -

E1 0

,I (\J II

20. .o

E It)

15

10

5 Ill I I , I / ./ /j,........ ,r I I I I I r 7 ~7 7'~

0 0

Figure 71 .

10 20 30 40 ~ 60 70 POWER (MW)

t~omograph for estimating turbine dia~eter from rated head and rated power output for bulb turbines.

Ill s.... Q)

+' Q)

E

c: ..... ..... :::X: N 0 "' -o

~ Q)

:::X:

25

20

15

10

E

0

C'\J

II

Cl

.--~------y-·----~-

I I

i --t- ---- -----+ I I I

- --- -------

5 I I I t I --J/'7/~:If''-77,c..'-------,--+------+------+------l--------l

04r------~r-------~--------~-------+--------+-------~ 0 10 20 30 40 50

Power, P in t~W

Figure 72. Nomograph for estimating turbine diameter from rated head and rated power output for tubular turbines.

60

-E -Q

<t w I

...... N ......

30~.------..-----~--------~--~--~------~--------~------~--------~------~

25 I

E ~

0 II

Q . 20

15

10

I

I ------r ----

~r-i

t- --+--------+- / I .

: _ _j i-

1

o~~~--~------~------+-------4-------+-------+-------+-------4-------~ 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

POWER ( MW) ., Figure 73. Nomograph for estimating turbine diameter from rated head and rated power output

for cross-flow turbines.

A synchronous speed must then be chosen utilizing the relation. 120 X f Np =

where Np = number of generator poles

f = electrical frequency in Hz.

Eq. (89)

The number of poles, Np, must be in multiples of two or four, usually

in multiples of four. Once a synchronous speed is chosen then the

actual specific speed, Ns, is calculated using, Eq. 4. The next step

is to use the actual, Ns, in an empirical equation to determine the

speed ratio, 0. For bulb turbines this would utilize regression

equation, Eq. 18. For propeller units the U.S. Bureau of Reclamation

Monograph No. 20 (1976) gives the following:

0 = 0.0233 Ns 213 Eq. (90)

As a final step the estimated turbine diameter can be determined using

selected turbine speed, N, the rated head, H, and the empirically

determined value of speed ratio, 0, in the following form of the speed-

ratio equation: Ho.s

D = 84 . 58 0 -- E q . ( 91 ) N

This equation comes from the basic definition of speed ratio. To

illustrate the procedure for this selection process for estimating tur-

bine diameter and turbine speed sample calculations have been presented

in the Appendix. The sample calculations have been performed for a

manufactured unit at a plant in Europe known as Isawerk 3.

Additional comments are presented on the advantages of different

approaches to diameter estimation following a presentation of compar-

isons.

122

COMPARISONS

With the various different regression that were performed it is

informative to make a few simple comparisons. Figure 74 is a compari-

son of several different experience curves relating specific speed,

Ns, to the rated head, H, for different kinds of low-head turbines

studies on this project as well as results from other published stud-

ies. The curves include two experience curves taken from the Figure 11

of the U.S. Bureau of Reclamation Monograph No. 20 (1976), the work of

de Siervo and de Leva (1977), the work of Lindestrom (no·date), and the

experience curves for the three different types of turbines (bulb,

tubular, and cross-flow turbines) studied on this project. Table 10

summarizes the information on the specific speed versus rated head

relations for low-head type turbines.

Because the U.S. Bureau of Reclamation Monograph 20 gives an

empirical equation relating the speed ratio, 0, to the specific speed,

Ns, that is used in preliminary speed and diameter selection a com

parison was made with similar relations developed in this study.

Figure 75 shows this comparison. The data gathered on this project

were used to develop a regression equation with the same exponential

power of the Ns as was reported in the U.S.S.R. Monograph 20, that

is, Ns raised to two thirds power. The regression equations for the

different types of turbines developed are indicated below:

0 = 0.6374 + 0 164 N 213 (Bulb) Eq. . s

0 = 0.2036 + 0 0227 N 213 (Tubular) Eq. . s

0 = 0.4356 + 0 0026 N 213 (Cross-flow) Eq. . s

It should be noted that the plotting of Equation 19 developed by

Kpordze-Warnick for bulb turbines shows a slight deviation from

123

{92)

(93)

(94)

"0 Q.l Q.l a.

I 000 -f--L-.~:::-t-'----.1-~:-f~'--t---t--------'-- - 0. 283 7 ---'------l N5 = 1520.26 H

800 Bulb (Kpordze-Warnick)

-0.48 N5 = 2419 H

Ka plan(de Siervo-600+--+~--~-~~---++-~+-~~~~~-----~-- de eva

N5=1107.303 H-0

·299

.....t--+----,11---1-- Ns= 2088 H-0.5

Propeller (USSR)

(/) 400 Tubular (Kpordze -Warnick)

u -·u Q.l

a. 300 (/)

en z

200

5 6 8

----1------Ns = 513.85 H-

0.505

10

Cross- flow (Kpordze)

15 20

H - Rated Head (meters)

Figure 74. Comparison of experience curves of specific speed versus rated head for different types of low-head turbines.

124

TABLE 10. COMPARISON INFORMATION OF REGRESSION EQUATIONS FOR N \/ERSUS H s FOR DIFFERENT TYPES OF LOW~HEAD TYPE TURBINES

Type of Regression Correlation Standard Number Period of Turbine Eguation Coefficient Deviation of Units Manufacture Authors

Propeller N = 2702H-0· 5 --- --- --- prior to 1976 U.S.B.R. s Propeller N = 2088H-0· 5 --- --- --- prior to 1976 U.S.B.R. s Kaplan N = 2419H-0·489

s 0.89 47.6 N.A. 1970-76 de Siervo

Bulb N = 1520.256H-0· 2837 0.40 118.24 119 1971-84 Kpordze-Warnick s Tubular N

5 = 1107.303H-0' 2998

0.62 92.71 54 1957-84 Kpordze-Warnick

' N = 513.846H- 0· 5047 1-' Cross-flow 0. 79 36.89 17 1966-82 Kpordze-Warni ck N (J1 s

Kaplan *N = 2400H-0. 5 ---s --- --- N.A. Lindestrom

*Median line as interpolated from Fig. 11 of report by Lindestrom

-e-~

0 •r-+-' ttl

....... 0::: I'V 0"1 " QJ

QJ c.

V>

4.0

3.5

3.0

2.5

2.0

1.5

1.4

1.2

f- ----· ----- ---

-!----··--

--

------=~ . /<P = 0.0389N °· 6013 Tubular -s , f-------- --+- d Kpordze-Warnick (1983) ~,.. f-· . --- an 2/3 ~;. / f----- <P = 0.2306+0.0277N _,....v .,/ - . s .7/ v ~

. \ / _,. _,... -~ ... \ ,--,<..-/ ~

1- "' / .,./ ~ =---~c--<P = 0.6374+0.164N;/3 Bulb -~ ,...-P/;_._ ... ;~ 1-t-

Kpordze-Warnick (1983) ~_,... L""~ /~~ / = /_:::.~/... <P = 0.0944N °· 4605

Bulb ----: ""' ~v s -~ ~: ........ ~ Kpordze-Warnick (1983)_

/1~ ± ~ -~~--- .... \......--~ -.~"/ _ .....

~~- /~ - ---v-.-? L?-- • = a. 79+1.61Xl0-3

Ns Kaplan

/ de Siervo (1978)

~- = 0.0233N 213 Propeller U.S.B~R. (1976)

~ -- r l.O

400 500 r-~~-~ 600 700 800

-- ---

900 1000 1100 1200 1300 1400

Specific Speed, N5

Figure 75. Comparison of experience curves of speed ratio versus specific speed for different types of axial-flow turbines.

Equation 92 at the two extremities of the plotted lines. The Kpordze

Warnick form of the relationship plots as a straight line on logarith

mic paper and has Ns raised to the exponential power value of 0.4605.

The correlation coefficient is slightly better for the Kpordze-Warnick

form than with the Ns raised to the two-thirds power. There is

essentially the same margin of error in the two forms of the equation

as indicated by the values of the standard deviation found in the

development of the two equations.

The plotting of Equation 38 developed by Kpordze-Warnick for tubu

lar turbine and the Equation 93 utilizing Ns raised to the two thirds

power for tubular turbine are so nearly the same it is not possible to

distinguish between the two lines on the scale shown in Figure 75.

Brief trial comparisons of using these different experience curves

shown in Figure 75 would indicate that in the middle range of situa

tions calling for turbine selection for Ns in the range from 700 to

900, reasonably similar results can be expected using de Siervo empiri

cal relations, the U.S.B.R. empirical equation for propeller units, and

the empirical equations for bulb turbine units developed in this study.

In ranges of Ns values outside the range 700 to 900 traditional

empirical equations should not give good results.

An additional comparison was made of the regression analysis

involving the plant sigma, a, and the specific speed, Ns. Figure 76

gives the comparison that includes a versus Ns for bulb turbines, a

versus Ns for tubular turbines and a reproduction of a KMW relation

between a versus Ns for all turbines manufactured by that company,

Lindestrom (no date). Plotted on Figure 76 is the empirical equation

for a versus Ns as taken from U.S. Bureau of Reclamation Monograph

20 (1976).

127

3.0

2.5

2.0

0

1.5

")

cu E 01 ...... l/1

+-' s::: cu

0...

1.0

0.9

0.8

0.7

0.6

0.3 450

=

o = 7.625Xl0- 5Ns 1· 485

Bulb turbines Kpordze-Warnick (1983)

3.987Xl0- 5Ns1 · 579

Tubular turbines Kpordze-Warnick (1983) Curve B (All units)

31. lOXl0- 5Ns 1· 242

Tubular turbines Kpordze-Warnick (1983)

· Curve A (No American Units)

= N 1· 64 All turbines s 50372 U.S.B.R. (1976)

I

= 11 X 1 0- 5h l . ~ All turbines KMW ( 1981 )

500 600 700 800 900 1000

Specific Speed, N s

Figurf 76. Comparative of experience curves of plant sigma versus specific speed for different low-head turbines.

128

The comparison shown in Figure 76 includes a stratification of

tubular turbine data (Curves A and Curves B) of those tubular turbine

manufactured outside the United States. The o versus Ns curve for

just the units manufactured outside the United States (Curve A) does

show that lower values of 0 will be predicted for corresponding values

of Ns. Curve B is for all tubular turbines studied including Ameri

can manufactured units and some European units and a few Japanese

units. This indicates that if units are submerged below tailwater (as

they usually are for bulb and tubular turbines) greater submergence has

been required on American manufactured tubular turbines. Likewise, it

would indicate that the experience curves show bulb turbines have been

submerged less than tubular units.

Review of an article by Khanna and Bansal (1979) revealed an

experience curve relating plant sigma, o, to the unit discharge,·

Q11, for bulb turbines. With the regression analyses performed on

this project involving the plant sigma, o, and the unit discharge,

Q11, for bulb turbines, Eq. 66 and for tubular turbines Eq. 68 it

was possible to make a comparison. The comparison is shown in Figure

77.

The equation listed for the reproduction of experience curves from

Khanna and Bansal (1979) were developed using curve fitting by the

authors of this report. The work of Khanna and Bansal (1979) also

included an experience curve for Kaplan turbines. It has also been

reproduced on Figure 77 for comparison purposes.

An analysis for comparative purposes was made of the characteris

tics of the draft tube exit velocities of 54 bulb units for which data

were available. Purdy (1979) reported that the exit velocity should

129

'o

0

E 0' ·-(/)

+-c 0

a..

10

8

6

4

2

---- --+- ----- -- ·--·-

I I

6 = 0.3074 0~'066------Tubular turbine data

1---1--- -·-f---- -

!A If/ /

/'..(_

-- --

v 6 = 0.4220 01.5486

II

{ KMW

I I ~

~I /; / b?

I / // w <J = o.575o o/i 1937 /: CJ: ~/ Bulb turbine data-

y} -~c--/ .._ c = o.432 o,:-286 --

I Bulb turbine - Khana

I 1.0

I ~ - 6 = o. 397 o:j503 ----~ -- -t--- -/It/ ----

=~~=r-~~ Kaplan turbine - Khana

0.8

0.6

0.4

0.2

0.1 0.1

71!' --

r-- -- -

JJ 1------ --vv ~L __ ·---------f-- 0 ---1----

1/// - ------

/ v/ 'I'

I 0 Q---11- 02 H0.5

0.2 0.4 0.6 OB 1.0 2 4 6 8 10 20

Unit Discharge, Q11

Figure 77. Comparison of experience curves for plant sigmaversus unit discharge for different low-head turbines.

130

not exceed 0.8 IRifor rated heads, H, of low-head turbines up to 17m.

Table 11 shows how exit velocity compares with the value of 0.8 IH for

each turbine. The recommendation of Purdy was based on the fact that

if higher velocities were permitted considerable power was lost but not

often considered in the real overall performance. This comparison

shows that many of the manufactured turbines have exit velocities that

exceed the Purdy recommendations.

To assess the difference that might be expected in using different

methods of estimating turbine diameter and turbine speed a comparative

study was made of eight hydro power plants that had data on rated head,

rated discharge, and rated power output. The data on the eight plants

also included the actual manufactured diameter and actual turbine speed

used at each plant. Five different methods were used in the assess

ment: (1) using the traditional approach as presented in U.S. Bureau of

Reclamation Monograph No. 20 for propeller turbines, (2) using the

regression equations developed by de Siervo and de Leva (1977 and 1978)

for Kaplan turbines, (3) using the nomograph from Lindestrom (no date),

(4) using the regression equation developed in the special study of KMW

manufactured units, and (5) using the regression relations developed in

this study using all the bulb turbines. Sample calculations showing

how the comparative numerical values for turbine diameter, D, and tur

bine speed, N, were obtained are presented in the Appendix 2. Table 12

presents the results of the assessment.

The results would indicate that the simplified selection procedures

suggested by the authors of this report have several advantages. The

procedures are simple and require only two parameters, rated head and

rated power, that are normally available early in feasibility studies.

A review and comparison of the correlation coefficients of the various

131

Table ll· COMpARISON OF DRAFT TUBE EXIT VELOCITY WITH PURDY'S RECOMMENDED LIMIT FOR r~NUFACTURED BULB TURBINES

CBS

1 2 3 4 5 6 7 !l 9

10 11 12 13 14 15 16 17 18 19 20 2l 22 23 24 25 26 27 28 29 30 31 32 33 J4 35 36 J1 38 3'7 40 41 42 43 44 45 46 47 48 49 5J 51 52 53 54

STATION

URSTEIN Al TEN wORTH ABWI~OEN-AS

ABWI NDEi~-AS MELK GREIFENSTEI Kl E 11\MUH.CHE N MA J I TANG ANKKAPURHA VAJUKGSKI ARGENT AT ARGENT AT LA RA~CE

ABZAC MARCKCLSHEIM RABUOANGES RHINAU GERSTHEIM GERS THF. IM STRASBOURG FANKEL MUDEN LEHMEN URSPRING SYLVENSTE IN LECHSTUFE20 GOTTFRIEOIII;G kEHllNGEN SCHOO EN SAN PEDRC GAo'olL EBRCt- GSS uUV I KFCSS SKOGSFORSEN HALLEFORS SPERL INGSHOUI PAKKI dGOUM LANOAFORS ASHE SOOEKFORS JUVELN TGRRG~

NASI AVESTAMATFCRS LILLA EuET 4 1\A$2 GkA,'IjtJUFCRSE:I\ wl/.ZrJAL TASJL hCT I :-1G VIFCRSEr\ IJAHC F"LLS PELTLN ~EREG.

MANU- YEAR CF FACTURER COMMIS

SIGNING

v v v VA v VA VA v TAM TAM v-c v-c v-c v-c v-c v-c v-c. v-c v-c v-c v v v v v v v v v v-c KMioo K(IIW KMie KMioo KM\o KMio KI"W KMioi KM~~o

KMioo KMW K,..w KMioo KM\oo

Kl"loo KMW J(o\ollo K/olloo v-c TAl" TAM TAM VA VA

1969 1976 1979 1979 1982 1984 1978 1984 1983 1984 1957 1958 1966 1958 1957 1959 1960

132

1967 1968 1970 1S62 1962 1966 1963 1960 1<;84 1977 1984 1984 1<;82 1HO 1975 1959 1<;66 196 7 1970 1975 19 76 1981 1979 1978 1978 1979 1982

1982 198() 1'180 1'JU 1978 1978 1982 1981 1982

DRAFT TUBE EXIT VELOCITY

lM/SECI

1. 7C905 2.44459 2.314~1

2.20013 2.44459 2..852u2 2.153~3

2.3u004 6.19493 6.C56::2 1.95942 2.95316 3.00220 2.57576 2. 33766 1.75520 1.25893 2.99847 1.14943 3.28240 1.20957 1.20957 1.20957 1.60643 2.02<;22 1.30782 1.50693 1.52827 1.52927 2.42915 2.04082 3.06122 1.61111 1. 73442 1.93798 2.12J94 2.24775 2.59259 2.90276 1.92157 2.381)95 2.39756 2.3101>3 2.24618 2.48830 2.24359 2.31063 .2.21017 1.16667 5.955£2 6.24527 5.67752 1.15272 2.34872

PURDY SUGGESTED VELOCITY

2.64121 2.<1<1333 2.25708 2.29085 2.29085 2.67731 2.71293 2.04900 2.50440 3.09839 3.25945 3.3370t 1.92666 1.18659 2. 46577 1.95959. 2.10143 2.66533 2.40000 2. 73057 1.6l98e 1.61988 1.84174 2.27684 ).86988 2.452 75 1.95~59 2.2C545 1.91)997 2.5044G 3.00400 1.93494 2.99333 2.19089 1.53883 2.65330 2.03961 1.1!4174 2.54244 1.69706 2.65330 3.48712 1.32428 1.84174 2.45927 2.03<161 1.P2428 1.95<159 1.137617 2. 77128 2.57992 2.16148 1.87617 2.6C46l

...... w w

Name of Plant

Parameters

Actual Parameter Values

USBR Equation N = 2702H-O.S s <1> = 0.0233N~/J

D = 84.47<t>HO:S/N

deSiervo Equations N = 2419H- 0·489 ~ -3 ~ = 0.79+1.61Xl0 Ns D = 84.5<t>HO.S/N

KMW Graph KMW Equations D = F(P/H) D = F(Q/N)

N = 1553 495H-0· 2918 ~- . <I>= 0.166N0.3728

s D = 84.6<t>HOlS/N N = F{P/H) N = F(N ) s N = F ( v'H/D)

K-W Equations D = F(P/H) D = F{Q/N)

N = 1520.256H-0· 2837 s ~ = 0.0944N~· 4605

U = 84.6),;H"fN N = {P/H N = (Q/N) N = (,·'R/D)

TABLE 12. COMPARATIVE RESULTS OF DIFFERENT METHODS OF ESTIMATING TURBINE DIAMETER AND TURBINE SPEED

llt!' (~c)'"' U~>

(F~~i) ~ 1-U: .... IIIIIt:'

El!) ,., .... , (N) v> ' .. (AC) KMW) lsawerk 3 G h . Brashereidf Koid Cak Lechstufe 20 Idaho Fall Lach· Granbof

D(m) N(rpm) D(m) N(rpm) D(m) N(rpm) D(m) ~(rpm) D(m) N(rpm) ~(m) N(rpm) D(m) ~(rpm) D(m) N(rpm) D(m) N(rpm)

2.45 157 1.60 333.33 5.80 88.20 3.40 150 5.40 125 12.85 176.50 4.85 94.70 6.90 93.80 5.80 75

2.01 2!i0 l. 36 375 5.83 93.75 3.03 187.5 5.33 115.38 2.50 214.29 4. 77 106.52 6.52 88.24 6.16 88.33

2:19 214.29 l. 41 375 6.14 88.24 3.15 187.5 5.81 107.14 2.58 214.29 5.00 100.00 7.02 78.95 6.56 75.00

- 200.00 - - 5.91 91.76 3.23 194 5.71 128.20 - - 5.14 86.36 6.57 98.92 6.39 70.71

2.17 1. 53 5.83 3.30 5.67 2.70 4.71 6.59 5.95 2.23 1.22 5.86 3.41 5.14 2.62 5.04 6.73 5.87

2.08 1.36 5.89 3.12 5.47 2.50 4.82 6.31 6.18

250 299.41 83.33 150 93.75 187.5 107.14 71.43 83.33

187.5 375.00 88.24 187.5 125.00 214.29 88.24 83.33 71 .43

166.7 375.00 93.75 187.5 125.00 187.50 88.24 88.24 75.00

2.21 l. 57 5.91 3.36 5.75 2.75 4.78 6.67 6.03 2.30 1.47 6.07 3.40 5.21 2.59 5.10 6.88 5.98

2.16 1.39 6.03 3.16 5.50 2.53 5.0 6.82 6.40 214.3 300.00 88.23 150 89.24 187.50 107.14 83.33 250. 375.00 88.24 150 125.00 214.29 88.24 83.33

166.7 300.00 88.24 187.5 125.00 187.50 106.52 88.24

regression equations used in the selection prodecures is revealing.

Table 13 shows the various regression relations used and the value of

the correlation coefficient for each relation for the various different

kinds of low-head turbines. This shows that for the functions

involving D = F(P/H), and N = F(IHI) the regression correlation D

coefficients are higher than the functions involving Ns and 0. The

author's suggested approach to estimation of turbine diameter and tur-

bine speed appears to give greater accuracy and consistency.

CONCLUSIONS AND RECOMMENDATIONS

This study of experience curves has collected data on rated head,

rated discharge, rated power output, turbine speed, and turbine dia-

meter on more than 300 manufactured low-head turbines produced through-

out the world since 1953. Additional information on turbine water

passage dimensions and on particular characteristic sizes of turbine

intakes and draft tube exits has been compiled. The data have been

subjected to an intensive mathematical analysis by regression techni-

ques in an attempt to develop useful predictive methods for feasibility

and preliminary design purposes. The following conclusions are made.

The information on rated head, rated discharge, rated power out

put, turbine speed and turbine diameter along with water passage dimen

sions has been catalogued in a convenient computer format (see Appendix

3). The catalogue in itself should be a valuable reference from which

comparisons could be made when choosing preliminary features of turbine

installations for a new hydro power sites.

A comprehensive collection of experience curves for the conven-

tional turbine constants and turbine selection approaches has been

developed for bulb turbines, tubular turbines and cross-flow turbines.

134

-

....... w U1

- - ....

Table 13. Comparison of value of correlation coefficients for the important regression equations.

Number of Units

Regression Relation

Ns vs H

¢ VS NS

D vs P/H

D vs Q/N

N vs P/H

N vs Ar o

Separate Study of

KMW Turbines

26

0.50

0.86

0.97

0.99

0. 77

0.99

Bulb Turbines

150

Tubular Turbines

28

Rim-Generator Turbines

-

Values of Correlation Coefficient

0.40 0.52 -

0.86 0.82 -

0.98 0.96 -

0.99 0.96 -

0.76 0.69 -

0.97 0.96 -

Cross-flow Turbines

17 ,

0.79

0.06

0.89

0.84

0.79

0.98

The experience curves have been developed using conventional hydro

power terms and turbine constants that have been applied to Kaplan tur

bines, Francis turbines and Pelton turbines of the impulse type. The

results have been presented in easy-to-use equation form and are also

presented graphically to show the scatter of the data in the various

relations that were developed.

The results of the study of cavitation characteristics of low-head

turbines using the relation between plant sigma, a, and specific

speed, Ns, did not show as good a correlation as expected. There is

considerable variation in the relation between plant sigma and specific

speed from company to company and the correlation coefficients of the

regression are not very high. Caution should be used in applying the

experience curves of plant sigma versus specific speed developed in

this study. Because the use of this cavitation coefficient in turbine

setting elevation determination is highly dependent on cost of excava

tion for the draft tube this becomes a difficult item to make authori

tative guidelines for preliminary design purposes.

The results of the study of dimensions of water passage, and their

relation to turbine diameter are reasonably good for the bulb turbines.

Insufficient data were obtained on tubular turbines to make regression

analysis of relations between turbine diameter and water passage dimen

sions. However, the latest recommendation of manufacturers with regard

to sizing water passages has been catalogued and presented in a useful

form for tubular turbines.

A significant and very simplified procedure for estimating turbine

runner diameter and turbine speed has been developed. This new proced

ure was tested and compared with the procedure presented in the

136

U.S.B.R. Monograph No. 20 and with other approaches. Results of the

comparison shown in Table 12 indicates that the new simplified proce-

dures give more consistent estimates of turbine diameter and speed than

other methods and are easier to apply using data that are readily

available early in the planning stage of a hydropower investigation. A

careful documentation of steps in the selection process for estimation

of turbine diameter and turbine speed has been presented in sample cal-

culations shown in Appendix 2.

Because these regression equations developed in this study are

from a much larger sampling of manufactured units that was used in

development of the empirical equations in U.S.B.R. Monograph No. 20 and I

because the study is for specific types of low-head turbines, the

empirical equations developed in this study should be relied on more

than using the older more traditional equations. It should always be

remembered that final design and confirmation of size of runner and

runner speed should be worked out with the individual manufacturers and

the· estimation developed from experience curves should be used as a

check on manufacturers recommendations.

In general good response from turbine manufacturers was obtained

but no data were obtained from Chinese and Indian manufacturers and

only limited data were obtained from Japanese firms.

Recommendations

The writers recommend that this information be incorporated in a

revised edition of the U.S. Bureau of Reclamation Monograph No. 20. To

make Monograph No. 20 most useful, the data on more conventional tur-

bines such as Pelton turbines, Frances turbines and vertical Kalpan

turbines should be updated and subjected to the same type of regression

analysis as was done in this study of low-head type turbines.

137

If desirable a nomograph for easy selection of each type of low

head turbine could be developed similar to that given in the work of

Lindestrom (no date). This nomograph could include further development

of the turbine setting restraint as limited by the plant sigma. A

recommendation here would be to develop some kind of standardized safe

ty factor that could be agreed to by a team of authorities. The result

could be developed as a family of curves of suction head superimposed

on an experience curve for selecting diameters given rated head and

rated power output. It is recommended that more careful appraisal be

made of the exit velocity from draft tubes in manufactured units of low

head turbines to see if reductions in velocities could improve future

hydropower installations.

The new procedures developed for estimating of turbine runner dia

meter and runner speed are recommended for use in preliminary design

and feasibility studies for low-head turbines because of the simplicity

and the evidence presented in this report of giving consistent results

when compared with other more involved procedures.

138

REFERENCES

Anderberg, M.R. Cluster Analysis for Applications, Academic Press, New York, N.Y. 1973.

Allis Chalmers, 11 Standard Definitions and Nomenclature- Hydraulic Turbines and Pump/Turbines ... Allis-Chalmers Corporation, HydroTurbine Division, 54X10084-01 York, PA., (no date).

Barr, D.I.H., 11 Similarity Criteria for Turbo-Machines, .. Water Power and Dam Construction, Vol. 18, No. 11, 1966.

Barrows, H.K. Water Power Engineering, New York: McGraw-Hill Book Co., 1927.

Cotillon, J., 11 Advantages of Bulb Units for Low-Head Developments, .. Vol. 29, No. 1, 1977.

Cotillon, J., 11 Bulb Turbines, .. Water Power and Dam Construction, Vol. 31, No. 3, 1979.

Cotillon, J., 11 World's Bulb Turbines, .. Water Power and Dam Construction, Vol. 33, No. 9, 1981.

Csanady, G.T., Theory of Turbomachines, New York: McGraw-Hill Book Co., 1964.

Davis, J.C. Statistics and Data Analysis in Geology, John Wiley & Sons, Inc., New York, N.Y., 1973.

de Siervo, F. and F. de Leva, 11 Modern Trends in Selecting and Designing Francis Turbines, .. Water Power and Dam Construction, Vol. 28, No. 3, 1976.

de Siervo, F. and F. de Leva, 11 Modern Trends in Selecting and Designing Kaplan Turbines, .. Water Power and Dam Construction, Vol. 29, No. 12, 1977, and Vol. 30, No. 1, 1978.

de Siervo, F. and A. Lugaresi, 11 Modern Trend in Selecting and Designing Pelton Turbines 11 Water Power and Dam Construction, Vol. 30, No. 12' 1978.

Doland, J.J., Hydro-Power Engineering, New York: The Ronald Press Co. ,1954.

Khanna, J.K. and S.C. Bansal, 11 Cavitation Characteristics and Setting Criteria for Bulb Turbines, .. Water Power and Dam Construction, Vol. 31, No. 5, 1979.

Kpordze, C.S.K., .. Experience Curves for Feasibility Studies and Planning of Modern Low-Head Hydro Turbines, .. M.S. Thesis, Civil Engineering Department, University of Idaho, Moscow, Idaho, 1982.

139

REFERENCES {continued)

Lindestrom, L.E., 11 Review of Modern Hydraulic Turbines and Their Application in Different Power Projects, AB KMW, Kristineham, Sweden, (No Date).

Pindyck, R. and Rubinfeld, D. 11 Econometric Models and Economic Forecasts. 11 Second Edition, New York: McGraw Hill Book Company, 1981.

Purdy, C.C., 11 Energy Losses at Draft Tube Exits and in Penstocks, 11

Water Power and Dam Construction, Vol. 31, No. 10, 1979.

Spiegel, M.R., Theory and Problems of Statistics, Schuam•s Outline Series, McGraw-Hill Book Co., New York, N.Y., 1961.

U.S. Bureau of Reclamation, 11 Selecting Hydraulic Reaction Turbines, 11

Engineering Monograph No. 20, U.S. Department of the Interior, 1976.

Warnick, C.C., Hydropower Engineering, Englewood Cliffs, N.J., Prentice Hall, Inc. (In Press).

140

11ependent Parameter

...... Ns -+::> ......

Ns

Ns

Ns

Ns

Ns

Ns

TABLE 14


RELATING TURBINE SPECIFIC SPEED TO RATEO HEAD FOR BULB AND TUBULAR TURBINES

FROM niFFERENT TURBINE MANUFACTURERS

Regression Correlation Standard # of Equation Coefficient Deviation Source Units

N = 1570 183 H -0· 2954 s • 0.49 114.92 KMW 24

Ns = 1752.508 H-0•3353 0.90 17.0 TAMP 4

N = 1119 n21 H-0•2191 s • 0.27 125.63 V-C 11

Ns = 2263.884 H-0•4520 0.75 101.17 VA 5

Ns = 1316.418 H- 0•2770 0.38 119.08 v 15

Ns = 977.618 H-0•1176 0.10 194.69 N 59

N = 820.288 H-0•0642 s 0.04 96.13 EW 27

Type of Unit

Bulb

Bulb

Bulb

Bulb

Bulb

Bulb

Bulb

TABLE 14 CONTINUED

Dependent Regression Correlation Standard # of Type Parameter Equation Coefficient Deviation Source Units of Unit

Ns N = 1653.119 H- 0•3230 s 0.98 17.86 KB 5 Bulb

Ns N = s 1340.564 H- 0•3053 0.38 107.43 FE 12 Bulb

~

Ns N = 1053.040 H-· 02679 0.53 103.57 TAMP 22 Tubular +=-N s

Ns N = 1452.099 H- 0•3229 s 0.89 23.30 V-C 2 Tubular

Ns N = 1335.510 H-0•3948 s 0.84 56.52 ALLIS 23 Tubular

Ns N = lo07.067 H- 0•5533 s 0.98 22.02 KB 3 Tubular

Dependent Regression Correlation Standard # of Type Parameter Equation Coefficient Deviation Source Units of Unit

0" ~ = 2.527 X 10-3N °· 9224 0.20 0.34 Tampella 13 Tubular s

cr ~ = 1.1529 X 10-SN 1•7918 0.80 0.29 Allis Chalmers 14 Tubular s

~ ~ = 2.135 X 10-11N 3.8269 . s 0.49 0.23 Vevey Chami 11 e 2 Tubular

() ~ = 4.549 X 10-6N 1•9082 0.58 0.84 KMW 12 Bulb ...... s ~ w

(} ~ = 9.723 X 10-8N 2•4794 0.92 0.15 Tamp 4 Bulb s

cr cr= 8.077 X 10-5Ns 1.4907 0.44 1.02 V-C 11 Bulb

(j 0" = 1.5416 X 10-3N 1•0153 s 0.84 0.20 VA 3 Bulb

(j U = 1.1143 X 10-4N5

1.4233 0.47 0.47 v 15 Bulb

APPENDIX 1

SAMPLE CALCULATIONS FOR TURBINE CONSTANTS CONVERSIONS

A series of sample calculations are presented using actual data

from the Rock Island power plant on the Columbia River. Different

forms of turbine constants are used in both the American system of

units and also the metric system of units. This is presented in case

engineers desire to use different forms of the turbine constants and

desire to work in different weasurement units.

144

SAMPLE CALCULATIONS FOR TURBINE CONSTANT CONVERSION

Given: Rock Island plant data as example

H = rated head = 12.1 m Q = Rated discharge = 481.0 m3;sec

= 54,000 P = Rated power output D = Turbine diameter = 7.40 m N = Turbine speed = 85.7 rpm

Required: To show conversion example calculations.

Analysis and Solution:

From general power equation.

ptheoretical = .9.!:!E.9. = (481)(12.1)(1000)(9181) 1000 1000

= 57,095 kw .. ~~--answer p

n = rated = 54 ,000 X 100 = 94.6% ·~~--answer pth 57,095

Using Eq. (4) Ns _ N /P _ 85.7 /54,000 = 882 .5 (metric) - H5/ 4 - (12.1) 1· 25

Ns American = 0.262 Ns metric

= 0.262(882.5) = 231.2 .. 4t----answer

or Ns American = N;'Phorse power (H ft) 1 .25

Pkip = Pkw/0.746 h = Hft = Hm/0.3048

Pkip = 54,000/0.746 = 72.386 hp Hft = 12.1/0.3048 = 39.7 ft

Ns American = 85 · 7 1~ 2 2~86 = 231.4 •4r----- Answer Check ( 39. 7) .

145

Using ECJ. (105) /H o = 84.58 cp N

Solve for speed ratio

4> = NO 1 = 85.7 (7 .40) 1 = 2.16 4~---answer metric 1fr 84 · 58 li2"":f 84.58 ===

This noted as Ku in Table 1 and deSiervo (1977) in the American system with diameter expressed in inches from Table 1.

dn

The dimensionless specific speed is computed from

N A . 231.2 = s men can = ..:::...:...,;_;_:::: ___ = 5.46 .. ~~-----answer w s 43. 5 In 43. 5 Ia. 946

Recognizing that the basic equation for dimensionless specific speed is from Table 1

wQ1/ 2 _ 2n85.7(481) 1/ 2 = = 5. 47 .. ~~--Answer Check

ws (gH) 3/ 4 - 60 [(9.81)(12.1)] 314

146

I .

APPENDIX 2

SAMPLE CALCULATIONS FOR DETERMINING TURBINE DIAMETER

AND TURBINE SPEED BY DIFFERENT METHODS

These sample calculations are executed to illustrate different

methods of estimating preliminary values of turbine speed and turbine

runner diameter. The traditional method as put forth in the U.S.

Bureau of Reclamation Monograph No. 20 (1976) is compared with publish

ed results of deSiervo, the work and methodology of Lindestrom of KMW

in Sweden and different approaches developed on this research project.

This illustrates the variability that can be obtained. Each method and

the appropriate equations require at least one empirical equation that

is based on experience curves based on performance of ~anufactured

units or from studies of model test data. Documentation as to where

each empirical equation came from is presented in these sample calcula

tions.

147

SAMPLE CALCULATIONS

Given: Isarwerk 3 plant as an example

H = Rated head

Q = Rated discharge

P = Rated power

Other assumption

= 4.5 m

= 32.5 m3fsec.

= 1200 kW

Speed to be based on the nearest possible synchronous speed using

multiples of 4-pole generators and 50 Hz frequency because the

Isarwerk 3 unit was manufactured for that frequency.

Required:

To make preliminary estimates of turbine speed and diameter using

different methods.

Analysis and Solution

A. U.S. Bureau of Reclamation Monograph No. 20 Procedure

Using the Equation

Ns = 2702 H-O.S from Fig. 11, p. 15 (U.S.B.R.-M20) Note: USBR-M20= U.S.B.R. Monograph No. 20.

determine trial Ns 1

N I = 2702 {4.5)-0·5 = 1273.7 s

Using the specific speed equation:

NIP from Table 2 and p. 14; {USBR-M20)

determine a trial speed N1 by solving for N in above equation

N I = {4.5) 514 1273.7

r--1200 = 241.0

148

Recognizing Np = 6000/N

Where Np = number of poles at 50 Hz

Then Np = 6000/241 = 24.9 poles

Therefore the nearest multiple of four poles would be Np = 24

Synchronous speed N = 6000/24 = 250 rpm (,----- ANSWER

Calculate the actual Ns from

N /P 250 /1200 = = 1321.3

H5/4 (4. 5)1.25

Now determine speed ratio from empirical Equation

2/3 ¢ = 0.0233 Ns from p. 14 (USBR-M20)

¢ = 0.0233 (1321.4) 213 = 2.806

Note, this equation is for propeller turbines

Now determine turbine diameter from Equation

84.47 ¢ iH 0 = from p. 14, (USBR-M20)

N

84.47 (2.806) 14.5 0 = -------- = 2.01 m <-

250

B. deSiervo and deleva Equations

Using the equation

ANSWER

Ns = 2419 H-0· 489 from p. 52 [deSiervo and deleva(1977)]

Ns = 2419 (4.5)-0·489 = 1159.4

Using the specific speed equation

NIP

149

determine a trial speed N• by solving for N in above equation,

{4.5) 1· 25 (1159.4) N I = ------- = 219.4

I 1200

Recognizing Np 1 = 6000/N

then Np = 6000/219.4 = 27.4 poles

Therefore nearest multiple of four poles would be Np = 28

Synchronous speed N = 6000/28 = 214.3 rpm <-- ANSWER

Calculate the actual Ns from

NIP N = -- = s 5/4

H

214.3 11200

(4.5)1.25 = 1132.7

Now determine speed ratio from Equation:

¢ = 0.79 + 1.61 x 10-3 Ns from p. 56 [deSierve & deleva (1977)]

¢ = 0.79 + 1.61 X 10-3 (1132.7) = 2.614

Now determine turbine diameter from Equation

84.5 IH 0 =----from p. 14 (USBR-M20)

N

84.5 (2.614) 14.5--0 = = 2.19 m <--

214.3

C. KMW Graphical Solution

ANSWER

From the KMW nomograph reproduced as Figure 70 as taken from

[Lindestrom (n.d.)]

N 200 this really falls off the scale of the nomograph

0 = less than 3

150

D. Special study of KMW Bulb Units Using Techniques and Regressions

Developed by Kpordze - Warnick

1. Determine turbine diameter by Equation:

p D = F(P/H) = 0.17633 (---) 0· 449

H

(1200)0.449

D = 0.17633 = 2.17 m <- ANSWER 4.5

Then using this value of D determine a trial value of N from Equation

vH N = F{---) =

0

IH 164.706 {---) 0•8876 from Table 9

D

(14

· 5)0.8876 N' = 164.706 = 161.42 rpm 2.17

For synchronous speed Np = 6000/N = 37.2 poles

choose 36 poles

Therefore N = 6000/36 = 166.7 rpm <-- ANSWER

2. Using D from above (1) and using empirical equation:

Q Q D = F (---) = 4.1604 (-) 0· 3064 from Tab 1 e 9

N N

and transposing solve for N

4.1604 3 264 N = ( ) • Q

D

(4.1604)3.264

N' = (32.5) = 272.0 rpm 2.17

For synchronous speed Np = 6000/N

Np = 6000/272 = 22.1 Use 24 poles

N = 6000/24 = 250 rpm <- ANSWER

151

3. Using empirical equation for N = F(P/H) solve for N and empirical

equation D = F(Q/N) solve for D using N from the solution of N = F(P/H)

Determine N from Equation:

N = F(P/H) = 3583.983 (P/H)-0· 4833 from Table 9

(-1200) -0.4833 N' = 3583.983 = 240.9 rpm 4.5

For synchronous speec Np = 6000/N

Np = 6000/240.9 = 24.9

N = 6000/24 = 250 rpm

Use 24 poles

Now using this N = 250 rpm determine turbine diameter D from

Q D = F(Q/N) = 4.1604 (-)0· 3064

N

(32 · 5)0.3064

= 4.1604 = 2. 23 m <- ANSWER 250

4. Using the more traditional approach, solve for Ns = F(H), then

find N from specific speed equation, then solve for ¢ = F(Ns),

then use D = F ( ¢/H) to so 1 ve for D. N

Using Equation:

Ns = F(H) = 1553.445 H-0·2918 from Tahle 9

Ns = 1553.445 (4.5)-0· 2918 = 1001.6

N H1· 25 1001.6 (4.5) 1· 25 s N' = = = 189.5 rpm IP l12oo


Np = 6000/189.5 = 31.66 Use 32 poles

N = 6000/32 = 187.5 rpm

152

•

Now find actual Ns

N lp 187.5 1!200 N

s = -- = ----- = 991.0 (4.5)1.25

Using Equation:

¢ = F(Ns) = 0.166 Ns 0· 3728 from Table 9

¢ = 0.166 (991.0) 0· 3728 = 2.173

Now solve for D using Equation

H0· 5 84.47 (2.173)(4.5) 0· 5 D=84.47¢ ---------------

N 187.5

D = 2. 08 m <;-- ANSWER

E. Study of all Bulb Units Using Techniques and Regression Developed

by Kpordze - Warnick

1. Determine turbine diameter by Equation:

D = 0.1826 (P/H) 0·4462 Eq. 25

(1200 )0.4462 D = 0.1826 = 2.21 m ~ ANSWER 4.5

Then using this value of D determine turbine speed by Equation

IH" N = F(-)

D

Iii = 169.199 (---) 0·926 from Eq. 30

D

(14."5) 0. 926 N' = 169.199 = 162.8 rpm 2.21

For synchronous speed Np = 6000/N'

Therefore Np = 6000/162.8 = 36.9 poles, Use 36 poles

N = 6000/36 = 166.7 rpm ~-- ANSWER

153

2. Using D from above (1) of 2.21 m = D and utilizing empirical

equation

Q D = F(-)

N

Q = 4.181 (-)0· 3175 from Eq. 26

N

or transposing to solve for N

N = (4.181)3.15 Q

D

4.181 3.15 N' = (-----) (32.5) = 242.1 rpm

2.21

For synchronous speed Np = 6000/N.

Np = 6000/242.1 = 24.8 poles Use 24 poles

N = 6000/24 = 250 rpm ~ ANSWER

3. Using empirical Equation for N = F{P/H) solve for N and use empiri

cal equation for D = F(Q/N) solve for D using the N from N = F(P/H)

as selected to agree with a synchronous speed.

p N = F(-)

H

p = 2152.856 (---)-0· 4062 from Eq. 28

H

1200 -0.4062 N' = 2152.856 (-) = 222.6 4.5


Np = 6000/222.6 = 26.9 Use 28 poles

N = 6000/28 = 214.3 rpm

Now using this N = 214.3 determine diameter D from Equation D = F(Q/N)

Q D = 4.181 (----) 0· 3175 from Eq. 26

N

( 32 · 5)0.3175 D = 4.181

214.3 = 2.30 m ~ ANSWER

154

4. Using the more traditional approach solve for Ns = F(H), then

find N from specific speed equation, then solve for ¢ = F(Ns), then

IH use D = F( ¢--u-) to solve for D.

Using Equation

Ns = F(H) = 1520.256 H-0· 2837 from Eq. 3

Ns = 1520.256 (4.5)-0· 2837 = 992.2

N H514 992.2 (4.5) 1· 25 s N' = = = 187.7 rpm IP I 1200


Np = 6000/187.7 = 31.97 Use 32 poles

N = 6000/32 = 187.5 rpm

Now find actual Ns

N /j) 187.5 /1200 N = = ----- = 991.0 s H5/4 (4.5)1.25

Using Equation

¢ = F(N ) = 0 0944 N °· 4605 from Eq. 19 s . s

¢ = 0.0944 (991.0) 0·4605 = 2.26

Now solve for D using Equation

H112 (2.26)(4.5) 112 D = 84 . 4 7 cp -- = 84. 4 7 = 2. 16m

N 187.5

D = 2.16 m <E-- ANSWER

155

F. Actual Manufactured Values of Diameter and Speed

0 actual = 2.45 m

N = 157 rpm

156

APPENDIX 3

COMPLETE TABLE OF DATA

157

8 U l B T U R 8 I N E S

--------------------- - ---------POWER DATE OF NAME OF RATED RATED RATED RU~.NER RUNNING MM!'IF IICfUHEP STATION CCMMIS- RIVER HEAD flOW. CAPACITY DIA- SPHIJ

SIUNING (MJ ( 3 I ) PE R UN IT liE lfR IRPMJ m S ( KW I ( •1J

-ARGENTINA RIO I.IUEQUEN 1982 - 4.15 5.5 170 1.00 425.0 ~I

AUSTRIA

RWTTE 1956 LHH 6.07 24.0 1210 2.2() 165.0 [W PAIHENSTEIN 1963 GR.f'UHL 9.60 26.0 2200 2.09 234.0 v T R AUNl E IT EN 2 1965 TR-UN 9.50 15.0 1200 GHUNDEN 1968 TRAUN 9.00 75.0 6520 3.30 136.4 UR S TF.IN 1969 SAllACH 10.90 125.C 12310 4.2A 12 5. 0 v 01 fEI~SHEIH I 973 DANUBE 9.10 250.0 20400 5.60 101).0 .~n

GHUNOENtSUPPl.J l911t TRAUN - - 6120 3.30 136.4 110

...... GABERSOURF 1914 MUll 8.61 115.0 9000 4.1'> 10 7.1 ru U1 fELTEN 1976 MUIIZ 6.40 30.0 1700 2. 311 176.5 r ;~ co Al TENWORTH 1976 DANUBE 14.00 300.0 38900 6.0() 103.4 v

OBERVOGI\U 1971 HUR 7.39 117.6 769:> 4.15 IC 7. I HI

ABW ltlOEN-A S TEN 1979 UAt.UBE 7.96 294.0 22130 5.70 93.7 v ABW INUEN-AS TEN 1979 0-NUBE 8.20 270.0 20000 5. 7•) 93.7 VA HELK 1982 DA'-UBE 8.20 300.0 22280 6.3C 85.7 v GREIFENSTEIN - DANUBE 11.20 350.0 ]5')00 6.50 93.7 v KLEINMUENCHEN 1978 TR-VN 11.50 65.0 6500 3.15 166.1 VA Bl SCHUF SHU FEN 1981 - - - 10000 - IJ6. 4 VA HAINIJURG 1982 - 18.24 - 55800 - 101).0 VA

BELGIUM

NEUVILLE-SUR-ROY 1962 - 4.00 75.0 2lt00 3.60 9 7. 5 PI

CAt\ ADA

JENPEG 1976 - 7. 30 lt48.0 2JJOOO 7.50 62.0 L"'l CENTRALE DE LA RIVIERE - ST E-MAR IE 5. 70 360.0 18000 7.10 64.3 flU. IS STE-MAR IE LAUHNE - ST-LURENCE 11.00 400.0 15001)' 6.9u 93.8 IIlllS

PEOPlE'S REPUBLIC OF CHINA

HA Jl TANG 1984 ll SHUI 6.56 310.0 18000 6. 3•1 75.0 v

- ·- - -6 u l 0 T U R 8 I N E S

---------------- ------- -----------POWER DArE OF NAME OF PAT EO RATED qATEO RU"lf\!FR RU~JNI NG f~IINUFACTURER S TAllON COtlo!IS- RIVER HEAD FlCW CAPACirY DIA- SPHD

SICNI"G CMJ (m3/s)

PEP UNIT METE II IRPf'!J CKWI I M I

-

FINLAND

ANK.K.APURHA 19A3 KYI'IJCKI 9.RO 225.0 I 9800 5.40 100.0 TA~ VAJUKOSKI 1984 KITII\EN 15.00 160 .o 2202J 4.6:1 136.0 To\M

FRANCE

GOLFECti 1973 GARONNE 15.50 180.0 230:10 5.13 125.0 t~ ARGENT AT 1957 UOROOGNE 16.60 98.5 14350 3.10 150.() v-c ARGENT AT 1958 DCRUOGNE 17.40 14.45 2220 1. 80 300 .I) V-l ARGENATAT 1958 DCROOGNE 16.50 - 144()0 ).RJ 150.J r ~ VILLENEUVE-SUR-LOT 1970 lOT 11. 10 128.0 14400 4.40 136.6 J CAMBEYRAC 1957 TRlYERE 10.80 55.0 500() 3.1:J 150.0 N CAMBEYRAC I 957 TRUYERE 10.80 55.0 5000 3. 3~ 136.4 J AHBIAL ET 1961 TARN 6.50 38.0 2000 2.50 187.0 sw

...... LA CROUX I 981 TARN 13.60 75.0 9280 3. 25 200.0 N c.n SAINT-MALO 1959 - 3.40 300.0 9000 5. ItO 81!.] f4 1.0 LA PANCE 1966 LA RANCE 5. 80 191.0 10000 5.35 •n.A v -c

GERSTHEIM 1967 RHINE 11.45 234.0 ZJAOO 5.6{) 100.0 ')

STRAS80URG 1970 RHINE 11.70 Z34.0 24500 5.6C I CO. 0 IJ GAMBSHEIH 1974 RHINE 10. 15 270.0 241)50 5.61) 100.0 N BEAUMONT-MCNTEUX 1959 I SERE II. 30 8Q.O P~OO 3.Rr) 150.0 N PIERRE-BENITE 1966 RHONE 7.80 333.0 20000 6. I•J 83. A A BEAUC.:AIRE 1970 RHONE 1 o. 10 400.0 35000 6.25 93.8 ~!

GERVANS 1911 RHCNE 9.75 405.0 30()01) 6.25 93.8 N SAUVETERRE 1 '173 RHONE <J. 40 400.0 33000 6.qJ 93.8 N AVIGNON 1973 RHCNE 9.10 400.0 3001)0 6.25 Q3.R N CADERUUSSE 1975 RHUNE 9.10 400.0 32500 . 6.25 93.8 N

AL BAS 1965• - 3.87 15.0 423 1.BG 176.5 N AGE 1981• - 19.00 15.4 2608 1.50 428 ~I

BERGERAC 1980• - 3.62 - 791 2.5() 1)6 N CAillADE 1<J58* - 3.50 5.3 154 1.1? 257 N CAPDENAC 1959• - 6.00 15.0 751 1. fhl 260 N MERCUS 1 1954• - 3.50 9.5 2113 1.65 182 ~· MERCUS 2 1959• - 3.'00 9.9 318 1.40 254 N HUll 1982• - <J.40 10.0 790 1.2 5 395 tl RCCHEREAU 1962• - Q.OO 6.6 500 1.01) 487 N VEROUM 1957• - 3.13 8.4 241 1.65 181 )\;

CAOl:ROUSSE 1975 RttONE 9.10 410.0 325JO 6.90 93.8 N PEAGE-OE-ROUSSillON I'H7 llHCNE 1?.00 400.0 4001)0 6.25 •n.8 Cl VAUGRIS 1980 Rt<CNE 5.65 350.0 18000 6.25 75.0 A VAUGIU S 1980 PHONE 5.65 350.0 18:JOO 6.9C 75.0 A ANGELEFORT 1980 RHGNE 15.01) 350.0 45000 6 .4,) 1117.0 "

8 u l 8 TURRINE s

-PCWER DATE CF NA"'-E OF RATED RATED Rfl TEO RUNNER RUNNING MfiNUFI\r;TUf<ER STAT ION CCMMIS- RIVER HEAU FI_OW CAPACITY uu- SPEED

StONING I M I ( 3 I ) pER IJN IT Mfl ER IRP'-11 m S II<.WI

·~· ------------------------ ---------------------RRENS 1981 PHONE 15.01) 350.0 45000 6.40 107.0 " llREGNIER-GCRDCN 1':}83 RHCf\E 11.40 350.0 35000 6.25 <n.a AelAC 1958 ISLE 2.20 8.5 lf:5.5 1.12 158.0 v-c

MfiRCKOLSHE:I~ 1957 RHif\E 9.50 14.4 1205 I. 60 P3.3 v-c RABGDfiNGES 1'159 ORf\E 6.00 7.6 401 1 • 40 3t5.0 V-L RHINAU 196J RHINE 6.90 14. 1 AbO 1. 70 300.0 V-L GERSTHEIM 1967 RHINE ll.10 235.5 231!50 5.b0 107.0 V-( GERSTHE111 19b8 PHINE 9.00 14.0 1113 1. 6(1 333.3 v-c STRASBUURG 1970 PHINE 11.65 257.8 21100 5.60 11)0.0 \1-(

STRASBOURG 1970 RHINE 14.50 21'~.2 29000 5.60 100.0 N CASTEl 1953 - 7.80 12.5 810 1. b5 250.0 N wADIHNAU 1957 - 4.50 31>.4 1480 3.05 107.0 II SAINT-MALO 1959 - 4.'!0 227.0 90:>0 5.RO 1:!8.3 ,~

........ GERSTHRIM 1957 9.80 258.0 23000 5. 6 1} 10 7. 0 r1 0"1 -0 BEAUCAIRE 1970 - 15.30 258.0 3500() 6.25 93.8 N

GERVANS 1971 - 12.0 - 30000 6.52 03.'1 N

AVIGNON 1973 - 10.50 350.0 30000 6.52 93.!l N GAMBSHEIM 1974 - 13.20 - 24500 5.60 100.0 N CHAUTAGNE - - 14.67 350.0 46f..OO 6.41) 101.0 N BEllEY - - 14.70 350.0 46670 6.40 107.0 rl

GERMANY

PAll EM 1964 MOSEllE 3.40 50.0 1500 3.60 78.0 '1h GREVENMAC.HER 1962 MOSELLE 5.50 59.0 2b00 J.20 120.0 F.w TRIERITREVESI 1958 MOSELLE 5.10 95.0 4400 4.60 78.0 EW DETZAM 1959 MOSEllE 7.00 95 .o 5"l00 4.20 92.5 HI WINTRICH 1963 HCSEllE 5.60 95.0 4900 4.60 83.0 E•.4 ZEL TINGEN 1964 MOSELLE 4.00 95.0 3300 4.80 (, 1.0 Ml\ ENKIRCH 1965 MOSELLE 5.10 95.0 4300 4.60 79.1) MA NEEFIST.ALOEGUNOI 1964 MC SEllE 5.50 95.0 4000 4.60 76.0 [W

FRANfi.El 1962 ~GSELLE 4.10 95.0 311l0 4.60 11.fl v MUOEr~ 1962 MOSELLE 4.10 95.0 3600 4.60 71.0 v LEHMEN 1966 MOSE:LL E 5.30 95 .o 46:JO 4.6J B5.C v BUCKENHUFEN 1960 ILLER 5.20 35.0 1 o;oo 2.45 166.7 lOW

..... -

R U l B TURBINES

-PCWER DATE Of NAME Of PAJEO RATED Rill EO RurmeR RUNNING M/UliJFA(TURER STATION CCMMIS- RIVER HEAD FLOW CAPACITY OIA- SPFEO

SIGNING CHJ (m3ts)

PER UNIT "1HER I R P '1 J IKWJ Oil

------------------ - -------IVORY COAST

SAN PEDRO 1982 SAN PEORO 9.80 30.0 2600 z.or; 272 0 7 v-c

JAPAN

...... HITCKIT A 1959 NATORI 12.00 12.5 1375 1. 50 ~33.3 Ml 0)

...... KUNAKAJIMA 1961 MABUCHI 9.20 29.0 2320 2.3'l zoo.o T AK1RASHIMA 1964 TEI:ORI 13.70 40.0 4800 2.31) 240.0 ~~ I UMATA 1960 WAOA 13.00 30.0 3350 2.n 2~0.0 rF JUGANJIGAWA(~U.1,2,3,4J 1964 JOGANJI 15.10 40.0 5340 2.4 7 21t0o0 F-E TAGUCHI 1Q66 HI POSE 12.40 58.2 6300 2.90 1117.5 FE KOIVE 1967 HIPCSE 12.90 7Ao1 AIJOJ 3.4J 150.0 r E YANAGIHARA 1967 HIPUSE 10.00 90.1 7850 4. O•J 125.0 T HIT UK IT A 1Q59 NATORI 12.00 12.5 1315 1.51) 333.') Ml KCSHI 1959 SE~OAI 8.oo 22.0 1640 1. 9~ 225.0 ~· SAIKAWA 1961 SA 1 111.30 13.5 2216 1.4 3 _450. 0 FF SHIP'OAKA 1962 KIT A 10.65 20.0 1840 1.84 240.0 FE TAMAYOOA 2 1964 ARA lb.80 30.0 4370 1.95 3JO.O FE MIZUKOSHI 1965 NIStiiKI 12.12 12.0 1410 1.31) 400.0 F./I~

SEKINE 1967 HI POSE 9.50 9~.0 8200 4.00 125.0 T KUROTORI 1968 NAP llfA 10.21 ?6.:1 2310 2.10 225.0 fF ISHII 1975 CHIKUGO 13.74 10.0 1176 1.27 450.0 re KURCKAWI\ 2 1ns SHIRO 22.70 11. 13 2194 1. 27 600.0 H IKEDA 1976 YCSHINO 10.73 62.0 5200 3. 1 "j 150.0 F/"1 AKAO 1'>78 SHO 17.40 220.0 34000 5.10 12!1.6 ff: FUTAKAWA 1979 SHilUNA1 12.00 73.0 7300 3.40 150.1) T 1\RAMAK I 1966 - 9. 50 108.0 8200 - 125.0 T SAKUMA l 1982 T Et\R YU 12.30 12.2 16800 4.49 125.1) fF" MCNIWA 1 961 - 16.3 - 1570 - 429.0 H KAKIO 1962 - 11.9 - 860 - 50C.O H OSAKABE 1962 - 10. J5 - 540 - 514.0 II

KCREA

NAM GANG 1972 - 8.70 •n .o 6500 3.00 1"'l.5 J PAL DANG 1972 - 11.80 zoo .o 21000 5.20 120.0 N

l U XF MRilllPt: -. -

B U l II TURBINES

------ --------------POWI:H CAT E Of NAME CF HATED RATED RATED HUtiNER RUNNING H.-.NIJfAC TURER S TA Tl ON CCMMIS- HI VER HEAD FLOW CAPACITY OIA- SPEEU

SIGNING IHI (m3/s) PER UN IT 14ETER I RPM I IKWI I M I

--------FINS lNG 1961 - 10.60 35.0 3000 2.30 214.3 v URSPRING l9(d LECH 8.10 52.0 3400 2.8'> 166.7 IJ LECH 3 1963 LECH 9.20 47.5 4200 2.115 166.7 I:W SYlVENSTEIN 1960 I SAR 23.40 12.5 2500 1.46 452.0 v lffl:lHE IM 1977 RHINE 11.70 267.5 21000 5.80 100.0 fW LECiiSTUFE 2 1968 LECH 15.20 52.3 750:1 2. 85 200.0 HI LECiiSTUFE 18 1973 LECH 12.80 47.5 6700 2.115 200.!) EW

LECHSTUF 23 l'H8 LECH 8.60 4 7. 5 5000 2.R5 187.5 EW ISARWERK 3 191'1 I SAR 4.50 32.5 1200 2.45 157.0 Ew LECHSTUFE 19 1980 LECH 8.70 47.5 4500 2.115 176.5 EW LECHSTIJFE 20 1984 LECH 9.1t0 47.5 4090 2.85 176.5 v l ECHS TUFE 22 - LECH 9.17 47.5 - 2.!!5 176.5 IJ GCTTFRIEOING 1971 ISAR 6.00 50.5 2710 2.92 135.0 v REH lNG EN 1984 SAAR 7.6 30.0 2080 2.30 1117.5 v SCHGOEN 1984 SAAR 5. 70 30.0 1550 2. 30 18 7. 5 v

HUNGARY ~ CJ') ~ Tl SZA 2 1973 - 6.40 138.0 7200 4.30 107.0 Gil

INDIA

GANLAK 1966 - 6.10 112.0 5500 4.10 107 .o f \~

KOSI 1984 - 7.70 - 50011 4.5\l 93. II H

wESTERN YAMUNA 1982 CANAL 19112 - - 73.3 9080 3.15 187.5 F-E

INDOI~ES lA

ANGKUP 1 1980• - 9.0 5.70 425 0.91) 659 N HAIWYAN 1980* - lt.85 5.0J 200 0.91) 4f0 N MEJAGUNG 19110• - l't.87 5.10 640 0.90 802 ~l

WGI'.CDADI 1980• - 3.60 8.30 235 1.25 280 ,..

IRAK

HOSUL 2 - Tl GR IS 10.5 16.0 - 5.00 115.4 v

ITALY

FIORINO NUOIJO 1966 PI AVE 16.50 62.0 9JOJ 3.00 187.5 RA HELLEA 1 - - 11.1) 2.5 200 0.63 770 N MELLEA 2 - - u.o 4.1 350 o.8o 603 ~·

..... - .. ...

B U l B TURBINES

-------------PO .. ER OAJE Gf NAME OF RATED . RATED RAJ EO RUt'4NER RUNtiiNG "41\NIJFAC TURER SJ AT ION CCHHIS- RIVER HEAD FlOW CAPAC I JY 014- SPEEO

StONING CHI (m3 is) PER UN IT METER (RPM I CKWI CHJ

----------------------- - --------NORWAY

GAMLEBRUFOSS 1cno lAGE~ l't.10 110.0 15610 to.20 150.0 K:~w

KlOSJERfOSSEN 1969 SKIEt.SElVEN 5.03 119.0 5HO 4.50 85.7 KHARK'lV ASMUOFOSS 1971 NA,.,SEN 10.00 135.0 12500 4.30 12'5.1) KB fUNNEFOSS 1975 GlCMio'A 10.30 220.0 20000 5.20 1CO. J Kfl KONGSVII~GER 1975 GlOHHA 9.16 240.0 19100 5.50 93.8 KO DUVIKFOSS 1975 ORAio'NEN SElVA 5.85 300.0 14700 6.40 75.0 KMW l.F I SKUHFUSS 1976 NA,.,SEN 6.20 130.0 6700 4.30 107.5 KD BINGFOSS 1976 GlOMHA 5.1)0 250.0 10600 6.05 71.4 KB URASKEREIOFUSS 1q79 GlCHHA 9.17 270.0 22200 5. 80 88.2 KR

...... Ph llll PP INES 0'1 w MAGAJ A 1984 - 3.50 13.80 3A 1 1.50 239 N

MAGAT B 1984 - 3.50 13.80 381 1. 50 239 N MAGAT C 1984 - 2.ao 11.70 253 1.5() 214 N MAG AT HAT ION 36 1985 - 9.96 10.28 637 1.2'5 400 ~

TALAVERA 1963 - 14.80 - 645 - - N PENARANDA 1983 - 1. RO - 323 - - N

POlAND

tiECHOC INEK 1984 lOioER 5.10 375.0 16600 7.10 65.2 -

PCRTUGAL

CRESJUMA 198/o OUlRO 10.25 423.0 39000 6.80 93.75 N BElVER 1990 TAJC 14.20 267.5 35300 6. •J') 100.0 EW RAIVA 1980 MOfiDEGO 16.00 75.0 12840 3. 30 200.0 EW

RC,.ANIA

IRON GA HS 2 1984 DAfiUBE 7.40 lt25.0 Z8000 7.5C 62.5 l Ml

SPAIN

CHERTA 1984 - u.co 296.0 26000 5.90 GARC lA 1984 - 8.00 210.0 17200 5.90 SANTIAGO-DEL-SIL 1965 Sll 12.00 86.0 1!300 3.30 1 '57. 5 [ 11

6 U l D T U R 8 I N E S

-------PCWER DATE OF NAME OF RATED RATED RATED RUNNER RUNr.JI~G ;~A~HJFI\CTURER

STATION CCMMIS- RIVER HEAD FLOW CAPACITY Dll\- SPHn SICNI~G on ( 3 · , PER UNIT METER IRP'11

m /S) CKWt pq

-ALCANADRE 1963• - 2.49 18.30 379 - 1)6.0 N

SASTAGO 1969* - 7.00 - 753 - - 'I ~IENGIBAR 1974• - 7.60 - 1700 - - ., SUDAN

KHASM-El-GI RBA 1967 ·AT8ARA 7.00 sc.o 2800 2. 70 1'iO.O Q

ShE DEN

...... SKUGSFORSEN 1959 AT PAN 14.00 29.0 HOO 2.1!1 ?50.0 K '1W 0'1 ~ HAllEFORS 1966 SVARTALVEN 7.50 32.1) 2180 2 ·'•5 190.0 '<"W

SPERLI NGSHOLM 1967 LAGA,._ 3.70 7.5o0 BOO lo 1t 5 175.\J KM\~

PARK I 1970 llJLEAL YEN 1lo00 I6Ao0 21200 4.QQ 115 0 4 K'~W

LGVLN 1973 FAIIALVEN 13.80 160o0 19800 4o'i0 136o ~ t1U GULL SPANG 1972 GULLSPANGSALVEN 21o00 6o0 1200 OoQO 750.0 Kr1w V 1 T T JARV 1974 LULEAL VEN 5.60 250o0 12300 5.80 75o0 K"~H

GAGOEDE 1'l73 STROHS 1';.00 180o0 24300 4o50 136o4 IU~W

BAGEUE 19 74 VATTUOAL 9o 30 160o0 1 330\) 4o50 125o0 I<IIW BOOUM 1975 ANGEP,.,ANALVEN 6.50 225o0 13000 5oAO 75.1) K ~~~~ FJAllSJC 1976 ANGEPHANALVEN 6.80 220o0 11200 5.'10 79.0 Y-"1rl

SIL 19 76 ANGERI"ANALVEN 6o40 225o0 12~00 5o~O 79o0 r,~~w

LANDAFORS 19H: LJLSt.AN 5. 30 350.0 16200 6. 1•0 M.2 K'1\ol LJUSNHORS 19 76 LJlJSNAN 6.70 340o0 1'l81)0 6o40 75oiJ ~ '111

ASELE 19~1 ANGERP'ANALVEN 10 o10 320o0 28300 6 0 10 <>3o 0 KriW ·soDERFORS 1979 OALAVEN 4.50 220.0 9400 6.10 62o5 t<r~w

JUV£LN 1978 lt.CALSALVEN 11o00 150o0 15700 4.20 1~6o0 1; '-~w TOR RON 1978 OALSALVEN 19o00 165o0 31600 4o'i0 1'i0o0 K"l·/ NAS 1 19 79 OALALVEN 5. 20 230.0 14700 5o flO 75.0 to•w AVESTIILILLFORS 1982 OAUILVEN 5.30 250.0 14100 6.10 68o2 K'1W MATFORS - - 9.45 250o0 21000 5o60 qJoO K"W LillA EDET 4 1982 GOTA Al V 6.50 2!10.0 18001) 6.10 7'io0 IUl\ol

.... - - -

8 u l 8 I U R R I N £ S

--------------------PO~ER DA 1£ or IUME OF PAlEO RA IHI RAifO RtJ'INER RUN'JIN.'", ,..t."'llr A£. I UP FP. SIAIION crotlll s- RIVER HE All Fl~ll CAPACIIT DIA- sr( r 0

SIONING '"' ( rfR UNII 11£ I£ R IPP~I

m /s •~w• I'll

------------Sl<lllERlAilD

NUCHLI G 1962 BIJ~lE ).)0 60.0 1600 ).10 H.O ~w

AU£ 1'161 ll IIIlA I 5.50 )8.0 111)0 2. 11) 136.4 r w Fl UIIEIIIHAl 1965 AAPE 1.50 1n.o 8JOJ 4.20 (Cl.J FW NE U-8ANN1oll 1965 AAPE 8.10 116.1 8420 4.20 I~ 1.1 rw lUF J~ON 1911 RELSS 10.9) 100.0 10060 J.qo 1~0.1) rw

- -UN IT EO I< INGOUH

AWE 1964 - 6.85 8.15 ~18 1.15 H5 " USA

RfJCI\ ISLAND 1918 tClUHBIA 12.10 ~81.00 5400\l 1.40 ~5.1 (l

VACE8UNG - - 8.40 )60.00 240JO 6-1~ '10.0 RACINE 1980 CHIO 6.ZJ H).5tl 24~00 1.70 62.1 rw MERCED IOAIN lANAl 1981 - - It). 20 2810 2.50 IAr.o H IDAHO FAllS 1981 SNAKE 5.50 165.0 Rl'JO 4.85 '14.7 YA DAWSON 1982 - 5.5 96.) 4660 1.81 120.0 ff l AWRENC£ 1981 - 5.80 - 1~no 4.0J 128.f. o\l

..... C) PH ION REREG. I9R2 DE SCHUIES 10.60 110. o I~OJO 4.85 112.5 YA

U'1 11. I. lOVE 1982 - ~.63 - 24100 6.10 q~.l) lj

USSR I\ I SlAYAGU8SI\ 1961 - 2.50 19.10 400 ). )J n.o lj

1\ lEV 1966 DNIEPER 1.10 2?0.0 2JOJO 6.0'} P5.1 Klf!IPJ<nv

I\ I SLUGU8SI\A~A 1965 - I. 2~ - 400 ).)0 12.0 II I\ AliA 1968 - 21.0 130.0 ZIROO 4.5\l 125.0 I 11l PEREPAO 1912 - ll. 20 2)0.0 20'>00 5.51'1 '11.8 I Ill SARAIOV 1'112 VOlGA 10.60 528.0 41100 1.50 15. (l l '<I 1\ANJEV 1912 8.40 240.0 IBZJO 6.oc R5. 1 IUII'\Pt'.OV

ICI<EREPOVE ll 1'16 7 15.00 I 15 .o 21000 5.5J '11.~ l'<l

YUGOSlAV I A

IRON GAlES 2 I 9A4 DAPiUOE 7.40 "'25.0 281)00 1.50 62.5 CAI\OVEt 1919 DR AVA 18.55 250.0 42240 5.40 IB.O ;j ~

t'IANUFAC:TIIR~:H.;:

ALL15 ~ ALLIS CIIAL~~~~; A l.;.lllC:1; All '== A:: f.) II I'rl,: n = II AT l·i~lnll.~'i; ,1;: - ,jl'"•:•lf'l; r'f.- ··••:.IJ:,tJi'-1"1

f/r. tnAHA/~llUJ:!l';JI~; ~J t.:iCitfR WY~O~; fr: - f'IJ.IJ rU:t·1:11c; r." :.. r;,,·;t: M".'J.\ :; !I= dJT.\Citl; .J "' ,I .:I'"')"IT;

.J ~; .J f:IJ r.ONT-:iCII N r: IIJ Eli; Kll 1\li~EP'Ii:.rt ll1t'IG; 1\'1:.: - t.A<'I.:ill\11~ :1:1\~ lJ'.~;" ·;r·nr·~f\1'~

1.:-o.:~"' l.i:!HNt;(t~O 11r.T"J. h'OR"-:~; ,),\ :- !",1\(E:h; ,, f"''lf:;lll\1';11(; 'i •.;rt.L (::11 :11·, JriR:IPFo ''I .-.~•·J.J:' 1 "i ,Ill ·····r~ .. ·l'J);

"F.YHIC; NO NOJ!r\B; ntv,,; ;.<i - SLI!Pii:rntr!-.a.·>rJw;uqu:;f; •"j()::·ltlt',; v .o, - v•1: ·; r- r, 1.1' ,., .. ;

Vrl l'fll; v -( VEVtY-LIIAil~lti.L~S:

DRAFT TUBE DIMENSIONS FOR BULB TURBINES

-------------------------------------------------------------------------------------·-------------------------------------------:; TAT I 011 Y E.~ H D lh- c 0 A F' (~ ,\ .J ;\ .. , ~ ·;' . -

MET E:l e 0 !\ c··· I I:) r~ ·~

--------------------------------------------------------------------------------------------------------------------------------URSTF.IN 1Yf><J lj. 'l~ 73. 14 11. 2 r, 7"1.14 - - 7 l. 111 1 'I. l 1 l. H v A LTENWOH'fil 1'l76 h. 70 10 5. 6B Pl. fl5 1 or,. 6H - - 1 2). 7 2 .!;>. ') ~~ .- J • , ' " A U\i Iti!JE!l-AS. 1 ') 7'J h. 4 7 105.68 1'). 91 1 ')r,. €r8 - 1 2.1• 7 I ~ 7. ('\ ~ ~. ~' v A Ulll:-l DEN-AS. 1 '}7'1 6.45 11) 5. f,B 1">. 4 0 10 5. hd 11 h. OJ - 1 <>2. n - - v ,· M ELK 1J:l2 7. 10 124.69 17. 1 () 1 or,. htl lj 'l. ')0 - 122. 7!. H.) ·~ r) • r 1 v G fl(;lf ftiSTEl N 1 ')fill d. 10 14 3. 14 1q.6Q 1 o:,. h8 "2. 1 J - 17.2. 72 l1. ,"\ J? • cl v" !< l.t:IN11TJ EtiCliF:~ 1 '17!! J • c,r, .1&. J2 'l.60 3o. 32 311.')1) - 30. 1 ') - v .. i1 il ,J I T f1 :H~ 1'184 7. J.O 1 2 ·~ • (,'I 1(). 4 5 1 2ll. fJ9 - 11'1. 71) l '). ') .10. r) v h ;1 1\ K A P IJ B !1 A 1 '1113 b. 20 95.0.1 1~.J'J 'J 'J. 0 J - ll. '):.t 1 ,, • 17. - - 'l' A .. ~ VAJliKOSKl 1 9Hil 'i.HO 73.21 13. fJ7 7 3. 2'J - 1). i)~"J ;~r,. 112 - - T ~ .,

ARGENT/IT 1 'J'i7 J. ;w 40. 72 11. 3 0 - - - c, ('>. ')_ l - - v- (~

A[lt;ENThT 1 'l ')~ 1. 70 8. J ,) 1!.00 15 • .14 f\.l't") i. r, n fj. 11 - 1!- ,.

LA RhNCE 1 ');,(, 4. 35 57. 41 10.f:>O 7 1 • t.>J 20. 01G )f,. :~ n ,, 3. b 2 - - v-c ABZAC 19 ')ij 1. 2 j - 2. 2 j - - 1. ') 7 J. ) •) - 'J-C ...... i1AHCKOL:,IIEIM 1'l57 1. 60 19. h 3 S.60 ii. 04 rl. •) ') 7. 3 7 0"> t>. 1 r, - - v-c

0> :lAflODANGES 19 S'l O.'l7 - 2.'>0 - - 7.26 II. J I - - v-c RIHNAU 1960 ).60 1'1. fd s. 7 0 25. 00 - 1 J .0 G 11. 2) - - v -1'

GEHSTIIEIM 1967 5. 15 66.Lifl 14.75 f]Jl. j r, 1 'l. 7<1 21.20 7 'l. r,tl - v- ,. GEHSTilEIM 1 '} 61:) 3.60 1Q.61 5.60 1 (,. 00 - 1 1 • 1 () J.>. Pl - - v-c STHhS IJOUilG 1 'J71) 5. 2J 6 'J. llO 13. so 'lil. )b 1 Y. 7'l ). l. 70 7:1. ··,II - - v- :· FhNKEI. 1962 3. A2 b 9. 40 12.50 (,]. ,, f) - - 7ft. c-)

11 1 7. ;)'j /. 1 • r, v M UlJEN 1'J 62 J. i:J2 69.ll0 12.5 0 (,y. ll') - - 7•!. ,.,,, 17. "': .! 1. 0 v L F.llr.E N 1 'lt>6 J. 82 6 ':l. 40 12.50 69. 40 - - 1 fJ • r, II 17. fill ;>1. (I v UllSPiiiN<; 1'Hd 3.30 J 2. J7 9.30 ·u. n - - !2. 17 1?. 1 l 1 (,. <.) v ~iYI.'H~N3T~!N 1 'J 60 - - - - - - h. 1 ,, - ~ l .. r, v L E:CilSTUFE20 1YUll 3 • .10 25.52 9.)0 2S. S2 - - ~~ • .12 1 1 .. 1 7 1 r) • (, \' (; OTH Rl 1-:D 1 NG 1 '177 3.80 41. 8r1 10.5') 311. 2 1 - - JL 1>! 1•.). ']II 1 1. r v R £Hll tH;EN 1 '184 2.60 1 'l. b) 7.67 1'l. til - - 1 'l. t.J 1 ;>. ()7 1'). '> v SCIIODEN 1'1H4 2.60 1 'l. b) 7.67 19. ,, l - - 1'l. fr 1 1 2. 1)7 11). ') v SAN PEOHO 19tl2 1. 7l 9.0il .l. 'l ') 'J. Ofl - q. (J 1/. • J rl V-C GAMLEiJROf'OSS 1Y7J 4. 50 4h.')h A.OO - - 1 \I • 'l ,, 1 • ·l ') - ~: •·. "

DOVlKFOSS 1'J7S 7. 10 1 OJ. tl7 14. 20 - - 7'l. 7 Y1l. 'l" - K ,.. ·.;

SKOGSFOflSEN 1'15'1 2. 40 1 I~ • 1 9 7.50 - - 11. ·)f1 1 'l. ') J - - K ·: ·;

ll ALLEf'OR:; 1966 - - 8.40 - - 11. ')0 1 d. ,, ~) - - ~ '~ \.' SPF.flLINGSIIOLM 1967 - - 7. 30 - - 1•) • . !~ 12. q •l - - :\ ;.~ . ./ PARK I 1':171) ~.'JU (,'I .4 0 1 1 •. 10 - /).11'1 7<}. ;> 1 - - \("'' ' ~ V ITTJ AR Y 1 <j 74 &.GO - 1 3. 10 - - - - - - K ~~ ·.~

IJODUM 19 75 h.60 - 1 J. 10 - - .! ,, •• ~I) 1 0". 1i' - l\'1" L AliDA FORS 1 'l7u 7. 10 10 .l. A7 14. 20 - - /'!. 7 0 1 J'). )(\ - - K ·n;

~ 0"1 -...,J

SfATION

LJUSNEFORS 1\SFLJ: SODER FOR!) J IJV ELN TOHilON N liS 1 fl VF.S'l' II-Mll'l'fO!lS LILLfl F.DET 4 N AS2 c:JlAN!IUf'OilSEN W INZtl AU 'f fiSJO HOT I NG V IFORSEN IO,\HO FALLS PELTON REilEG.

MANUFACTURERS:

YEl\h

1976 19tl1 197'1 1'lB 1978 1 'l7 'l 198L

-1982 19fl0 1980 1962 1978 197fl 1982 1981 1982

lJili~ETF.il

7. 10 6. flO 7. 10 r,. 1 0 5. 20 6.60 5.00 6.45 7. 10 6.60 6.60 0.'10 11.60 5. 10 5.JO 5. 46 5. ll2

DRAFT TUBE DIMENSIONS FOR BULB TURBINES

c n "e F

103.87 1 4. 20 - -11).10 - - -113.10 1 2. 70 - -')6.75 11. JO - -bJ.o2 1 J. u 0 - -

11 3. 10 1 3. 00 - -113.10 15. 51 - -103.87 1 2. 50 - -137..73 12.d0 - -11 J. 10 1 J. 00 - -11A.82 1 3. 10 - -

2.54 3. 15 2. 5 1 ~ -46.J2 1 2. 115 116. J2 -c;H.Jo 111. 07 58.% -5!l.J6 13. 38 5U. 5& -73.90 1 ) • )() 73. 91) 4 1. 0 76.98 14. JO 76. 'Hl 4().7

r, r, o ,J K

- - - -'.n. '10 1 10. 2 II -2:l. 'I '1 111J.ij•l - -7.'>.01} i) l. I):) - -2'>. 20 6 >j. 'l /. - -2 7. 'i I) ')'}. 5 lj - -27.40 111. 1 r -2''· I, 0 1 Ji). lj 7 - -27. ,,o 1211. H') - -27. r> 0 '11. ')II -L9. 00 ·n. 5·1 - -

7. r,o 4.)() - -4.50 :n.'~'l - -~). 0 s /.(i.:. 2 -'). ·15 26.!+2 - -- 1 4 1. 1 'I - -- 77..3'1 - -

ALLIS = ALLIS CHALMERS; A ALSTIICM; AD = 1\NDHI'I'Z; [3 = BATlGNOTLfo:~; d:1 =~jJ(;~;rJFT; CL = cr~;~t!:;I!7-LOI·l~·:;

E/1': EBAH A/ :H; 10 ENS HA; Eil ESCitER WYSS; FE = FUJI ~:LECT:liC; r.M = r;ll!lZ rl!.V,\1:; 'I~ ;ITT.\CIII; .1 c J;::J''O'n';

JS JEUMONT-SCHNEIDEU; K£l KVAER'lER BH 1JG; K '1 li = 1\ II II L S 'I' ll fl S :'1 r. 1\ II :II ~; 1\ ~ V 1·~ in' :; T ,, fl ;

~ . .\~;II~-! CT nn !~r;

i\:lt' I·~ •; ~:

K '4 fl ,, ;\'1i:

t.; ,'' ~'

t; ~ ; .. · f'V" . ·' i<l·:·.; ".\'1,'·: y '" ., ~.;·:··:

v-c T' 'i

T \ '' T ,\ .,

v~

v ;\

1.:12 LENINGHIID ~ETAL WORKS; liA = 111\IER; MI = MITSIJ£J1Sill; :. = SF'AC (::>TF 01·::; FPfl~H·~s !''! ~"!'1\I.l'<!"; Llll C!r~IJ~;<JT);

N Nr:YRPIC; NO NOIIA!l; k RIVA; Sl< = SCBIIEIDEil-i<lt:STU!:;IfOUO.E; T ='fO:_j'!Jil\; v•. = V'Ji::;'f-~LI"l!!!o;

v VOITI!; v-c V EV EY-C IIA il!H I. u;s;

..... m co

!'OilER STATION

FINLAND

OKSAVA KALLIOKOSKI KALAJARVI HE RRFO RS FI NNIIOLII PADINGINKOSKI KATTILAKOSKI SOININKOSKI HATTAR KA NNUSKOSKI SIIKAKOSKI KUSIANKOSKI HANHIKOSKI KLAGARO

NEil ZELAND

11UNTALTO

NOWAY

DLAFALLI FLATEN FOSS ROSTEFOSSEN IIAGO A

SWEDEN

KA LSATER RATTORP KNISLINGE

DATE OF COI11USSIONING

1<J75 197b 197b 1978 1978 1979 19 79 1980 1981 1957 1959 1962 1967 1981

1980

1981 1969 1984

1976 1976 1976

T U B U L A R

NA11E 01' BIV ER

KALAJOKI PYilAJOKI SEIN AJOK All1A VANJOKI AHTAVANJOKI KALAJOKI AHTAVANJOKI KOKFIIAENJOKI AHTAVANJOKI

RANGITATA

IIA1REFJOBDEN NIDELV

ANDELVE!f

T U R D I N E

RATED READ (II)

10. 5 6.0

13.5 4.0 6.0 4.0

10.5 7.5 6. 1 4.6 3.4 8.8 7.06 3. 1

1. 1

27.0 10.0 9.5

7.2

6. 8 24.0 4.0

RATED PLOII

(rn3;s)

20.0 13.0 15.0 12.0 12.0 30.0 27 .o 22.0 20.0

31.0

36.7 60.0

12.0

D A T A

RAT ED CAPACITY PER UNIT

(KII)

2610 633

1802 4 10 635

1040 2540 14J3 1080

2 30 1015 250 755

2215

2000

A750 534" 1545

770

500 ROO 310

RUNNER DIA-... F.T Ell

(1'1)

2.40 1. b5 1. 7 2 1.72 1. 7 2 2.65 2.20 2.20 2.20

2.65

2.0<J l.20

1. 72

RUNNING SPEED (R Pl'1)

25'l.O 22 2. f) 300.0 167.0 222.0 141.0 250.0 2~0.0

179.0 250.0 10 5. n 500.0 250.0

flfl.O

HS

J. 6 5 3.59 0. 6 1 2.4b .1.26 4. ]J

1.] 0 3.60 2.<J5

159.0 3.8]

333. J -S.9b 167.0 1.30 2AO.O 214.0 4.46

306.0 765.0 27 3. 0

sir.~ A

0.61 1. Ob 0.70 1. 91 1. 12 1.10 o. 8l 0.85 1. 17

1'11\NUFACTifRP.R

Tl\1'1 TAI"' TIIM Tl\1'1 THI TA., TAI'I TAI'1 TAI"' TAll TAI'I TAP'! Tl\11 TAll

0.81 TAI'1

0.61 v-c n.A7 Tl\1'1

Tllrol 0.7f> TAM

TTl"' Tl\1"1 TAI"'

...... C"' 1.0

POWER STATION

SWITZELAND

LESSOC KALLNIICII

USA

SA WI'IILL SAWMILL TRAICAO TRUMAN LOWER PAINT TURNIP CHECK SWIFT RrtPID 10TH STREET P.E.C.22.7 AS HOKAN KENNEBUNK CONSOLIDATED PrtPER CO. ORILLIA WATEH,L.&POWER CITY OF NORWICH OZARK DAM WEBER FALLS CORNELL PROJECT DOLBY PROJECT BAKER lULL GISBORNE DEY. PROJECT BROWN PAPER COMPANY SALT RIVER PROJECT WOODWARD DAM GARYINS FALLS IMPERIAL IRRIGATION

DATE Of' COIII!ISSIONI NG

1973 1960

1981 1982 1960 1962 1964 1965 1965 1967 1972 1974 1976 1979 1979 1980 1960 1960 1960

TUBULAR

NAI'IE OF RIVER

SABINE AAR

ANDROSCOGGIN ANDROSCOGGIN

COLU!'IBIA

III SCONSIN SWIFT RAPIDS CONNECTICUT ARKANSAS OKLAHOIIA liiSCONSIN rlr.INE !lAINE NOVA SCOTIA !'lAINE ARIZONA CALIFORNIA NEW HAriPSRIRE CALIFORNIA

T 0 R B I N E

RATP.D HEAD (II)

20.7 17.5

5.3 5.3 7.0

13.0 6. 1 5.0

14. 3 4.7

15.8 21.3

'>.5 6.7

14.3 4.7

10.7 10.7 11. 0 14.6 14. 9 19.0 5.3

10. 6 14. 6 9. 1 6.9

RATED FLO II

(m3ts)

16.1 115.6

16.6 16.6

1]8 .o

50.0 12. 7 7.4

35. 5 21. 0 36.0

290.0 290.0 107.0

JJ. 0 11. 5 22.0 19.0 17. 0 23. 5 42. 0 311.0

D r. T A

Rnf.D CAPrtCITY PER UNIT

(KW)

2940 7050

760 8.27 257

3 1500 116 420

2500 1441) 6'>"0 2430

301) 2090 2610 1490

2 5200 25200 10400

4237 1500 3700

877 1560 3000 ]3Fl0 2070

RU~INP.R

DIA"F.TER

("')

1.7 2.5

2.'1 2.0

6.5 0.75 1.5 2.0 2.75 2.n 1. 4 1.22 2.794 1.956 2.794 A.OOIJ 6.000 11.651) 2.290 1. '>00 2.000 2.000 1.750 2.000 2.750 2.'>00

RUNNING SPEED (RPI'I)

HS

4]2.0 0.60 250.0 -6.6'1

514.0 216.0 277.0 12'1.6 225.1) 401).0 323. () 150.0 277. 'l

12 9. 0 60.0 60.0

100.0 212.1) 306. 0 26 2. 0 194.0 237.0 21 3. 0 16 R. '> 176.0

-0.4(1

3. A 1

1. 35 2.00 J. 00 1. O'l 1.00 1. 08 0.45

SIG.,A !lldW'PACTURER

o.41 v-c o. 'H v-c

0.97

0.54

0.59 0.40 1.27 O.R1 0.61 0.99 1. 4 0

ALLIS ALLIS ALLIS ALLIS ALLIS ALLIS ALLIS ALLIS TAM TAll ALLIS ALLIS AI. LIS ALLIS ALLIS ALLIS ALLIS ALLIS ALLIS ALLIS ALLIS 1\LLTS ALLIS ALLIS IlLLI S

-" 0

POWER STATION

WOONSOCKET FALLS IHLEY IHLL BLACKSTONE FALLS WELLS RIVER CITY OF STURr.IS SH 11\IMUT

DATE OF CO~I"JIS

SJONI NG

1981 1981 1981 1981 1982 19 82

T U B U L A R

NAIH 01" RIVER

RHODE ISLAND !lA INE BIIODE ISLAND VER!IUNT PIICHIGAN PlAINE

T U R f3 I N E

RATED HEAD (1"1)

5.9 6. 1 4.0

22.9 7.6 6.4

RATED f'LOW

(m3;s)

23.0 26.0 12. a f>.O

12. I) 35. 5

D A T A

RATFO CAPAC TTY PER UNIT

(K W)

11 33 1390

4 20 1150

fl1() 2000

RUNNER 0111-IHfER

(~)

2.000 2.25rJ 1.hi)Q 1.000 1.'iO'l 2.750

RUNN IN(; SPEED (HPM)

2011.0 177.0 200.1) 6'l'i.O 294.0 161).1

HS

1.70 -:~.2A

1. 40 -').50

0. J'j

1. 6fl

STG,.. A

1.42 2. 0 1 2. 1 A 0.67 1. 25 1 • 3 1

M~NU'F'AC

TURf.R

IlLLIS ALLIS IlLLI S II !.LIS II I.I.T S ALLTS

------------------------------------------------------------------------------------------------------------------PIANUFACTURER:

ALLIS = ALLIS CHALPIERS; TA PI TAMPELLA; V-C = YEVEY-CHARI"JILLES;

CROSSFLCW 'IURBINES

------- ------------- --NAME OF DATE OF NAME OP RATED RATED RATED RUNNER TURBINE PO WEB COM IUS- RIVER HEAD FLOW CAPACITY DIAMETER RUNNING STATION SIONING (M) (M /S) PEB ONIT (fi.l) SPEED

(KW) (RPM}

---------------- ----AUSTRIA

KROHLACHNER 1979 • 4.8 5.85 228 1. 0 90.0

BELGIU!!

JOSEPH GAl'.~ BY 1970 4.25 3.1 124 0.8 97.0

CANADA

GOUIN 1975 S'I.t!AUBICE 12.5 3.0 306 0.8 180.0 RODDICKTON 1980 MARBLE 42.0 1.29 440 0.6 450.0 KINGCC~E 1982 KINGCOL'!E 147.0 0.072 84 0.4 1200.0 GRAET FALLS 16.76 235.8 35660 5.87 112.5 POI~TE-DE 13.72 250. 1 30950 6.23 97.3 EIOS

FRANCE

CERNAY 1981 3.0 6.00 377 1.0 177.0

PORTUGAL

ALMONDA 1966 8.25 4.55 294 0.8 143.0

SWEDEN

BANS- 1Y81 S.H 4.33 2G5 O.H 123.0 GAiiDAE~~AS

BOSAGENS 19UO 6.95 7.00 J96 1. 0 113. 0

SWITZERLAND

NIEDERGLATT 1965 9.33 4.8 353 0.20 152.0

171

CROSS FLOW IURBDlES

--- ---- --NAME OF DA'IE O.F NAME OF RATED RATED BATED BONNER TORBDIE POWER CO MMIS- RIV Eft HEAD FLOW CAPACITY DIAMETER RUNNING STATION SIONING (!1) (M /S) [lER ONIT (M) SPEED

(K W) (RPM)

------- ---------- --------OSA

GOODYEAR 1980 9.8 8.5 654 1. 0 131. 5 LAKE 1 GOODYEAH 1980 • 9.8 11. 5 885 1.25 103.0 LAKE 2 COHNEL 1 1981 PALL CREEK 35.0 2.5 712 0.8 325.0 CORNEl 2 1981 PALL CREEK 35.0 3. 5 997 1. 0 261.0 BRADFORD 1982 WAITS 21.64 6.0 1057 1.0 195.0 BRADFORD 1982 WAITS 21.64 3.0 528 0.8 244.0 GEORGETOWN 1983 CANAl 57.00 0.974 708 0.6 618.0 SPOTTED BEAR 1982 • 37.19 0.26 52 0.3 800.0

YUGOSLAVIA

BE SOTESKA 1975 4.7 6.3 241 1. 0 84.0

172

STANDARD TUBULAR TURBINE WATER PASSAGE DIMENSIONS

----------------------------------------------------------------· MANUFACTURER DIAM- AE 11 L ft AO

METER ----------------------------------------------------------------· NEYPICERYPIC 0 .. 45 0.554 1 .. 72 4 .. 48 2.76 0 .. 64 NEYPICERYPIC 0 .. 63 1.039 2. 1 0 5.93 3 .. 83 1.254 NEYPIC 0.83 1. 839 2.70 7. 11 4.41 2.020 NEYPIC 1 .. 00 2.630 2.90 8.20 5.30 3.170 NEYPIC 1.25 4.600 3.20 9.66 6.46 4.930 NEYPIC 1. 50 5.515 3.70 11.:l3 7.53 7.08 NEYPIC 1.80 7.793 4.06 12.94 8.88 10.24 VOITH 0.50 1. 91 2.63 8.53 5.90 VOITH 0.70 1.91 2.63 8.53 5.90 VOITH 0.90 1.91 2.63 8.53 5.90 VOITH 1. 15 1.91 2.63 8.53 5.90 VOITH 1. 40 1.91 2.63 8.53 5.90 VOITH 1.70 1. 91 2.63 8.53 5.90 VOITH 2.00 1.91 2.63 8.53 5.90 VOITH 2.25 1. 91 2.63 8.53 5.90 VCITH 2.50 1. 9 1 2.63 8.53 5.90 VOITH 2.75 1. 9 1 2.63 8.53 5.qo VOITH 3.00 1. 9 1 2.63 8.53 5.90 ALLIS 0.75 1. 6 1 2.50 3.00 ALLIS 1.00 1.47 2.JO 3.00 ALLIS 1.25 1.41 2.20 3.00 ALLIS 1. 50 1.37 2.20 3.00 ALLIS 1. 75 1. 3 5 2.20 3.00 ALLIS 2.00 1. 3 3 2.00 3.00 ALLIS 2.25 1. 3 1 2.00 3.00 ALLIS 2.50 1. 29 2.00 3.00 ALLIS 2.75 1.27 2.00 3.00 ALLIS J.OO 1. 17 2.00 3.00 TAM PELLA 1.40 6.45 1. 50 8.25 9.00 TAMPI:;LLA 1. 6 5 9. 18 1.80 9.75 12.96 TA~PELLA 1.90 12.30 2.05 11. 2 5 16.81 TAL'IPELLA 2. 1 5 15. 18 2.30 12.70 2 1. 16 TAMPELLA 2.40 19.2 4 2.60 14.20 27.04 TAM PELLA 2.65 16.80 2.50 11.20 25.00 TAl'IPELLA 2.90 20.01 2.80 12.20 30.25 TAM PELLA 3.20 24.00 3. 10 13.50 36.00 TAMPELLA 0.90 3.20 2.40 5 .. 30 4.00

173

STANDARD TUBULAR TURBINE WATER PASSAGE DI~ENSIONS

MANUFACTURER DIAM- AE L1 L M AC METER

----------------------------------------------------------------· TAMPELLA 1. 15 5.00 3.05 6.80 6.25 TAM PELLA 1. 40 7.50 3.70 8.25. 9.00 TAM PELLA 1. 6 5 10.44 4.35 9.75 12.96 TAMPELLA 1.90 13.74 5.05 11.25 16.81 TAMP ELLA 2.15 17.48 5.70 12.70 21.16 TAMPELLA 2.40 21.84 6.35 11.20 27.04 TAMFELLA 2.65 26.97 3.80 11.20 25.00 TAMPELLA 2.90 32.13 4.20 12.20 30.25 TAMPELLA 3.20 38.64 4.60 13.50 36.00

174

APPENDIX 4

COMPUTER PROGRAMS

175

CMS PI IN DISK BULB4 DATA A (PEB!II;

* SAS PROGRAM FOR COMPUTING TORaiNE CONSTANTS CP BULB TYPE UNITS; • THE DATA OF THE BULB UNITS ABE IN A FILE NAMED BULB4;

DATA KOJO.NS; INr'ILE IN; LENGTH STATION $ INPUT STATION &$

C D E F

20; YEAR G H

PI = 3.14159265;

HEAD FLOw POWER J K;

W = (2.0*PI*SPEED)/(60.0); N11 = (SPEED*DIAM)/SQaT(HEA~);

Q11 = FLOW/((DIAM*•2)*SQRT(HEAD)); P 11 = POW E B I ( ( D I AM** 2 ) • (HE A I:** 1 • 5) ) ; NS = (SPEED•SQRT (POWER)) I (flEAD*'*1. 25); ws = W*SQRT (FLOW) I ( (9. 81•HfAD) ••O. 75); QCN = FLOW/SPEED; POH = POWER/HEAD; EFF = POiER/(9.81*FLOW*AEAD); PHI = (PI/(60.0*SQRT(2.0*9.81)))*N11; PHIFUN = (PHI*SQFT(HEAD))/SPEED; IF NS =. THEN DELETE; L N 11 = LOG 1 0 ( N 11) ; LQ11 = LOG10(U11); LP11 =LOG10(P11); L N S = LOG 1 0 ( N S) ; LWS = LOG10(loiS); LQON =LOG10(QON); LPOH = LOG 10 (POH) ; L D I AM = LOG 1 0 ( D I AM) ; LHEAD = LOG10 (HEAD); LEFF = LOG10 (EFF); LPO~ = LOG10 (POwEJ); LPHI =L0~10(PHI); LFLOW = LOG10 (FLOW); Li?HIFUN = LOG10 (PHIFUN);

176

DIAM SPE~D MANUF &$ B

* THE NOTATIONS BELOW REFER 10 TUREINE CIVIL WCBKS DIMENTIONS;

FPG = (F+G); DFG = (D + G) ; VEL = (FLO./E) ; DOE = (D/E) ; LFPG =LOG10(FPG); LDPG = LOG 10 (DPG) ; LVEL =LOG10(VEL); LB =LOG10(l3}; LC = LOG10 (C); L D = LOG 1 0 ( D) ; LE =LOG10(E); L F = LOG 1 0 (F) ; LG =LOG10(G}; L H = LOG 1 0 ( H} ; LJ = LOG 10 (J) ; LK =LOG10(K); LDOE = LOG10 (DOE); KEEP STATION YEAR HEAD FLOW POWER DIAM SPEED MANUF B C D E F

G H J K FPG DPG VEL N11 Q11 P11 NS iS QON POH DOE PHI EFF PHIFUN LN11 LQ11 LP11 LNS LWS LQON LPOH LHEAD LPOW

LDIAM LEFF LFPG LDPG LVEL LB LC LD LE LF LG LH LJ LK LFLOW LDOE LPIII LPHIPUN;

PROC ~RINT DATA=KOJC.NS PAGE; VAR STATION YEAR HEAD FLCW PG~ER DIAM SPEED MANOP B C D E F G H

J K N11 Q11 P11 NS WS QCN POH ~FF FPG DPG VEL DOE PHI PHIFUN LN11 LQ11 LP11 LNS LWS LQON LPOH LPOW LDIAM LHEAD LEFF LFPG LDPG LVEL LB LC LD LE LF LG LH LJ LK LDOE LFLCW LFLOW LPHI LPHIFUN;

177

SA~PLE COMPUTER PROGRAM FOR CC~FUTING REGRESSION aELATIONS

CMS FI KOJO DISK A A A; DATA INSET;

SET KOJO.NS; IF NS=. THEN DELETE; IF YEAR <= 1965 THEN GROUP =65; ELSE IF YEAR >1965 THEN GROUP =84;

PROC SORT; EY GROUP; PROC GLM DATA=INSET; BY GROUP; MODEL LNS=LQ11;

OUTPUT OUT=B.NEW01 (KEEP=GROUP NS LNS PLNS Q11 LQ11) P=PLNS; PROC PRINT; VAR NS LNS PLNS Q11 LQ11; EY GROUP;

PROC GLM DATA =INSET; BY GROUP; MODEL LNS = Lf11; OUTPUT OUT=B. NEW02 (KEEP=GROUP NS LNS PLNS P1 1 LP11) P=PLNS; PROC PRINT; VAR NS LNS PLNS P11 LP11; BY GRCUP;

PHOC GLM DATA=INSET; BY GROUP; MCDEL LP11=LC11; OUTPUT OUT=B.NEW03 (KEEP=GROUP P11 LP11 PLP11 Q11 LQ11) P=PLP11; PROC PRINT; VAR P11 LP11 PLP11 Q11 LQ11; BY GROUP;

PROC GLM DATA=INSET; BY GROUP; MODEL LNS= LN11; OUTPUT OUT=B. NEW04 (KEEP=GROUP NS LNS PLNS N11 LN11) P=PLNS; PRCC PRINT; VA~ NS LNS PLNS N11 LN11; BY GRCOP;

PROC GLM DATA=INS~T; BY GROUP; MODEL LPHI= LP11; OUTPUT OUT=B.NEQ05 (KEEP=GROUP I:HI LPHI PLPHI P11 LP11) P=PLPHI; PROC PRINT; VAH PHI LPHI PLPHI P11 LP11; EY GROUP;

PROC GLM DATA=INSET; BY GROUP; MOtEL LPHI = LNS; OUTPUT OUT=B.NEW06 (KEEP=GROOP PHI LPHI PLPHI NS LNS) P=PLPHI; PRCC PRINT; VAH PHI LPHI PLPHI NS LNS; EY GROUP;

PROC GLM DATA=INSET; BY GROUP; MODEL LDIAM = LPOH; OUTPUT OUT=B.NEW07 (KEEP=GROUP DIAM LDIA.ll! PLDIAM POH LPOH} P=PLDIAM; PROC PRINT; VAR DIAM LDIAM PLDIAM POH LPCH; BY GROJP;

PHOC GLM DATA=INSET; BY GROUP; MCDEL LDIAM = LPHIFUN; OUTPUT OUT= B. N EW08 (KEEP=GROUP DIAM LDIAM PLDIAI1 P:HFUN LPHIFUN)

P=PLiHA:1; PBOC PRINT; VAR DIAM LDIA~ PLDIAM PHIFUN LPUIFUN; BY GRCUP;

178

SAMPLE SAS GRAGH PROGRAM FOR PLOTTING GRAPHS OF REGRESSION RELATIONS

C~S FI B DISK A A A; DATA INSET;

SET TUBE.NEW01; SET TUBE.NEW02; SET TUEE.NEi03; SET TUBE.NEW04; GOPTIONS DEV=TEK4662;

PROC GPLOT; PLOT LAE*LDIA~; SYMBOL1 I=RL V=: L=1; SYMBOL2 I=RL V=PLUS L=2;

TITLE1; FOOTNOTE .H=S FIGURE 98.LOG OF ENTRANCE AREA VERSUS LOG OF RUNNER DIA~

METER FOR STANDARD TUBE TURBINE; PHOC GPLOT; PLOT LAO*LDIAM; SYMBOL1 I=RL V=: L=1; SYMBOL2 I=RL V=PLUS L=2;

TITLE1; FOOTNOTE .H=5 FIGURE 99. LOG OF EXIT AREA VERSUS LOG OF RUNNER DIA~ETER FOR STANDARD TUDE TURBINE;

PROC GPLOT; PLOT LL1*LDIAM; SYMBOL1 I=RL V=: L=1; SYMBOL2 I=RL V=PLUS 1=2;

TITLE1; FOOTNOTE .H=5 FIGURE 100. LOG OF L1 VERSUS LCG CF RUNNER DIA~ETERFOR ST ANDARD TUBULAR TURBINE; PROC GPLOT;

PLOT LM*LDIAM; SYMBOL1 I=RL V=: L=1; SYMDOL2 I=RL T=PLDS L=2;

TITLE 1; FOOTNOTE .H=5 FIGURE 101. LOG OF M VERSUS LOG OF RUNNER DIAMETER FOR STA NDArtD TUBULAd TUREINE;

179

APPENDIX 5

LIST OF TURBINE MANUFACTURERS

180

liST OF TURBINE MANUFACTURERS

Manufacturer Name Address Phone Contact Contact Person Type of Units

·I. Ateliers Bouvier 53 rue Pierre-Semard (76) 96.63.36 P, F, K, T 3800 Grenoble (France)

2. All is Chalmers P.O. Box 712 (717) 792-3511 Helmut Wirsha 1 P, F, K, B, T

3. Barber Hydraulic Turbine, Ltd. York. PA 17405 (USA) Sel im Chacour Barber Point Box 340 Port .Colborne. Qntar:io. l3K 5Wl Canada (41fi)R14-Q103 M. R. Wfhnn p • F

4. Canyon Industries 6342 Mosquito lake Road (206)592-5552 Don New p

5. Dependable Turbines. ltd #7-3005 Murray St. (604)461-3121 Robert Prior P, F, K, Tu Port Moody, B.C. V3H1X3 (Canada)

6. Escher Wyss, ltd CH-8023 (01) 44.44.51 Dimtri Foca P, F, K, T Zirich, Switzerland (Swiss) Sulzer Bros. Inc. (212)949-0999 200 Park Ave. New York, NY 10017 (USA)

..... 7 . General Electric Installation & Service Engineerinq (518)385-7097 D.W. lyke P, F, T co Division-Small Hydro Operation (480)974-4729 P.O. Box 6440 ..... One River Road Salt lake City, UT

Schenectady, N.Y. 12345 84106 8. Gilbert Gilkes & Gordon, Ltd Kendal Cumbria lA9 7BZ England (0589)20028 O.S. Shears P, F, T, Tu

Gilkes Pumps Inc. P.O. Box 628 (713)474-3016 Alan S. Fife P, F, T Seabrook, TX 77586 (USA)

9. Hitachi, ltd. 6-2 Otemachi, Chiyoda-ku (03)270-2111 M. Suzuki P, F, K, T Tokyo 100 (Japan)

10. Hydro-Watt Systems 146 Siglono Road Mert. J. Junking P, C Coos Bay, OR 97420 (USA)

11. Independent Power Developers, Inc. Route 3, Box 174H (208)263-2166 W i II i am De 1 p P, C Sandpoint, IO 83864 (USA) Charles Green

12. AB Karlstads Mekaniska Werkstad Fack S-681 01 0550/15200 Hans G. Hansson P, F, K, T KMW or KaMeWa Kristinehamn (Sweden) lars-Erik lindestrom

13. Kraerner Brug A/S Kvaernerveien 10 (472)676970 James Victory P, F, K, T Oslo 1, (Norway) Kvaerner Moss, Inc.

(212)752-7310 31st Floor, 800 Third Ave. New York, N.Y. 10022

14. James Leffel & Co. 426 East St. (513)323-6431 Kim Brock! P, F, T Springfield, Ohio 45501 (USA) Kenneth W. Berchak

15. leroy Somer Boulevard Marcellin-Leroy 003345.62.41.11 B.P.119-l6004 Angouleme (France) NEEDS New England Energy Development Systems, Inc. 109 Main St. ( 413)256-8466 Michael Pill T Amherst, MA 010002 (USA)

16. little Spokane Hydroelectric P.O. Box 82 (509)238-6810 Mike Johnson P, T Chattaroy, WA 99003 (USA)

....... 00 N

Manufacturer Name

17. Mitsubishi Heavy Industries, Ltd.

18. Neyrp ic

19. Obermeyer Hydraulic Turbins, Ltd

20. Ossberger-Turbinenfabrik

21. Small Hydroelectric Systems

22. Tampella

23. Toshiba

24. Vevey Engineering Works, ltd

25. J.M. Voith GmbH

B = Bulb turbine C = Cross-flow turbine F = Francis turbine K = Kaplan turbine

LIST OF TURBINE MANUFACTURERS (continued)

Address

5-1 Marunouchi 2-chome Chiyoda-ku Tokyo (Japan) Groupe Creusot-loire B.P. 75 Centre de Tri 38041 Grenoble Cedex (France) GE/Neypic 969 High Ridge Road Box 3834 Stanford, CT 06905 (USA) 10 Front Street Collinsville, CT 06022 (USA) D-8832 Weissenburg/Bay Pastfach 425 Bayern (West Germany) F.W.E. Stapenhorst, Inc. 285 LaBrosse Ave. Pointe Claire, Quebec H9R 1A3 (Canada)

Phone Contact

Tokyo 212-3111 (415)981-1910 (76)96.48.30

(203)322-3887

(203)693-4292

0 91 41/40 91

(514) 695-2044

5141 Wickersham (206)595-2312 Acme, WA 98220 (USA) Engineering Division SF-33100 Tampere 10 (Finland) Power Apparatus Export 1-6 Uchisaiwai-cho , Chyoda-ku, Tokyo 100 (Japan) 1800 Vevy (Switzerland) P.O. Box 1940 07920 Heidenheim (West Germany)

P = Pelton turbine T = Tubular turbine Tu = Turgo turbine

(931)-32 400

(021) 51 0000 51

(07321)32.25.61

Contact Person Type of Units

Kenji Fukumasu F, 0 Billy M. Tanaka lucien Meqnint

Michael Guer P, F, K, B, T

P, F, B, T, C

F.W.E. Stapenhorst

William Kitching P

Georg von Graeveniyz P, F, K, B, T

Hideki Yamada

J. P. Kaufmann P, F, K, B, T

Peter Ulith P, F, K, B, T Franz Wolfram

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