computer-aidedanalysis of hydraulic reaction turbines · 2018-06-26 · hydroelectric, reaction...

Computer-aided analysis ofhydraulic reaction turbinesF. MOUKALLED and A. HONEIN, Faculty of Engineering &Architecture, MechanicalEngineering Department, AmericanUniversityof Beirut, PO Box 11-0236, Beirut, Lebanon

Received 30th October 1995Revised 6th February 1996

A microcomputer-based educational software package designed to help mechanicalengineering students 10 understand hydraulic reaction turbines is described. The software isinteractive, menu-driven, and easy-to-use, is written in the Pascal computer language, andruns on IBM PC, or compatible, computers. The program can handle radial, mixed. or axialflow turbine problems by solving for unknown variables through a complete set of equationscovering the turbine installation. Using similarity laws, model-prototype problems oroperation under different conditions can also be tackled. Furthermore, the program isequipped with graphical utilities that include many diagrammatic sketches of reactionturbines, some recommended charts, and the possibility of drawing velocity triangles whencorresponding variables are available. The most important feature of the package is anoption that allows one to plot the variation ofany parameter versus any other one. Throughthis option, the student can easily understand and discuss the effects of varying designparameters on the overall performance of the machine. Finally, some special features thatare important in making the package user-friendly and encouraging-to-use are alsoavailable, and the comprehensive example problem provided demonstrates the capabilitiesof the package as an instructional tool.

NOMENCLATURE

bphh'h"

HIH2HBHenh

nsPalmpephpis

brake power (W)net head (m)effective head available at runner inlet (m)extracted head from water that is transmitted to the runner (m)total energy head at runner inlet (m)total energy head at runner exit (m)total energy head at inlet to the scroll case (rn)total energy head at tailrace (rn)hydraulic efficiencyspecific speed (N m-3/2 s-3)1/2atmospheric pressure (N/m2)

water power at runner exit (W)hydraulic power loss (W)power input to shaft (W)

International Journal 01MeclvJnical EnginMring Education Vol 25 No 2

74

U2

VIV2

v2

Va2VrgVlgVUI

VU2

ZB

ZBmax

F. Moukalled and A. Honein

water vapour pressure (N/m2)

rotative speedrotative speed at maximum efficiencyvolume flow rate flowing in runner (m3/s)

radius of runner at which water enters (m)radius of runner at which water leaves (m)torque input to shaft (N m)runner velocity at exit (m/s)absolute water velocity at runner inlet (m/s)absolute water velocity at runner exit (m/s)relative water velocity at runner exit (m/s)axial water velocity (m/s)radial water velocity at exit from the guide vanes (m/s)tangential water velocity at exit from the guide vanes (m/s)tangential water velocity at runner inlet (m/s)tangenital water velocity at runner exit (m/s)elevation of the scroll case assembly above tailwater (m)maximum elevation of the scroll case assembly above tailwater (m)

angle between VI and ul (degree)angle between V2 and u2 (degree)direction angle of the guide vanes (degree)inlet angle of runner vane (degree)exit angle of runner vane (degree)specific weight (N/m3)

density (kg/rrr')cavitation parametercritical cavitation parameter

INTRODUCTION

The recent rapid evolution in the development of reliable and cheap microcomputers hasbroadened their accessibility and utilization and has influenced the teaching/learning approach in almost all disciplines. Research has shown that [1] students from all disciplinesstudying at their own pace using student-oriented computer programs demonstrate increasedmotivation which translates into improved achievement of course objectives. In the area ofengineering curricula, the use of computer-based learning tools not only allows students tolearn difficult concepts by interactive dialogues, but also offers the possibility of trainingthem in problem-solving skills. This is achieved by designing easy-to-use programs [2-7]that allow students to tackle a wide range of applications of a certain principle by employingvarious types of problem-solving approaches. Therefore, teaching methods using personalcomputers seem to best complement an engineering education.

Hydraulic turbomachinery is an important area within mechanical engineering that dealswith the design and operation principles of hydraulic turbines and pumps This topic isusually introduced to mechanical engineering students in a course on applied fluidmechanics. Details of the subject matter can be found in most fluid mechanics textbooks(e.g. [8-11]). An important category of hydraulic turbomachines is the hydraulic reactionturbine. In addressing hydraulic reaction turbine problems, beside computing velocities,

International Journal ot Mechanieel EngiMering Education Vol 25 No 2

Computer-aided analysis of hydraulic reaction turbines 75

losses and other variables, the main aim is to study the effects of varying certain parameterson the performance of the machine and to investigate conditions that minimize losses andmaximize power and efficiency. Owing to the extensive computations involved, handcalculations are not feasible. This forces the student to investigate, at best, the effects onmachine performance of varying some selected variables and to accept without proof theeffects of varying the remaining parameters. The majority of engineering students now haveaccess to a personal computer and can benefit from the advances in this technology (speed,graphical capabilities, etc.) to solve the above time-consuming problem.

To this end, this paper describes REACTION, a microcomputer based, interactive, andmenu-driven software package developed at the American University of Beirut for use inexploring the effects of design changes on the performance of hydraulic reaction turbines.REACfION relieves the mechanical engineering student from the monotonous task ofperforming repeated hand-calculations, it is much easier to use than a spreadsheet, which isstill time-consuming as it requires development of all equations and formatting of graphics.

THE HYDRAULIC REACTION TURBINE

A hydraulic reaction turbine is one in which a water pressure drop occurs through both theguide vanes and the rotating runner vanes. The two types of reaction turbines in general useare the Francis turbine and the propeller turbine. The flow through these types is classifiedwith respect to the flow line direction at entrance and discharge edges of the runner. For theFrancis type, the design may be purely radial flow, where both entrance and discharge edgesof the runner vanes are parallel to the axis of rotation (Fig. l(a»; radial flow, where thedischarge velocity has both radial and axial components (Fig. l(b»; or mixed flow, whereflow lines have radial and axial components throughout the runner vanes (Fig. l(c». For thepropeller type, both entrance and discharge edges of the runner vanes are perpendicular tothe axis of rotation (Fig. l(d». The transformation of potential energy into useful work in ahydroelectric, reaction turbine-based, power plant is described next.

After exiting the penstock (Fig. 2(a», water enters a scroll or a spiral case (Fig. 2(b» andthen moves through a series of guide vanes where the flow is accelerated and given a definitetangential velocity component. For large turbines, stay vanes exist between the entry to thescroll case and the guide vanes; their main function is to support the weight of the generatorabove the runner. Water velocity also increases in flowing through these vanes because oftheir decreasing cross-sectional area. After leaving the runner, water enters a draft tube (Fig.2(a» which has an increasing cross-sectional area so as to reduce the flowvelocity. and hence the head loss at submerged discharge.

For a reaction turbine the net head is defined as the difference between the total head atentrance to the scroll case and that at the tailrace (Fig. 2(a»

(I)

The head effectively available at the runner. h', is the difference between the net head andthe head losses in the draft tube and at submerged discharge. The head h" that is extractedfrom water and transmitted to the runner is the difference between h' and head losses in thescroll case. guide vanes, and runner vanes. The extracted power rQh" is further degraded bybearing friction and air resistance losses to yield shaft power.

Applying the angular momentum equation for a control volume enclosing the runner, thetorque input to the shaft [8] is found to be

International Journal 01Mechenical EngiMering Education Vol 25 No 2

Axial-Flo" ~uJic Turbine

76

(a)

(c)

F. Moukalled and A. Honein

RwIia1-FIo" Francis Turbine

~

'~~I UI\...1 \u...l

o..l"''''_ _.~Url......1'1_

(b)

(d)

Fig. I. Schematic of hydraulic reaction turbines.

(2)

where the meanings of the terms in the above equation and the equations to follow are asindicated in the Nomenclature. Using the above equation, corresponding equations can bederived for the tangential force, hydraulic and overall efficiencies, output power etc., and arenot presented here for compactness.

The specific speed of the reaction turbine is defined as [8]:

(3)

As given by the above equation, the specific speed is not a dimensionless quantity. However,units are omitted in this paper in conformity with adopted practices in the literature. ForFrancis runners, when using the 51 system of units, specific speeds range from 40 to 400; for

International Joumal 01Mechanical EngiMering Education Vol 25 No 2


Reaction Turbine Installation

(a)

I j~~l ': OI~ -,

O. r> : . U.

: 'Ur>

( b)

Spiral Caset-..elton <.> : Inlet

to ttMi acroll e•••2-sec:tion (b) : Inlet

to the ata... "an4la2-.-etlon (c) : outl.t

'ron tt-. at.., ",.,...a""-• .etlon Cd) : Inlet

to the eu IlM:d vanes .V.loclt" trlan"l••are ldent lea. to tho••of the prec:edln9 ••ctIon. wi th Ud.. Utd .. andUrd 1m-leAd

S-section <,) : outl.tfrDf' the ., ldH ,,-.w• .U.locUw trl~l••are ldenl leal to tho• •of the precedlrtlil ••ctlona w lth Uv . Uttl .. ..-.dUrw Inat.Ad

B-lnn.r disk

Fig. 2. (a) Reaction turbine installation; (b) scroll case assembly.

Intemalional Journal 01Mechanical Engineering Education Vol 25 No 2

78 F. Moukalled and A. Honein

propeller runners, where high power output is obtained under low heads, the range is from400 to WOO.

Finally, cavitation occurs in reaction turbines whenever the local absolute pressure dropsto the water vapour pressure at the given temperature. This results in pitting, mechanicalvibration, and low efficiencies. The critical factor in predicting cavitation is the verticaldistance from the runner to the tailwater ZB (Fig. 2(a», and it is used to define [8] acavitation parameter a with the following equation

o =Patm/r- pv/r-ZB

h(4)

The minimum or critical value of the cavitation parameter eTc [8], which is determinedexperimentally as a function of the specific speed, sets a maximum limit for the elevation ZB

given by

ZBmax = Patm/r- pv/r-heTc (5)

For complete details of the subject matter and of the equations used in the program, thereader should consult reference [8].

DESCRIPTION OF THE PROGRAM

The program is written in the Pascal computer language using the Turbo Pascal compiler,version 6 [12J, and it runs on IBM PCs, or compatibles. The PC environment was chosen toprovide an easy-to-use and cost-effective workstation. The user-friendly, menu-drivenstructure of the program provides a powerful teaching aid.

The software is divided into three major modules. The first provides menus and dataentry windows for variables and assumptions. These windows can also be used for separatedata retrieval. A complete set of mostly used unit systems is available, and the user can inputand view each variable in any system of units. The purpose of the second module is to solvefor unknown variables in an iterative manner, using the appropriate set of equations. The roleof the third module is to output results in tabular forms employing either the Imperial or the51 system of units. An important feature of the program is its ability to plot the variation, as afunction of a chosen variable, of up to five quantities at a time. Finally, diagrams of the inletand discharge velocities can be drawn if corresponding data are complete.

Other options and features are also included to facilitate its use and enhance itscapabilities. The first option is a file-handling utility that allows saving, opening, printing,and deleting data files consisting of input and output data for problems. Using this option,easy correction of erroneous or missing data is permitted. Moreover, this facility allows theuser to return variables to their initial or previous values. Another feature of the programconsists of three recommended charts [8] (Figs 3(a), (b) and (c) showing the variation ofsome variables versus others. The user can retrieve values from the charts, and data can beused directly in solving problems requiring some initial assumptions and guesses. Alsoincluded in the package are graphical utilities consisting of six diagrammatic sketches of thereaction turbine [8J. The first (Fig. 2(a» shows the turbine installation. The following foursketches (Figs I (a), (b), (c) and (d) illustrate the various types of reaction turbines, and thefinal one (Fig. 2(b» displays the spiral case assembly. These sketches help clarifying andvisualizing some variables used in the software (dimensions, head losses, velocity triangles).Furthermore, the program is equipped with an on-line help, for all available options, so as to

International Journal 01Mechenical Engw-ring Education vol 25 No 2


j=1!fOOh."~~:=:F::=!;;;~.1~~r-=:\=~¥R=...

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no

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r. r el_ .r.n M'" C", lft ..

(c)

(b)

Fig. 3. (a) Recommended optimum values of turbine efficiency at a given specific speed; (b)recommended turbine dimensions and characteristics at a given specific speed; (c) recommended

limits of specific speed for hydraulic turbines under various effective heads.

guide the user and to permit his learning about the utilities of the software easily. Finally,errors in any input operation, errors that will stop the execution of the program, and illegalinput values for variables (negative dimension or loss factor greater than one) are carefullyprevented.

The hierarchical structure of the software is shown in Fig. 4. The program is menu-drivenand every interaction with the user is done in a user-friendly environment. The executionstarts by typing REACfION at the DOS prompt, which causes the small menu to bedisplayed leading to the main menu which offers eight entries (Figs 4 and 5). By selectingthe first entry (HELP), the user can access some information and instructions related to thesoftware. The second entry (FILE) permits loading previously saved problems in addition

International Journal of Mechanical EngiMering Education Vol 25 No 2

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to saving, printing, and deleting data files (Fig. 5(b), left-hand side). To start a new problem,the INPUT entry should be chosen. Here the student may select sub-entry MODEL orPROTOTYPE. Entry PROTOTYPE should be picked if similarity laws are to be invoked.Having decided on a sub-entry, known variables may be entered to the program. As depictedin Fig. 5(a), the menu-driven structure of the package facilitates this task by guiding the userthroughout the data-entering procedure. Solution is then obtained by choosing the SOLVEentry. At this and the previous stage, data can be saved in a file that can be read at any latertime. Results can be viewed using the OUTPUT or the INPUT entries (Fig. 5(b), lower lefthand side) and can be printed using the FILE entry. The effect of varying a parameter onother parameters is obtained, as shown in Fig. 5(b), in the VARIATIONS entry. This facilityallows a comprehensive analysis of the different parameters involved in the problem andpermits the optimization of the machine performance. The recommended charts (Fig. 3) andthe diagrammatic sketches (Figs I and 2) can be accessed through the CHARTS andORAWINGS entries, respectively. Using also the last command, velocity diagrams can bedrawn.

If the IBM 'graphics' module has been loaded at the beginning of the session, a hard copyof figures displayed on the screen can be obtained using the 'Print Screen' command with asuitable printer.

EXAMPLE CALCULATIONS

In this section, an example problem demonstrating the computational and graphical capabilities of the program and how it leads to a deeper understanding of the subject material ispresented. Records of the input and output data of the problem are listed in Table I. The taskis to select the outlet angle of the inlet guide vanes (ag) , the decision being based onoptimizing some performance parameters such as power input to shaft (Pis), net head (h),

and hydraulic efficiency (nh)' The variation of the power input to shaft is depicted inFig. 6(a). To generate this or any other plot, the user should select the x and y variables bychoosing the VARIATIONS entry from the main menu (Figs 4 and 5(a». Having done this,the user will be asked to specify, in simple dialog boxes, values for the low and high limitsof the x variable, y variable(s) (maximum number of five), and the corresponding pair ofsystem units. The resulting specification will be shown in a window similar to the one on theright-hand side of Fig. 5(b). Then, by choosing the plot command, the x interval will besubdivided into 45 sub-intervals and the problem will be solved 45 times in order to computeand store y values for the graphical plots.

As shown in Fig. 6(a), the power input to shaft (Pis) maximizes for a definite value of ago

To understand this behaviour, the plots of Figs 6 and 7 and the following explanation areneeded. Since the mass flow rate is constant, the radial velocity of water at exit from theguide vanes (Vrg) should be constant. Then, as ag increases, the tangential water velocity atexit from the guide vanes (Vlg) will decrease (refer to the velocity triangle in Fig. 2(b».Since by neglecting losses the moment of momentum in the space between the guide vanesand rotor inlet is conserved, the tangential water velocity at rotor inlet (VUt) should decrease,as depicted in Fig. 6(b). Since the losses in the stay and guide vanes are neglected, the totalhead at inlet (HI) will be equal to the total head at inlet to the casing (HB) and will remainconstant at constant mass flow rate. Therefore, the decrease in VUI at constant head (HI) androtational speed (rpm) will lead to a decrease in the tangential water velocity at exit (Vu2)

(Fig. 6(c», work being done on the rotor. Now, with the aid of the velocity diagram at existshown in Fig. I(d), the decrease in VU2 at constant runner velocity (u2) and axial water

International Journal of Mechanical Engineering Education Vol 25 No 2

Tab

le1.

Inpu

tan

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data

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'a ..aa:..

,-- : I j-t -t- +--+ -+-! l j

: I..an.c. ~il+!-t-+-+!-+-

l 1 '1 i• .uc... __ .L--L_. I 1 ,

10 .000 82 .500 . " .000 57 . 100

(a)

i .i ,o .1'57 h + - t-- t-+ -+- +-+--i, iI !

+---+--+-+-+--11-1i I

i i i !; ..... +--+!-i-!-f""+-'+Iiii

I ; ! I !~;.....t-+--t i! I

~ ! i I !! .. I

3""1~--W-.l.--4I-.l.--4I-·--' _!• •000 U .SOO • •000

(b)

(e)

i 'nK-t--i- j._-i,· -1-+-+1-,!i

t ,_OOI U -1 ! J,'-i-I -+.-+1- li--+.-ir-T-- "l-r-r-rl l !

, . 0000 00I t~ ---l-r-r-r--n-j1;1' , - -1-

HM»4 ~ ~ i-h-l.'...n f~±=j=tJ=LJ-i -I

11 .500 10 .000

(d)

Fig. 6. Variation with guide vanes direction angle of (a) power carried by water exiting theturbine runner. (b) net head, and (c) hydraulic efficiency angle.

velcoity (Va2) (since the flow rate remains unchanged) will first result in an increase in therelative exit water velocity (v2) and a decrease in the absolute exit water velocity (V2) untilVU2 changes sign. When VU2 becomes negative, v2 will still increase but, on the other hand,V2 will start increasing. Since the hydraulic power loss (Ph), or rotor friction loss, is proportional to v2, and the exit water power (pe) is proportional to V2 when no draft tube is used,the behaviour of the curves in Figs 6(d) and 7(a) is understood. Moreover, because the powerinput to the runner is constant and equal to the sum of pis, ph, and pe, it should be apparentthat the increase in ph and the decrease in pe will result in a value of CXg that will minimizetheir sum and maximize pis (Fig. 6(a».

The effect of varying ag on the net head (h) is as depicted in Fig. 7(b). This behaviour isexpected because in this problem, where no draft tube is employed, h is the differencebetween the head at inlet to the casing HB and the total head at rotor exit (H2), which isproportional to pe at constant mass flow rate; therefore, HB being constant, hand pe should

Internaliooal Journal of Mechanical Engineering Education Vol 25 No 2

88 F. Moukalled and A. Honeln

(a)

O.MlOr-'!- -. --::;:'",- -..,.- ,---:---==~.--l- ~ :--.l-i

i:=~~1. ...l ~~ ! ! 1 !

::::lliIEttJ:tel ,GOO n .SOO 41 ,000 17 .100 J'Q,ODO

( b)

o.rnL__.: .- l- l -,-_!-.-;._+-_

\:=[~Fft~~i ! i ! I 1 I ! I i

o 'hCI~--t-.-H- __ ,l._ l

H'-i-t-t-: : !-i• .!UO &..--'--,l._--l..-.-I_~

20 .000 1.1.100 .-s .1IOO " .100

( c)

Fig. 7. Variation with guide vanes direction angle of (a) power carried by water exiting theturbine runner, (b) net head, and (c) hydraulic efficiency angle.

vary in an opposite way (compare curves in Figs 7(a) and (b». Finally, since the hydraulicefficiency (nh) is defined as the ratio of the head extracted from water (h") to the net head h,and since h" is proponional to pis , nh will first increase with the sharp increase in b" and thendecrease as h" decreases and h remains approximately constant (Fig. 7(c». This is to beanticipated since the overall effect of increasing lXg is to continuously increase the frictionlosses in the runner and decrease the losses at exit to a value approximately constant overmost of the range of ag o Using the value of a g that maximizes pis, say 30 degrees, theproblem is solved, and the values of the various quantitites are displayed in Table I. Thevelocity triangles at inlet and exit from the runner are shown in Figs 8(a) and (b), respectively. Moreover, the variations of the blade angles at inlet (/31)and exit <f32) from the runnerwith rl are shown in Figs 9(a) and (b) respectively. The values obtained are to be used whenthe runner is to be designed under these flow conditions. Finally, doubling the rotationalspeed and increasing the diameter by a factor of 1.25, the performance of the turbine is easilyobtained using similarity laws (Table I).

International Journal 01Mechanical Engineering Education Vol 25 No 2

cd


ul

Entrance Uelocities

Ua t: ~ .

Uul U1

(a)

u2

Uat:··..··u~ ....· U2

(b)

v1Ul = 31.920 It/s, 9.7291 m/sul = '17.2'11 It/s, 1'1.399 m/svl =27.3'10 ItIS, 8.3332 m/sUul = 26.'193 It/s, 8.0750 m/sUa = 17.80'1 ItIS, 5.'1267 m/s011 = 33.903 deQrees131 = 139.37 deQrees

132 Discharge Uel oci ti es

U2 = 21.313 ItIS, 6.'1962 m/su2 = '17.2'11 ftlS, 1'1.399 m/sv2 = 39.737 Itls, 12.112 m/sUu2 = 11.715 ItIS, 3.5708 m/sUa = 17.80'1 ItIS, 5.'1267 m/s012 = 56.655 degr ees132 = 153.38 deQrees

IPress any key I

Fig. 8. Velocity triangle at runner (a) inlet and (b) exit.

CONCLUSION

An educational software package for the analysis of hydraulic reaction turbines was described. The program, capable of solving radial, mixed, and axial flow hydraulic reactionturbine problems, provides an efficient educational tool for mechanical engineering students.The comprehensive example problem presented demonstrated the various features of thepackage. Finally, copies of REACTION will be provided to users upon request.

ACKNOWLEDGEMENT

The financial support provided by the University Research Board of the AmericanUniversity of Beirut through Grant No. 48816 is gratefully acknowledge.

REFERENCES

[1] Belland, J., et al., 'Varied self-paced micro-computer based instructional programs for addressingindividual differences when acquiring different levels of instructional objectives', Rest. TheoryDiv. Proc., 1985, pp. 146-163.



160 .580 ·r········T·········r··..· ···T····_···T··-T-~·····_· ·· · .r· · ·· ·· ··· ·; ··· ·· ·· · ··t· · · ··· · · · ·;· ·· · · ·· ·· · ·; · ··_··· · .~. ·--1·_·_····t··_· u ·-i

1..0. t<47 .~ ; ~ i : L._•....•.~ ~..u i

~ 18 . 71~ .t:::::::::!::::::::::I:::::::··:!::..: : :::::I :: :~:::::L:~:::l::::::::::i::::::::::l; 89 . 28 1 l:::::::::I~~~::::t· ::..:::::l:::::: :::J:=L~L:~j:=j

l t l l i.._._.-L---~.._ l _._.!

~ 78 . - t·········I···· ····t··········I···········I·_..·--~- ·..··I·······..·t-..·'-1

~ 58 . ~15 f:::: ::: ·:: :·::::::::I::: : :::: ::r::::::::~I::~::~~F:~::::I:::::::::+~::~::!.. i..··· ·····!········..·~····· ··· · ·~ · · · · · · · ····!··········t·_- ~ ~ !

37.883 : L · ~ ..!. i··· .L. ·: L...·..lo.750 1. 063 1.375 1. 688 2 . 000

(a)

I ::::E [ EE]:==E:; _-~::::: i~ l 1 ; i ! l j i~ f·........·~ ·..·······f..··......:· ··..·..·:··· ·f · ·~..· ·..f i· . . .· . . . . . . . .· . . . . . . . .· . . . . . . . .

1<4.5 . 8 2 0 ·~· · · · · · · · · · f · ··· · · · ·· ·~ · · · · · · ·· i · ······ · · ·· i ····· ·· · · ·~· ·· ·· · ··· ·i ·· ········ .;. ···· ·· ·· ·· i

~ i i : i i i i i j

; 137 . 8~5 .t:::::::::I:::·::::..l: : : :: : ::: :1:: : : : :: : : : :I :~:~:=I::~:=:]~~~~::1:: : :::~~1I f · · · · · · ·· ··~··..······t·····..···!········..·!···.._··t..········!·· t..·_·..·!j 128 . 370 ~..... ··1···..·····t·······..·i·....·....·)·....·..··t·......···i..· ·t..........)• ~ l ~ ~ ~ ~ l ~ ~IOl : •• ••••••• ; • • • • • • • • • •~ •• ••••• • • • ; • • •••• • • • • • I ~.•••••.•••. ~ ~ •• .• •. . •. . ,

!121.095 L L l. L ) L L L jN ! ~ 1 ! i 1 ! 1 !& :. •••••••••i· ~ i ··i ~ i ~.· · i

: 1 ! 1 ~ ~ 1 ! ~112 .81S . ·..······:.. ·.... .. · ~ ·......·.. :.. .... .. ..·i..·_..··J.·..·..·_·!..........l ....-·..1

0 .750 1.063 1.375 1 .688 2.000

rt wheel r.adu ia at .,..tranc. ( ...tar)

(b)

Fig. 9. Variation of blade angle at runner (a) inlet and (b) exit with wheel radius .

Intemational Joumal of Mechanical Engineering Educet.,n Vol 25 No 2


(2) Diab, H., Tabbara, H., Moukalled, F., Kaysi, I., and Raad, L., 'GEOCAD: an educational tool forflexible pavement design and maintenance', The International Journal of Applied EngineeringEducation, 7(4), 307-315 (1991).

(3) Moukalled, F., and Lakkis, I., 'Computer aided analysis of gas turbine cycles', lntemationalJournal ofMechanical Engineering Education, 22(3), 209-227 (1994).

(4) Moukalled, F., Nairn, N., and Lakkis, I., 'Computer aided analysis of centrifugal compressors',International Journal ofMechanical Engineering Education, 22(4), 246--258 (1994).

[5] Evans, R. L., and Mawle, 'Microcomputer-based analysis of steam power plants', InternationalJournal ofMechanical Engineering Education, 17(3), 217-230 (1989).

[6] Brychcy, M. L., and Taulbe, D. B., 'Calculation and graphics display of airfoil and wingcharacteristics', International Journal of Mechanical Engineering Education, 18(3), 157-168(1990).

(7) Moukalled, F., and Honein, A., 'Computer-aided analysis of the Pelton wheel', InternationalJournal ofMechanical Engineering Education, 23(4), 297-314 (1995).

[8] Daugherty, R. L., Franzini, J. B., and Finnemore, E. J., Fluid Mechanics with EngineeringApplications, McGraw-Hili, Singapore, 1989.

(9) Streeter, V. L., and Wylie, E. B., Fluid Mechanics, 7th edn, McGraw-Hill, Tokyo, 1979.[W] Massey, B. S., Mechanics ofFluids, 4th edn, Van Nostrand Reinhold, London, 1979.[11] Nagaratnam, S., Fluid Machines and Systems, Tata McGraw-Hili, Bombay, 1971.(12) Turbo Pascal Owner's Handbook, Borland International, Scotts Valley, California, 1989.


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