Investigation of flow in a centrifugal pump

Item Type text; Thesis-Reproduction (electronic)

Authors Day, Raymond, 1932-

Publisher The University of Arizona.

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INVESTIGATION OF FLOW IN A CENTRIFUGAL PUMP

fryRaymond Day

A Thesis Submitted to the Faculty of theDEPARTMENT OF MECHANICAL ENGINEERING

In Partial Fulfillment of the Requirements For the Degree ofMASTER OF SCIENCE

In the Graduate CollegeTHE UNIVERSITY OF ARIZONA

1 9 6 5

STATEMENT BY AUTHOR

This thesis has been submitted in partial ful­fillment of requirements, for an advanced degree at The University of Arizona and is deposited in The University Library to be made available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable without special permissions provided that accurate ac­knowledgement of source is made« Requests for permission for extended quotation from or reproduction of this manu­script in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in their Judgment the proposed use of the material is in the interests of scholarship. In all other in­stances, however$ permission must be obtained from the author„ / O . (z" X

SIGNED

APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown belows

&

Mechanical Engineering

ACKNOWLEDGEMENTS

The author is deeply indebted to Professor A., Ralph Yappel for his technical supervision and advice throughout this investigation, in addition to his numerous valuable suggestions on the preparation of the written portion of this thesis,

A debt of graditude is also due Mr, 0, B. O^Brien and Mr, G. B, Fields who provided technical assistance during the fabrication of the experimental equipment.

ill

TABLE OP CONTENTSPage

LIST OP ILLU STR AT I ON S oooooooooooeooooooeooooooooo IT!, %LIST OP TABLES oeoeooeoeooooooooedooooeeodoooooooo VjLHABSTRACT0000000000^0000000000000000000000000^0000 13E

J. INTRODUCTION 0000000000000000000000000000000 I1 o X Ce3?%e%*al oooooooeoooeoooooooooeoooooooo XX o2 Purpose of the Study 0 o»»«= o«»»«,»»o ©« 3

2 THEORETICAL CONSIDERATIONS© 0000000000000 = 00 52 © X IntroductXon000000000000 = 000000000000 5202 Dimensional AnalystSooooooooo = oo©oooo 52 © 3 V eloo1ty Diagrams0000000 = 000 00 = 0000 = 0 ^2 o^ Pump Heads=oo0000000000 = 0000000000000 9

2 e4oX Theoretical Head (He)»=«»= = = = 92 o4„2 Ideal Head (Hi)«= 0 = =, = = =»»=«= 132=4=3 Actual Head (H)©..©.....0=000 14

2=5 Plow Through the Impeller. = =. = = = =.. = = 152.5.1 Modification of the Euler

He aU> 000000.000000000000000000 X 52 o 5» 2 Circulationooooooeo.ooooooo.o X 62,5=3 Pressure Distribution.00.==0. 18

2=6 Additional Theoretical Background.=.o 192 o6 0X Equations of Motion, =. = = = = = =. 19

2 o6=2 Potential Theory............. 19

iv

VPage

3 DESCRIPTION OP APPARATUS................... 213.1 The Centrifugal Pump............o.... 213.2 The System Accessories............... 22

3.2.1 ImpeHer s.................... 223=2.2 PXexi=>glass Pump Casing

Pace oooo.o.oo.ooo.o.oooooo.oo 223.2.3 Reservoir and Connections.... 24

3.3 Instrumentation.......ooo.oo..ooeo... 243.3.1 Pressure Measurement......... 243.3.2 Plow Measurement............. 253 = 3.3 Speed Determination.......... 263.3=4 Temperature Measurement...... 273.3=5 Power Determination.......... 27

3.4 Plow Visualization................... 284 TESTING PROCEDUREoo.o.o.@oo.ooo.oooo......o 31

4.1 Test Parameters.ooooo................ 314.2 l?cst Procedure...ooo.oo.............. 314.3 Conformance with Test Codes.......... 32

5 REISUIjTS . . . o o o . o . o . . . . . . . . . o e o o o o . . . 0 . . . . . . . 34

5=1 Numher of Tests.o.oo*..oo...ooo@.o.o. 345.2 Data I^ed%%ctionoooo0o......o..o....... 33

6 ANALYSIS AND DISCUSSION OP PUMP TESTS...... 4l6.1 Three-vaned Impeller................. 41

6.1.1 Modifications in Design...... 4l6.1.2 Discussion of Results........ 42

ViPage

O e P P V aZled. impe IL3.e3r o o o o o o e e e e o o o o e o o e ^ 56*2.1 Modifications in Design...... 456.2.2 Discussion of Results........ 48

6.3 Curved-vane Impeller................. 526.3.1 Modifications in Design...... 526.3=2 Discussion of Results........ 52

7 CONCLUSIONS AND RECOMMENDATIONS............ 547.1 Conclusionso......................... 547.2 Recommendations for Further Study.... 55

PlEP* jiEENCES .e..©.................................. 57APPENDIX A ORIFICE CALIBRATION CURVE............ 59APPENDIX B MOTOR EFFICIENCY AND PRONY BRAKE

CALCULATIONS. . . . . . . . . . . e . . . . . . . . . . . . . 61APPENDIX C CHARACTERISTIC CURVES................ 63APPENDIX D SAMPLE CALCULATIONS.................. 83APPENDIX E FORTRAN PROGRAM...................... 89APPENDIX F SAMPLE OF LABORATORY TEST DATA....... 92APPENDIX G SAMPLE OF COMPUTED PRINTED RESULTS... 94

LIST OP ILLUSTRATIONS

Figure123456

789101112

13141516

17

18

PageVelOOlt^ Diagrams„ e e e o o o o o o o o o o o o o e o o o o o o 8Velocities in an Impeller© © © o © » © © 0 « o © © o © © 9Relative Circulation and Relative Plow© © © 17Pressure Distribution of Impeller Vane©.© 18Tesu Pump © © © © © © e © © © © © © . © © © . © © © © © © © © © © © © © © 23Plexl~glass Pace and Inlet Pipe©......... 23Model 83R Tacblite©©o©©*©©©©©©©©.©©©©©©©© 26Prony Bralee©©©o©©©©©.©©©©©©©©©©©©©©©©©©©© 28Air Injection System.©©.,©©.©©©,© © ©.© © ©.. 29Impeller Vane Modifications© ©©©.© = .©©. = ,= 35-37Unmodified Three-vaned Impeller,.© ©.© © © © © 44Three-vaned Impeller with 9 Holesat Tip Q 0 © e © 0 © 0 © © © © © 0 © 0 0 0 0 0 © 0 0 © © © 0 0 0 » 0 0 © 0 0 44Comparison of Efficiencies©,=,,©©=©©..©©. 46Turbulence Behind Unmodified Vane..=©©..© 47Result of Profiling Vane Tip.,»©.©©©=©=»© 47Turbulence in Unmodified Four-vanedImpeller ©©©©©©©©©o©©©©©©©©©©©©,©©©©©©©©.© 59Turbulence in Concaved Four-vanedImpeller © © © © © © © © © © © © © © © © © © o © © © © © © © © © © © © © © 5^Comparison of Efficiencies©.,©.,©©©.©©©©« 51

vil

LIST OF TABLES

Table12

PageSample of Laboratory D a t a * 93Sample of Computer Results as Printed bytlflO Computer o o e e o o O Q e o o o e o o o o o o o o o o o e o o o e o 9 5

vlii

ABSTRACT

The frictional losses In centrifugal pumps are partly due to boundary layer effects on the impeller vanes. The purpose of this investigation was to deter­mine whether or not these losses could be reduced by "energizing" the boundary layer on the vane»

To conduct this investigation a special centri­fugal pumping system had to be assembled and. properly instrumented, A series of test impellers were fabricated to allow for various impeller vane modifications*

To the best of the writer8s knowledge0 the technique used for the boundary layer control was unique (insofar as pump technology is concerned) in that pressure gradients inherent in the pump were used to supply the energizing fluid. Various methods were tried to channel this fluid into the boundary layer„ The effects of variations in vane geometry were also in­vestigated.

The experimental results obtained indicated that the techniques used to energize the boundary layer were effective in certain instances. When the boundary layer was energized near the vane tipj, an increase in pumpefficiency was noted. However9 the converse was true when boundary layer control was attempted near the base

ixy

of the vanQo Tapering of the trailing edge of the vane tip resulted in the greatest increase in total pump efficiencyo

CHAPTER 1

INTRODUCTION

1.1 GeneralThe progress made in pump design has been accom­

plished primarily by experimental methods. The manufac­turing industry has developed highly efficient pumps by considering gross efficiency as the main criterion for improvement In the performance of pumps. Over the yearse a wealth of empirical Information concerning all types of pumps has been accumulated.

Engineers have used this data extensively when confronted with a new pump design situation. If a new Impeller is to be designed for certain operating condi­tions p the designer chooses a suitable "model" from existing impellers which have the same general per­formance characteristics. By applying the laws of modelings the dimensions of the model9s impeller can be changed to account for the operating conditions of the new pump. To design a new impeller for which no model is available0 designers use "design factors" established experimentally from successful pump designs. These "design factors" are dimenslonless ratios of various pump performance parameters.

1

2To apply the above mentioned design procedures

the design engineer has to know little about the internal fluid flow of the pump. This is partly due to the fact that there is little actually known about the internal flow and associated losses in pump passages.

These pump losses are of particular interest because they cause the difference between the "ideal" or theoretical pump and the actual pump. It is generally agreed that pump losses can be divided into three cate­gories s hydraulic, mechanical$ and leakage losses. The least understood of the above losses are the hydraulic losses, because there are so many inter-related contri­buting factors. In general9 hydraulic losses are caused by skin friction, eddy losses and separation losses due to change in direction and magnitude of the fluid flow.

If the exact nature and magnitude of these losses were known, methods for their reduction might be readily apparent. Also, the performance characteristics of any pump could be accurately predicted by mathematical analysis.

The approximate behavior of the flow within the pump has been analyzed mathematically by a number of authors. Sorensen (19^1) applied complex variable theory to the problem, assuming the flow to be two di­mensional. Acosta (195*0 made a mathematical analysis assuming a two-dimensional, incompressible, inviscid and

irrotational fluid so that the methods of potential theory could be employed. This approach is an over­simplification of the problem and hence does not satis­factorily account for all the effects of real fluids.

Although a complete mathematical explanation of pump flow is still lacking9 excellent experimental work (Lewinskey and Kesslltz, i960) has been done to determine the actual flow patterns in centrifugal pumps. The results of this research have given some idea of the actual pressure distributions and relative velocity patterns within the centrifugal pump.

1.2 Purpose of the StudyPreviously established experimental information

about pressure and velocity distributions was used in an attempt to reduce the magnitude of hydraulic losses in the impeller channel. A series of experiments was con­ducted on four ,8two-dimensional” impellers with varying geometries. By trying various modifications of each impeller it was hoped that the hydraulic losses could be reduced. This would be manifested by improvements in the following pump performance characteristics: total headg power consumption, and pump efficiency. No attempt was made to quantitatively evaluate individual hydraulic losses or to give equations or methods for calculating hydraulic losses in various parts of the pump.

4To accomplish the objectives of this thesis a

properly instrumented test pump was used. The various impellers used for the experimentation were either specially built for this test or were a modification of an existing impeller.

The pump had a special "plexi-glass” face to allow flow visualization. To aid in the qualitative description of the flow patternss photographic techniques were used. The actual photographic procedures used are the subject of a separate thesis conducted in conjunc­tion with the investigations performed in this thesis.

CHAPTER 2

THEORETICAL CONSIDERATIONS

2.1 IntroductionIn an attempt to reduce the impeller hydraulic

losses by vane modificationst a sound theoretical basis for such modifications is desirable. In order to develop such a theoretical background@ the following sections will deal with those items that are pertinent to pump performance, For the sake of brevity$ a complete treat­ment of each important factor will not be attempted.Only sufficient depth is desired to accurately describe the flow conditions in qualitative terms,

2.2 Dimensional AnalysisThe techniques developed by Buckingham (1915) as

applied to centrifugal pumps are important in the analysis and design of these pumps. The physical quantities that influence the operation of centrifugal pumps are well enough known so that the methods of dimensional analysis are applicable,

The most pertinent quantities used for the di­mensional analysis ares capacity^ energy supplied to the

5

pump shaft, speed of the pump shaft, impeller diameter9 fluid densityg and absolute viscosity. These six de­scriptive quantities are measured in the fundamental units of lengths times and mass. The resultant dimen- sionless parameters of importance concerning studies of centrifugal pump performance are: Reynolds number, specific speed, specific capacity, and specific head.

give rise to the "affinity laws" for turbomachines„ These affinity laws are of particular importance when the performance curves for a pump at a known speed are given, and when it is desired to obtain new curves at a different speed. The variation of head, capacity and brake horsepower will vary with speed as given by the following equations (Karassik and Carter, I960):

The results of this dimensional analysis also

where:N = speed (rpm)Q = capacity (gpm) H = head (feet)P = brake horsepower

subscript 1 = conditions at known speed subscript 2 = conditions at new speed

Since all the performance curves are plotted for a constant speed (1000 rpm) in this thesis„ correspond­ing curves for any desired speed within certain limita­tions could be found by applying the affinity relation­ships.

2.3 Velocity DiagramsThe actual flow through an impeller can be de­

scribed accurately only in terms of curvilinear motion.To trace the curvilinear path of a fluid particle from the entrance of the impeller until it is discharged would be a formidable task. For the purpose of simpli­fication s one-dimensional flow pattern is,usually assumed

When an analysis is made of the velocity of the fluid particle it is sometimes convenient to consider only conditions at the inlet and exit of the impeller.It is also convenient to treat all velocities as "average velocities (averaged across the inlet and exit cross- sections ) even though this is not the case in a real flow situation.

The quantities considered ares the peripheral velocity (U)$ the velocity relative to the impeller (W), and the absolute velocity (C) with respect to the fixed pump casing. With these velocity components the familiar

3velocity diagrams for a centrifugal pump can be con­structed. Using the notation of Stepanoff (195?) the following diagrams represent the velocities at the entrance and exit of the impeller.

m

Wu CUl

u- W ,ua c

u

Entrance diagram Discharge diagramFigure 1

Velocity Diagrams

The subscript (u) refers to the tangential components of the relative and absolute velocities and the subscript (m) refers to the component of absolute velocity normal to the peripheral velocity. This com­ponent will be radial for the type pump used in this thesis; this velocity component is commonly referred to as the meridional velocity. Angleyf is the representative flow angle between the relative velocity and the tangential

9direction. Angle <X. represents the true direction of the fluid with respect to the tangential direction.

2.4 Pump Heads2.4.1 Theoretical Head (He)

The theoretical head is commonly called the Euler head and can be developed by applying the prin­

ciple of angular momentum to the mass of fluid going through the impeller passage. The theoretical head does not account for frictional losses or non-uniform velocity effects.

- — r

Velocities in an Impeller

Initially, at time t = 0, a mass of fluid isentrained between the impeller passage, occupying space abed in Figure 2. After an infinitesimal amount of time (dt) this same mass of fluid now occupies space a'b'c'd*. In the increment of time (dt), a finite amount of fluid actually leaves the pump, which will be denoted as (dm). The displaced fluid is graphically represented by space dec"d0. An equal amount of mass will enter the channel during the same time interval, this is shown as abb8a ’. The change in the angular momentum of the whole channel •is due only to the change of the angular momentum of mass entering and mass leaving the channel. If X is the moment of the external forces, then;

where the summation is over all of the blade passages.It should be noted that this relationship is

derived by considering a steady flow through a control volume (Shapiro, 1953)• Wall friction and turbulence effects are neglected and radial forces have no moment about the axis of rotation.

through the impeller. This flow rate can be expressed

X S? (r ,Cu )dt 1 ii i(2.1),

out in

Assuming that the flow is continuous, the sum ofthe flow will represent the mass flow rate

11QYby where Q is the volumetric flow rate. Substituting sc

this value in equation 2,1 results in:

X = (r Cu ) - (r Cu ) (2.2)sc 2 2 Sc 1 1

If both sides of the above equation are multi­plied by CO 9 there results a relationship for the input power. Power = (moment) (angular velocity) or P = X CO .

P = x o = c l (r Cu - r Cu ) (2.3)sc 2 2 1 1

Using the fact that peripheral velocity is equal to the angular velocity times the radius (U = r O ) and assuming co is constant9 equation 2.3 can be rewritten.

Power = ^ (U Cu - U Cu ) (2.4)®c 2 2 1 1

For a theoretical pump with no losses this power will be converted into the theoretical pump output or:

P = H X Q (2.5)e

where H is the theoretical head; or e

12

H T q = | J ( U C u - U Cu ) (2.6)e se 2 2 1 1

Dividing both sides by Q Y yields:

H = ~ (U Gu - U Gu ) (2.?)e o 2 2 1 1

This equation represents both the kinetic energy changes and pressure energy changes of the flow. This can be seen more readily if the equation is expanded by using the law of Cosines as applied to the velocity triangles

or

Cos*. - g l t - S l r . g f (2.8)2UC

U ~ V + Cl2 - Wl2 (2.9)1 20 Cos <X

1 1

U = U2 ^ C2 W2 (2.10)2

13Substituting these values into equation 2.7 results in;

_2 tt2 .,2 _2 n2 „2 H _ 2 * 2 ~ ' 2 Cu2 - C1 + U1 ~ 'h "U1 (2.11)e “ 20 Cos cc g 20 Cos <x. ‘ g

2 2 c 1 1 c

Remembering that 0 Cos = Cu and 0 Cos ec. = Gu1 1 1 2 2 2

equation 2.11 can be re-written

h ... 4 - 4 . 4 - 4 , - 4 (2.i2)e 2g 2g 2g

c c c

The first term of this equation now represents the contribution to the theoretical head due to a change of kinetic energy of the fluid. The last two terms represent a change of pressure energy between the inlet and outlet passages. •

2.4.2 Ideal Head (Hi)The ideal pump head does not account for losses

in the pump due to viscous friction and turbulence, How­ever, the ideal head does account for the non-uniform velocities within the impeller channel. The loss due to non-uniform velocities is usually denoted by pump engineers as the slip factor (yL<). This factor is equal to the ratio Hi/He. The values of various slip factors have been experimentally and theoretically obtained by

14Stanltz (1952). Knowledge of the slip factor allows the energy losses to be estimated during the design of a new impeller. This parameter was found to be independ­ent of all impeller variables except the included channel anglej which is governed by the number of impeller vanes„

2.4,3 Actual Head (H)This is the actual delivered fluid head after

the fluid particles have been acted on by all external influences. There is no way to predict with assurance what the exact magnitude of these influences are. Due to the lack of sufficient knowledge in this area there is no way to calculate the actual head mathematically; it is necessary to rely on empirical data and engineer­ing experience to estimate the actual head.

The ratio H/Hi is commonly referred to as the hydraulic efficiency of the pump ). The actualhead can be related to the Euler head by the hydraulic efficiency and "slip" factor of the pump

H = >7 A H (2.13)o h e

Approximate values of /y /K.h.ave been determinedh

experimentally and are tabulated for different types of pumps, (Shepherd, 1956)= This allows the design

15engineer to obtain a close estimation of the actual head based on the value of the calculated theoretical head.

2.5 Flow Through the Impeller2.5.1 Modification of the Euler Head

From Figure 1 the following relationships are established:

2 2 2 2 2 2 C = Gu + Cm C = Gu + Cm1 1 1 2 2 2

and:

2 2 2 . 2 2 2 W = Wu + Cm W = Wu + Cm1 1 1 2 2 2

Substituting these values into Euler’s head equation (2.12) will result in:

(2.14)

Jj Up - 'jf (CUp + Cm2) - (Cu2 + Cm^) (Wu| + Cm^) - (Wu|& = + 2i + 2g

c c c

which reduces to:

H u2 - ul Cul - Gui Wuf - Wu| (2»15)e = 2g + 2 g ^ .. 2g

C 0 c

+ Cm IXI

16This equation contains only tangential velocities

as the radial velocity terms cancel out.2.5.2 Circulation

The velocity distribution is affected by the relative circulation within the impeller channel. If the working fluid is assumed to be composed of friction- less particles and if it Is further assumed that there is no "prerotation" of the fluid before it enters the impeller9 Helmholtz6s second law is applicable. This law states that the vorticity of a frictionless fluid, as seen by an observer moving with the fluid, does not change with time. Therefore, if the flow at the inlet to the impeller is irrotational the absolute flow must remain irrotational throughout the impeller. Thus if there were no flow through the impeller the fluid in the impeller channels would rotate with an angular., velocity equal and opposite to the impeller angular velocity (Figure 3a). The relative flow through a rotating impeller may be considered to be the vector sum of the flow through a stationary impeller and the flow produced by the relative circulation.

Figure 3b shows how the relative flow through the impeller is not perfectly guided by the impeller

vanes. The flow is deflected away from the direction of rotation of the impeller. Therefore, the angle of

17the fluid velocity relative to the vane is reduced.The amount by which this angle is reduced is less on the back face of any given vane than on the front face of the following vane.

cj CO'

(a) Relative circulation (without flow)

(b ) Relative flow

Figure 3Flow Through the Impeller Channel

132.5.3 Pressure Distribution

In order to transmit energy from the impeller to the fluid, the pressure on the leading surface of the vane should be greater than the pressure on the back side of the vane (Figure 4).

Figure 4Pressure Distribution of the Impeller Vane

Lewinsky and Kesslitz (I960) were able to take pressure and velocity measurements within an experiment­al pump. The pressure and velocity distribution natterns obtained generally substantiated the theories developed by other investigators such as Acosta (1954) and Sheets(1950). These experimentally determined pressure and velocity distributions were used as guidelines for the various vane modifications in this thesis.

192.6 Additional Theoretical Background

2.6.1 Equations of MotionThe flow through a centrifugal pump is a three-

dimensional flow, and of such a complex nature that an exact mathematical solution is not obtainable. However$ various attempts have been made to apply the equations of motion to a fluid particle in the impeller channel in an attempt to approximate the real flow situation.By making various assumptions9 Sheets (1950) was able to obtain an approximate solution to the differential equations describing the fluid motion. This enabled him to plot velocity and pressure distribution in the channel in relation to the impeller vane.

This approach may be useful for making predic­tions of flow conditions' for impellers of specific types of geometries. However, even with the most uncomplicated type of vane geometry, these equations do not adequately represent the real fluid flow situation.

2.6.2 Potential TheoryAnother approach to the problem of•prediction of

velocity distributions and head development was made by the application of complex variable theory (Acosta, 1954). To apply complex variable theory to this flow situation the assumption was made that the fluid moved in a two- dimensional rotating vane system. To further simpli fy

20the problem the fluid was also assumed to be imrlscid9 incompressible and irrotational.

This type of analysis involves the numerical solution of the governing flow equations subject to certain boundary conditions. The differential equation to be solved is Laplace’s equation in two-dimensional form 9

where U can either be the stream function or the velocity potential for the flow. In order to obtain a solution to this problem, a conformal mapping is employed which transforms the geometry of the Impeller blades in the Z-plane into a circle in the W-plane.

Acosta tried experimentally to confirm his theo­retical results and found reasonably good agreement at certain operating points. He attributed discrepancies between the observed and predicted quantities to real fluid effects, which were not accounted for in the simplified two-dimensional problem (Acosta and Bowerman,

1957).

CHAPTER 3

DESCRIPTION OP APPARATUS

3.1 The Centrifugal Pump.1,'li vi t ; r, nm', , mrm'p ru,.*' ,ni*„imrrrTT%i w n *nrrrmi9&a

The pump used during the experiment was a modi­fied industrial centrifugal pump manufactured by the Worthington Corporation, model 1& CGLA, group No.9059B. This pump has a voluted casing, a horizontal input con­nection and a vertical discharge connection (Figure 5)•

A one horsepower, 3 phase, type CSP Westinghouse motor was used to drive the pump. This motor was a constant speed motor that operated at 1175 rpm. The motor was connected to the pump shaft by means of ad­justable belt driven pulley assembly. The speed of the pump could be adjusted by changing the ratio of the pulley drive by means of an adjusting handwheel.

The shaft of the pump was supported by ball bearings, and the stuffing box was packed with a con­ventional packing, adjusted by means of a stuffing box gland. Due to excessive wear, a new shaft was fabricated for the pump and all bearings and packings were replaced by new items. Also, a re-machining of the pump casing was required due to excessive wear on this surface.

21

3.2 The System AccessoriescmscucwBfe eew »-i iriVnwiirviniir wvii-■r»in iiiyii*r.FL iywrpry™»

3.2.1 ImpellersSince the original impeller was used to pump

slurry it was badly eroded and could not be used for the tests under consideration.

Three new impellers were fabricated from one- inch thick aluminum stock. Also, one commercially-made splral-bladed impeller was modified to fit in the test pump. The three aluminum impellers were 3 inches in diameter and were composed of three, four, and five radial vanes, respectively. The four-vaned and five- vane d impellers were fabricated with a back shroud; the three-vaned impeller was shroudless. These fabricated impellers allowed a great deal of flexibility in attempting various modifications to reduce boundary layer effects.

3.2.2 Plexi-glass Pump Casing PaceBecause flow visualization was required for

this study the original solid metal pump face was dis­carded. A two-inch thick sheet of plexi-glass was machined to the required dimensions to replace the metal face plate $ and a two-foot length of plexi-glass inlet pipe was cemented to the face plate„ (Figure 6). The plexi-glass allowed visualization of the flow process with negligible optical distortion.

23

Figure 5 Test Pump

Figure 6 Plexi-glass Face and Inlet Pipe

3.2.3 Reservoir and ConnectionsA rectangular metal tank, with a capacity of

approximately 185 gallons, was used as the hydraulic reservoir for this system. Metal conduit, with an Inside diameter of two inches, was used for the connect ing piping. The water was recirculated back to the reservoir when it was discharged from the pump. The amount of water pumped was regulated by a flow control valve located on the discharge side of the pump.

3.3 Instrumentation3.3*1 Pressure Measurement

To obtain sufficient pressure information to plot the characteristic curves for each test run, a total of three manometers was used.

A standard 15-inch "U" type manometer was used to measure the pressure differential across the orifice This was a type 15" CODC, graduated in tenths of inches manufactured by the Meriam Instrument Company. The inside diameter of the tubing was i inch, making it possible to read the maniscus to the nearest half grad­uation. This differential manometer was connected to the piping so that all pressure lines were filled com­pletely with water from the system. Mercury was used as the indicating liquid.

25Two other manometers were used to measure the

discharge and suction pressure heads. These manometers were fabricated in the laboratory by bending 1/3” glass tubing in a "U" shape around a meter scale. Both were open end ”U"-tube manometers with mercury as the indicat­ing fluid.

The discharge pressure head manometer was a "wet-tube” manometer, with the connecting line between the pressure tap and the manometer filled with water.The suction head manometer was a "dry-tube" manometer, with air between the pressure tap and the mercury column. The smallest graduation on the scale was one millimeter for both instruments; all readings were obtained to the nearest millimeter.

For barometric pressure determinations in the laboratory an adjustable well type manometer manufactured by the Eberback Corporation was used. The instrument had a vernier scale which allowed direct readings to the nearest .01 centimeter.

3.3.2 Flow MeasurementA thin plate orifice was fabricated to be used

in conjunction with the differential manometer, as the flow measuring device.

The orifice was directly calibrated in the lab­oratory by weight measurement of fluid per unit time.

26A total of forty-nine welght-time measurements were made which were plotted as the orifice calibration curve (Appendix A).

The specifications for plate thickness, open­ing edge thickness, and location of pressure taps were obtained from Tuve (1961).

3.3.3 Speed DeterminationA constant shaft speed of 1000 rpm was main­

tained by using a model 332 "Tachlite" manufactured by Power Instruments Inc. This test equipment consists of a tachometer with sensitivity controls, a photoelectric pick-up, and a strobe light (Figure 7).

t a c h o m e t e r

s t r o b elight

p h o to e le c t r ic pick-up head

Figure 7 Model 332 Tachlite

2?The photoelectric pick-up head has a lamp and

pick-up photoelectric cell. Steady light is emitted from the lamp in a narrow beam and reflected from a selected spot on the shaft back to the pick-up cell (operating range 100 to 500,000 rpm) at a rate propor­tional to the shaft speed. The tachometer indicates the rpm and the strobe light is driven in step with the shaft speed.

This instrument was calibrated against the 60 cycle line frequency before each test run to minimize any instrument drift. The inherent errors in the instrument are believed to be small compared to the human error in reading the meter. With the meter range selector set for maximum sensitivity, speed variations greater than ± 5 rpm from the desired 1000 rpm are readily apparent. Detection of speed variations below this figure was subject to human limitations.

3.3.4 Temperature MeasurementAll temperature readings were made with standard

o olaboratory thermometers, range -30 to +120 F, and read to the nearest degree.

3.3.5 Power DeterminationThe electrical power input to the pump motor was

measured by a type V-3-A General Electric polyphase watt- hour meter.

28The mechanical energy output of the pump drive

motor was obtained by using a special fabricated wood- cleat type prbny brake (Figure 8).

3 f t a r mr m

shaft

scale

wood b locks

,Figure 8 Prony Brake

This test was necessary in order to calculate the efficiency of the electric motor (Appendix B ). The test wos performed according to the procedures outlined by Messersmith and Warner (1950).

3.4 Plow VisualizationBlack and white still pictures were taken of

the fluid flow inside the pump by using a model 95A Polaroid camera and type 47 Polaroid 3000 speed film.

29The flow pattern was evidenced by Injection of

air bubbles Into the base of the Impeller (figure 9).The air passed through the connecting tubing, through the Impeller hub and eventually out through the Impeller passage. The air had a natural tendency to flow Into the Impeller passage due to the pressure gradient with­in the pump.

a i ri

pTPli iI I

v a l v e - Vi •'I'i i

s ta t io n a ry tub ing

i, i

ro ta t in g tub ing —

p lex i -g lass

Figure 9 Air Injection System

The air bubbles, when illuminated with the strobe light, provided an excellent contrast against the dark background of the pump casing.

CHAPTER 4

TESTING PROCEDURE

4„1 Test ParametersOnce an impeller was modified and the desired

performance characteristics were decided upon, the following parameters were held constant at a particular test point: the water flow rate (Q), the pump shaft speed (Ng), the diameter of the impeller (D), and the geometry of the modified impeller vane»

Those measured parameters which were variable during the testing were: barometric pressure, room tem­perature , water temperature, and the power consumed bythe pump in maintaining a specified flow rate. Also,

«

the suction and discharge pressures varied with specific flow rate for each impeller tested.

4.2 Test ProcedureBefore the testing of a particular impeller

commenced, the barometric pressure, room temperature? and water temperature were measured and recorded. The pump was then operated for several minutes to purge the system of trapped air and to clear the manometer pressure lines of air. During this time the "Tacholite" was calibrated and the pump speed was adjusted to 1000 rpm.

31

32After regulating the flow valve at the dis­

charge side of the pump, the flow rate could be deter­mined by the pressure drop across the calibrated orifice. The initial test point for each impeller was set at a capacity of approximately 25 gallons per minute (gpm)..Subsequent test points were at increasing increments of about 5 gpm until the maximum capacity was reached. The exact maximum capacity varied with the particular impeller being tested. However, most impellers produced a maxi­mum flow rate of approximately 75 gpm.

At each test point a time measurement was made for 10 revolutions of the watthour meter indicator dial. With this a time-averaged power measurement could be obtained.

To complete the set of test data the inlet and discharge pressure readings were recorded at each test point,

4.3 Conformance with Test CodesThe American Society of Mechanical Engineers

(ASME) Power Test Code for Centrifugal Pumps (1954) was used as a guide for these tests. This code pro­vides standard directions for conducting and reporting tests on commercial centrifugal pumps. All phases of pump testing were in agreement with procedures in the test code with the following exceptionss

The test code recommended that pressure tap manifolds be used instead of the single tap method that was used in these tests. It was felt that the greater accuracy obtained with the pressure manifolds was not necessary during these pre­liminary tests.The code recommends a cradled electric dynamo­meter as the most desirable way of obtaining mechanical power measurements. However, a Prbny brake is acceptable and was used in this test due to the nonavailability of a suitable electric dynamometer.The test code stated that the three-phase power into the electric motor should be measured at the motor terminals. The power measurements were actually made by using a watthour meter mounted on the laboratory wall. There was a small inherent error Introduced into our calculations due to the line losses between the meter and the motor.Since this loss was practically constant for all tests, its effects were disregarded.

CHAPTER 5

RESULTS

5.1 Humber of TestsA total of nineteen test runs was performed on

four different Impellers. Three of the impellers were modified in various ways In an attempt to reduce the boundary layer effects. Figure 10 shows a single vane of the impeller which characterizes a particular modi­fication.

Figure 10 (a) to (j) illustrate the three-vaned impeller. All modification holes were l/l6 of an inch . In diameter. The holes entered the leading face of the vane and proceeded upward at an angle of approximately 60° with the horizontal, emerging at the trailing face.

Figures 10 (k) to (p) show the various configur­ations of the four-vaned impeller. All the modifying holes in this impeller were 1/8-inoh in diameter. Not shown is the back shroud which was used during all test runs with the four-vaned Impeller.

Figures 10 (q.) and 10 (r) show the modified and unmodified curved-vane impeller. This impeller was modified by drilling four l/l6-ineh holes near the tip of the vane. This impeller was also equipped with both a front and back shroud.

34

U)35

original

three holes

(e)nine holes

<p

one hole

(d)six holesU)

twelve holes

Figure 10Impeller Vane Modifications

36OJ

twenty-one holes

03

tapered vane

k)original

CO'*'

(h)nine holes at tip

co

(j)tapered with nine holes

(1)two holes

Figure 10 (continued)Impeller Vane Modifications

37u>

(m)two holes

co

(o)concave vane

6J‘

(q)original

::o(n)

two holesCaJ ^ '

(p)tapered vane

co

(r)four holes at tip

Figure 10 (continued)Impeller Vane Modifications

385.2 Data Reduction

In order to compute the performance characteris­tics for each tested impellers, the following information was recorded at each test point:

(1) Barometric pressure (P^)(2) Specific weight of water (}fw )(3) Specific weight of mercury (YHg)(4) Pump flow rate (Q)(5) Pump inlet pressure (P )s(6) Pump discharge pressure (P^)(7) Time interval for ten revolutions of

wattmeter dial (T)These parameters were necessary in order to

calculate the total pump head; power consumption; and pump efficiency. When these three items were plotted as a function of pump capacity the familiar pump characteristic curves were the re>sult. These curves indicated the performance characteristics of each impeller and were a basis for impeller performance evaluation. The characteristic curve for each test run is contained in Appendix C.

The equations used to arrive at the pump perfor­mance characteristics are explained in Appendix D, These equations are algrebraic relationships involving the seven parameters listed above. Due to conversion of

units and the number of individual operations involved, a complete solution to the basic equations at each test point by slide rule methods would have been quite tedious and time consuming. Therefore, in order to alleviate this situation an International Business Machine (IBM) 7072 digital computer was used as an aid in data reduc­tion, The automatic computing techniques used involved FORTRAN, a procedural programming language for communica­tion with computers (Organ!ck, 1963). The complete FORTRAN program, as punched on individual IBM cards, appears in Appendix E. The seven numerical items of information, necessary to solve the basic equations, were automatically read into the program by having this information punched on data cards. The laboratory data that was transferred to data cards is tabulated in Appendix F. The main program instructed the computer to print the results of the solved equations after each card from the data deck was processed. A sample of the printed out-put from the computer (pump efficiency, power consumed, and total pump head) is listed in Appendix G.

The advantage of using the digital computer can be readily appreciated by examining the main program, which contains forty-two separate arithmetic operations. These operations were performed on each of the 170 cards

in the data deck. This means that over seven thousand arithmetic operations were performed by the computer in the total data reduction; in addition to this the computer printed the results in a tabular form.

CHAPTER 6

ANALYSIS AND DISCUSSION OP PUMP TESTS'

6 o1 Three"Vaned Impeller6.1.1 Modifications In Design

The vane pressure distribution developed by Lewinsky and Kesslitz (I960) was used as a model for modifications attempted in this experiment. Even though the degree of similarity between their experimental set­up and that of the present work is unknown, these pressure distribution patterns were the most complete that could be obtained as general guidelines to follow.

Various techniques were attempted in this in­vestigation to energize the boundary layer on the lower pressure side of the impeller vane„ Each involved the routing of fluid from the hl'gh pressure side of the vane to the lower pressure regions on the trailing side of the vane. The fluid was channeled through l/l6=inch holes drilled in the vane at an angle of approximately 60° to the horizontal. A greater angle of incidence was desired but available equipment and materials placed a practical limitation of this angle„

Test runs number 2 through number 6 were con­cerned with attempting boundary layer energization in

41

42the lower half of the vane. During these test runs one, three,. six, nine, and twelve holes were drilled in the lower portion of the vane«

The remainder of the tests on this impeller were, concerned with • the upper portion of the vane. In an attempt to energize the boundary layer in this region, an array of nine holes were drilled at each vane tip.Tests were conducted with only these holes present in addition to twelve holes at the base of the vane.

In conjunction with energizing the boundary layer in the region of the vane tip, a variation of tip geome­try was made. Only the trailing side of the vane tip was modified in an attempt to improve pump performance. After the vane tip was modified by tapering the trail­ing side, tests were conducted with and without the nine holes at the tip.

6.1.2 Discussion of ResultsAll attempts to reinforce the boundary layer in

the lower portion of the vane resulted in a degradation of pump performance. The boundary layer in this region was not as pronounced as in the tip area. Injecting fluid into this region probably induced the formation of "eddies” in the region of the holes, which increased the turbulence with resulting increases in friction losses. Also, the holes in the base of the vane may have created undesirable "leakage" losses through the vane.

43Figure 11 shows the path injected air bubbles

follow over the un-modified vane. The irregularity of the bubble path is indicative of the degree of turbulence along the low pressure side of the vane.

When the modification holes were placed near the tip of the vane an increase in efficiency resulted. Visually it could be determined that the region directly behind the vane tip was the most turbulent region of the entire vane profile. By introducing energizing fluid to the boundary layer in this region the magnitude of the turbulence was reduced. Figure 12 shows that when the vane had nine holes at the tip, the magnitude of the turbulence was reduced from that of the pre­vious illustration.

One of the most Interesting results of these tests occurred when the vane tip was tapered. Varley (I960) conducted a similar experiment that resulted in a slight increase in head and a decrease in efficiency; The results of this experiment showed an increase in both head and efficiency. Ferguson (1963) explains that profiling the trailing edge of the vane should increase the head because of the change in the fluid exit angle. Varley agrees with the above statement but further postulates that unfavorable changes in the velocity distribution and increased mixing losses in the volute

Figure 11 Unmodified Three Vaned Impeller

Figure 12Three Vaned Impeller With 9 Holes at Tip

45may result from this modification. The results ob­tained from this experiment indicate that Varley’s hypothesis may not be generally true for all impeller- pump combinations, but probably depends upon the exact nature of the modification made. Whereas Varley ex­perienced a 2% loss in efficiency, the results of this experiment indicated an 11% increase in efficiency due to profiling the vane. Figure 13.

The turbulent region behind the vane tip can be seen in Figure 14, The combined effects of vane profil­ing and fluid injection at the vane tip can be visually evaluated in Figure 15. Both of these photographs were made with a maximum injection of air into the pump passage to present a more frothy appearance.

6.2 Four-vaned Impeller6.2.1 Modifications in Design

The results of the tests with the three-vaned impeller indicated that modifications in the region of the vane tip gave the most advantageous results. There­fore, attempts at boundary layer control using the four- vaned impeller were concentrated in the region of the vane tips.

With this impeller attempts were made to use centrifugal effects to cause a flow from the base of

fes t 01 inaT vAheholes in base

a T e s t 11red t

Test 14

u r e 13of E f f icl2_ m n

siencteo m p r i sone e Va

Y (GCAPACIT4 k :

Figure 14 Turbulence Behind Unmodified Vane

Figure 15 Result of Profiling Vane Tip

48the vane at the trailing face to the more turbulent regions at the tip. This technique was used in test run numbers 12, 15 and 16. Holes were drilled from the base of the trailing face of the vane to the vane forward face at the tip, to the vane tip end, and to the trailing face at the tip.

As with the three-vaned impeller, profile modi­fications were also applied to the four-vaned impeller. One profile modification necessitated the removal of metal from the trailing face of the vane without dis­turbing the dimensions on the tip of the vane. This was done in an attempt to obtain a more uniform velocity distribution in the impeller channel. It should be pointed out that profiling the vane will change the discharge a n g l e . The velocity diagrams (Figure 1) readily indicate the effect of this change on the merdional and tangential components of the fluid exit velocity.

6.2.2 Discussion of ResultsThe attempts at boundary layer control, by

routing the fluid through the vane $ resulted in a slight increase in both head and efficiency. Visually, it could be determined that the fluid was entering the holes at the base of the vane and was being discharged at the tip of the vane. The effect of this was to add

energizing fluid to the turbulence region at the tip.There was little difference between the performance curves of the three tests wherein this technique was used; all showed Increased efficiencies over the un­modified impeller.

The results of curving the vane, which had the effect of increasing angle^^, also indicated a slight increase in performance over the original vane. Visually, the size of the turbulent region behind the vane tip was seen to decrease due to this modification. This can be observed by comparing Figures 16 and 17, where a large amount of air was allowed to enter the pump for flow visualization purposes.

Just as in the three-vaned impeller, the most»advantageous modification was the tapering of the vane

tip. Figure 18 compared the efficiencies of the various types of modifications attempted with the four-vaned impeller. It can be readily seen that there is a large increase in efficiency over the original vane. Also, the capacity of the pump is increased by seven gallons per minute. Removing metal from the trailing side of the vane tip causes an increase in the average exit a n g l e g , thereby increasing the Euler head.

Figure 16Turbulence in Unmodified Four Vaned Impeller

Figure 1?Turbulence in Concaved Four Vaned Impeller

r e . 18C om p son

RAC IT 5 5

526.3 Curved-vane Impeller

6.3.1 Modifications In DesignDue to the inherent limitations of this impeller,

and its physical dimensions, only one modification was attempted. Four 1/16-= inch holes were drilled near the vane tip in an attempt to energize the boundary layer in this region. Although this technique was confined to the impeller vane tip, its effects would be felt throughout the entire length of the vane. As with the other impellers, the fluid was to be routed from the high pressure to the low pressure side of the vane. A piexl-glass front shroud was fabricated for this impeller in an attempt to reduce the wall effects in the flow channel.

6.3.2 Discussion of ResultsOnly two tests were run with this impeller and

the results (Figures 9 and 1? in Appendix C ) showed a correlation with the other impellers having similar modifications. While both head curves, were almost identical, the modified impeller reached a maximum efficiency of 21.0$. While this difference is ad­mittedly very slight, it nevertheless appears to be a real effect. It should be pointed out that in all cases presented, the test resuits plotted very smoothly, i.e. there was very little scatter.

Visually it was difficult to interpret theflow patterns in the impeller channel. However„ a slight decrease in the turbulent region behind the vanes could be detected after the vane was modified.

CHAPTER ?

CONCLUSIONS AND RECOMMENDATIONS

7.1 ConclusionsThe results of this preliminary investigation

indicate the feasibility of utilizing the pressure difference between the leading and trailing faces of the impeller vane to reduce boundary layer effects.By "energizing" the boundary layer on the trailing face, the overall efficiency of the pump was increased. How­ever, this increase in efficiency was noted only when the highly turbulent region near the trailing face of the vane tip was energized. A slight decrease in efficiency resulted when the boundary layer control was attempted near the base of the vane.

This investigation also showed that the geometry of the vane itself has a pronounced effect on pump per­formance characteristics. For the particular series of changes used in this investigation, the modification of tip geometry resulted in better pump performance character­istics than did the attempts at boundary layer control.

54

7.2 Recommendations for Further StudyThe following recommendations are made cognizant

of the limitations and capabilities of the existing test apparatuse All of the following suggestions can be performed with only minor modifications to the basic test equipments

1. It is suggested that a photographic analysis of the fluid flow be made utilizing the high speed motion picture camera available in the University of Arizona AME Department. In this way9 with suitable flow indicators, a more complete picture of the actual flow path could be obtained.

2. The effects of introducing the energizingfluid parallel to the rear surface of thevane should be investigated. This couldipossibly be a more effective way to energize the boundary layer. This approach may necessitate the design of a new series of test impellers to facilitate such a fluid Injection.

3. Another approach to the problem of boundarylayer control would be to remove part of the boundary layer by suction techniques. It could be experimentally determined whether

the gain in pump performance would offset the energy expended to reduce the boundary layer effects.To obtain more meaningful results an attempt should be made to obtain quantitative details of the internal flow in conjunction with future flow visualization experiments. This would necessitate the instrumentation of the pump casing with the proper sensing devices. To increase the accuracy of the existing instrumentation it is recommended that the pressure taps be connected by a manifold9 as specified in the ASME Test Codes. The use of inclined manometers would increase the accuracy of the readings.

REFERENCES

Acosta, A. J. "An Experimental and Theoretical Investi­gation of Two-Dimensional Centrifugal Pump Impellers9" Trans. ASME, 76, 1954$ 749.

Acosta, A. J., and R. D. Bowerman. "An Experimental Study of Centrifugal Pump Impellers,M Trans. ASMS. 79, 1957, 1821.

Buckingham, E. "Model Experiments and the Forms ofEmpirical Equations," Trans. ASMS, 37, 1915s 263.

Ferguson, T. B. The Centrifugal Compressor Stage. London: Butterworth & Co., Ltd., 19&3.

Karassik, I. J., and R. Carter. Centrifugal Pumps. New York; F. W. Dodge Corp., I960.

Lewinsky, H. P., and Kesslitz. "Experimental Determina­tion of Flow Patterns in Centrifugal Pumps,"The Engineers Digest, 22, 1961, 77.

Messersmlth, C . W., F. C. Warner, and R. A. Olsen.Mechanical Engineering Laboratory. 2nd ed.New York; John Wiley & Sons, 1958.

Organlck, Elliott I . A FORTRAN Primer. Palo Alto;Add!son^Wesley Publishing Co., 1963.

Shapiro, Ascher H. The Dynamics and Thermodynamics of Compressible Fluid Flow. New York; The Roland Press Co., 19^3.

Sheets, H. E. "The Flow Through Centrifugal Compressors and Pumps," Trans. ASME, 72, 1950, 1009.

Shepherd, D. G. Principles of Turbomachinery. New York; The Macmillan Co., 195&.

Sorensen, E. "Potential Flow Through Centrifugal Pumps and Turbines," NACA Technical Memorandum, 973, April, 1941.

57

Stanitz, J. D. "Some Theoretical Aerodynamic Investiga­tions of Impellers in Radial and Mixed Plow Centrifugal Compressors," Trans» ASMS, 1952,473.

Stepanoff, A . .J. Centrifugal and Axial Flow Pumps.2nd ed. New York: John Wiley & Sons, 1957«

Test Code for Centrifugal Pumps. PTC 8.1. New York:The American Society of Mechanical Engineers, 1954.

Tuve, G. L. Mechanical Engineering Laboratory. New York: McGraw-Hill Co., 19oll

Varley, P. A. "Changing Centrifugal Pump Performance,"Engineering, 1£0, I960, 484,

APPENDIX A

£5-

9.5- ORIFICEi t -t

FI. DAY

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APPENDIX B

62PHONY BRAKE AND MOTOR EFFICIENCY CALCULATIONS

Electric Horsepower Into the MotorHP = (revolutions of-- wattmeter dial) (meter constant)

8 (time of revolutions)(conversion factor5HP = (3600 sec/hr)(10 rev)(2,4 whr/rev)

(49.6 sec) (7^6 watts/hp)

HP. - - B W - - 2 -3 3 h p

Prony Brake CalculationsBEP = 2TT r P n

33»000where %

r = length of brake arm (ft)P = net force acting on scales (lb) n = shaft speed (rpm)BHP = horsepower absorbed by prony brakeBHP = (2) (3.14) (3 ft) (3.1 lb) (1100 rev/mln

33,000 ft-lb/hpBHP = 1 . 9 3

Electric Motor Efficiency

^ = i ; = H I = °-829

APPENDIX C

4

63

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APPENDIX D

84SAMPLE CALCULATIONS

The following calculations are in the sequence that they occur in the computer FORTRAN program.

Variable parameters used during each test Q - capacity (gpm)PH = discharge manometer reading (cm Hg)PA = barometric pressure (cm Hg)PS = inlet manometer reading (cm Hg)TIME = time for 10 revolutions of wattmeter dial (sec)

3SWM = specific weight of mercury (lb/ft )3SWW = specific weight of water (lb/ft )

Constant quantities for each test Speed = 1000 rpmZD = distance above pump datum of discharge pressure

tap (0.416 ft)ZS = distance above pump datum of inlet pressure

tap (0 ft)2G = gravitational constant (32.174 ft/sec )

2AIN = area of inlet pipe (0.0122 ft )2AOUT = area of outlet pipe (0.0218 ft )

Flow rate conversion (gpm to f t y s e c )0.002228 ft^/sec = 1 gpm QC = capacity (ft^/sec)

SAMPLE CALCULATION (Con9t)85

QC = (Q gpm) (0,002228)QC = (26.3) (0.002228) = 0.0599 ft3/sec

Conversion of measured pressure readings (cm Hg to ft Eg) PHPT = discharge pressure (ft Eg)PHFT = (PH cm Eg) (0.3937 in/cm) (1/12 ft/in)PHPT = (50.2) (0.3937/12)PHPT = 1.648 ft Eg

PSPT = inlet pressure (ft Eg)PSPT = (PS cm Eg)(0.3937/12 ft/cm)PSPT = (0.2)(0.3937/12)PSPT = 0.00654 ft Eg

PAFT = barometric pressure (ft Eg)PAFT = (PA cm Eg)(0.3937/12 ft/cm)PAFT = (62.25)(0.3937/12)PAFT = 2.04 ft Eg

Calculations for the variable water column height associated with the discharge "wet" tube manometer X = total water column (ft)X = (normal height of column)4-(added height due to mano­

meter deflection)X = (1.54 f t ) 4- (PHPT/2.0)X = (1.54)+(1.648/2.0)

86SAMPLE CALCULATIONS (Con’t)

X = 1.54 + 0,823 = 2.363 ft

XX = net water column acting on Indicating fluidXX = (distance from pressure tap to maximum ordinate of

water) - XXX = 2.0 - 2.361XX a - 0.361 ft

Head calculations AA = SWM/SWWAA = 845.7 / 62.25 = 13.6

VD = discharge velocity (ft/sec)VD = QC / AOUTVD = = 2.75 ft/sec

0.0218, ft

VS = inlet velocity (ft/sec)VS = QC / A IN

VS = = 4.91 ft/sec0.0122 ftz

PHEAD = total discharge head (ft)xrr)2

PHEAD = — + Z D + X X + A A (PAPT + PHPT)2Q

PHEAD = ft/secj2 + 0.416 ft - 0.361 ft t 13.6(3.688)ft2(32.174 ft/sec )

PHEAD = 0.1175 ft + 0.416 ft - O.36I ft + 50.2 ft PHEAD = 50.37 ft

8?SAMPLE CALCULATIONS (Con*t)

SHEAD = total Inlet head (ft)VS2SHEAD ss — - + ZS + AA(PAFT - PSPT)2G - 2

SHEAD = +0-5- 13.6(2,04 - 0„006)ft2(32.174 ft/sec )

SHEAD = 0.375 ft + 27.6 ftSHEAD = 27.97 ft

HEAD = total developed head (ft)HEAD = PHEAD - SHEADHEAD = 50.37 ft - 27.975 ftHEAD = 22.39 ft

Liquid horsepower (WHP)WHP = (lbs of liquid pumped per minute)(total head)

ft=lb/hpThe above equation can be modified so the capacity

can be expressed in gpm at standard conditions,0.12 gpm = 1 Ib/min

WHp =0.12(33,000 ft-lb/hp)

Since we do not normally operate at standardconditions the above equation will have to contain aspecific weight ratio correction term;

_ (gpm)(HEAD ft) , SWW operation temp.39962.5 S¥W at 68? P

88

WHP =

WHP =

Power BHP = BHP =

BHP =

BHP =

BHP =

SAMPLE CALCULATIONS (Con’t)

(26.3 gpm)(22.39 ft) 62.25 396275 6273(0.1485)(0.999) = 0.1484 hp

(BHP)(electric hp input)(efficiency of electric motor)(fSPlatt/hp) (0'829)(3600 seo/hr)(10 rev.of wattmeter)(meter const.2.4)(.829)

(TIME)(?46 watts/hp)115.82 (0.829)TIME

i i f i f (0-829) - °-872 hp

Efficiency (EPF)EPF = ™ = 0.1484 = Ool69

input BHP 0.872

APPENDIX E

89

90FORTRAN PROGRAM

1F0RMAT(42X$43H THIS IS THE OUTPUT FROM THESIS EXPERIMENT/SIX3 22H BY ReDAY AND J.LINKA/51X924H MECHANICAL ENGINEERING//)

2FOBMAT(40X,46H TABLE OF PERFORMANCE PARAMETERS FOR TEST PUMP) 4F0RMAT(10X9l4H CAPACITY(GPM)s10X9l6H TOTAL HEAD(FT)919X914H EFF95Xs11H POWER(HP) /)

5FORMAT(2X,l495X,F10.3,l6X9F10,3s17X8F10.39l3X,F10.3)PRINT 1 PRINT 2 PRINT 4

6READ 7,RUN$Q,PH,PS$TIME$SWM8SWWsPA?PORMAT(I1097fl0e3)QC=Q«0o002228SPEED = 1000,0PHFT = PH * (0,3937 / 12.0)PSFT = PS * (0.3937 / 12.0)PAFT = PA * (0,3937 / 12.0)X = 1.54 + (PHFT / 2.0)XX = 2.0 - XG a 32.174ZD = 0.416ZS = 0.0AA = SWM / SWWAIN = 1.766/144.0AOUT = 3o140/144.0

FORTRAN PROGRAM (Gon’t)91

VD = QG / AOUTVS = QC / AINPHEAD = (VD**2.0) / (2,0*G) -i- ZD -5- XX -t- AA * (PAFT-KPHFT)SHEAD = (VS»»2=0) / (2.0*G) + ZS + AA * (PAFT - PSFT)HEAD * PHEAD - SHEAD WHP = (Q*HEAD»SWW) / (3962.5 * 62.3)BHP = (115.82 / TIME) * (0.829)EFF = WHP / BHPPOWER = (QC*HEAD*SWW) / (EFF * 550.0)PRINT 5o RUN 9Q ,HEAD,EFF »POWERGO TO 6END

APPENDIX P

TABLE 193

SAMPLE OP LABORATORY DATA

Test Number 01 Impellers Unmodified three-vaned impeller Dates 9 Febo 1965 Speeds 1000 rpmWater temperatures 75°P Air temperatures 68°PBarometric pressures 69,7 cm EgSpecific weight of waters 62.25 lb/ft3Specific weight of mercurys 845.7 lb/ft3

Capacity Discharge Pressure (cm Eg)

Inlet Pressure Time* (sec)

78.5 21.9 18.9 81.970.3 24.4 17.1 84.2

4 65.6 29.1 14.7 86.760.6 32.9 12.2 90.455.1 36.6 9.9 93.049.7 40.1 7.6 94.443.9 43.4 5.2 98.736.3 46.6 2.8 104.032.0 48.2 1.6 108.026.3 50.2 0.2 110.0

®Time for 10 revolutions of Watthour meter Indicator dlal0

APPENDIX G

95TABLE 2

SAMPLE OP COMPUTER RESULTS AS PRINTED BY THE COMPUTER

Test Capacity _LseslL.

Total head (ft)

Efficiency Power-ilml

1 74.700 16.745 0.269 . 1.1721 70.300 17-240 0.268 1.1401 65,600 18.412 0.275 1.1071 60.600 19-150 0.276 1.0621 55-100 19.937 0.268 1.0321 49.700 20.613 0.254 1.0171 43.900 21.150 0.241 0.9731 36.300 21.668 0.215 0.9231 32.000 21.923 0,199 0.8891 26.300 22.274 0.169 0.873

etc*