ME 4621-1-C-B

Pump Performance

By

Yvette Triay

Associates: Joseph Tran

Robert Roland

Experiment Performed: 28 June 2011 Report Submitted: 7 July 2011

Department of Mechanical Engineering Louisiana State University

ABSTRACT

The understanding of pump performance is crucial when choosing a design for an application. Important characteristics of pump performance are head, power and efficiency. This experiment focused on relating these characteristics to volumetric flow rate and demonstrating the self-similarity of pumps. The experiment used an Armfield pump unit with sensors that transmitted certain measurements to a DAQ system for motor speeds of 30, 40, and 50 Hz. These measurements were recorded and used to compute head, power, and efficiency. Plots were then generated for the performance characteristics. Non-dimensionalized values for pressure increase and flow rate were also computed and plotted, proving the pump to be self-similar. The results showed that as flow rate increased, pressure, head, and efficiency decreased and power increased. In order to achieve a better understanding of pump performance, it is recommended to run the experiment with two pumps either in parallel or series.

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Table of Contents Introduction………………………………………………………………………………….…….3

Theory………………………………………………………………………………………..……3

Experimental Apparatus and Instrumentation………………………………………….…………5

Experimental Procedure…………………………………………………………………………...6

Uncertainty Analysis………………………………………………………………………………6

Presentation of Results……………….……………………………………………………………7

Analysis and Discussion of Results……………………………...……………………………..…8

Conclusions and Recommendations………………………..……………………..………………9

Reference Material………………………………………………………………………….……10

Appendix I……………………………………………...………………………………..………11

Appendix II……………………………………...……………………………………………….14

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Introduction

Pumps are machines that add energy to a liquid by performing work on it. They are

considered to be turbomachines, which are dynamic fluid-handling devices that direct the flow

with blades or vanes attached to a rotating member called an impeller. Centrifugal pumps can be

classified further as pumps with radial flowpaths [1]. Pumps are extremely important machines

that affect peoples’ everyday life. Pumps can be found in many applications, including

automobiles, pumping stations, and industrial applications such as oil refineries supplying and

removing chemicals and wastes [2]. This experiment focused on comparing pump pressure,

head, power, and efficiency to volumetric flow rate in order to understand the characteristics of

pumps. Charts were generated and compared to theoretical trends. These results were then used

to prove how the pump performance was self-similar.

Theory

In centrifugal pumps, the fluid approaches the moving impeller blade at a certain velocity.

The velocity of the fluid changes as it exits, as well as the angle of the blade to the fluid. An

exchange of momentum occurs, and an increase in pressure results from the change of the

velocity back to its initial state [2]. The equation used to find the pump head can be derived

from Bernoulli’s equation. Making certain assumptions yields Equation 1,

ℎ!"#! = Δ!/!" (Equation 1)

where ΔP is the pressure increase across the pump, ρ is the density of the fluid, and g is gravity.

The hydraulic power is the rate of mechanical energy input to the fluid, which is the flow

rate multiplied by the increase in pressure across the pump, as can be seen in Equation 2.

! = !Δ! (Equation 2)

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The mechanical input power needed to drive the pump is related to the hydraulic power

by defining the pump efficiency as can be seen in Equation 3.

! =!/!! (Equation 3)

Typical characteristics of pumps include producing a smaller head and an increase in

input power as the flow rate is increased [1]. The performance characteristics should also remain

self-similar. This is shown by plotting the non-dimensionalized pressure rise against the non-

dimensionalized flow rate and then obtaining results that collapse onto one another [2]. The

equation for non-dimensionalized flow rate and non-dimensionalized pressure can be seen in

Equations 4 and 5, respectively.

!∗ = !!!!

(Equation 4)

Δ!∗ = !!"#!

!!!! (Equation 5)

The variable w is the motor speed, and D is the diameter.

Experimental Apparatus and Instrumentation

The Armfield pump unit consisted of a centrifugal pump attached to a motor. The pump

was connected to a water tank by means of piping, which had several valves to regulate flow.

Several sensors were placed throughout the unit to measure pressure differences, water

temperature, flow rate, and motor speed. These sensors transmitted the measured data to the data

acquisition system, and the computer program displayed these values onto the screen. The errors

in the DAQ system were ±0.3 Hz for the motor speed, ±0.00004 m3/s for the flow rate, ±2.0 kPa

for the pressure difference across the pump, and ±1.0 Watts for the motor power. The ambient

pressure and temperature were also recorded with an error of ±0.01 cmHg and ±1.0°F,

respectively.

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Figure 1: Schematic of the Pump Unit Apparatus Used [3]

Experimental Procedure

Before beginning the experiment, it was appropriate to measure and record the ambient

temperature and pressure in the laboratory. Once the Armfield pump unit was connected to the

computer, the corresponding icon on the desktop was clicked to initialize the DAQ system. The

main gate valve was then fully opened, and flipping the appropriate switches turned on the motor.

Only one pump was chosen to operate for this experiment. Next, the motor was set to a desired

speed, and the flow rate was varied by opening and closing the gate valve. Ten samples for three

different motor speeds of 30, 40, and 50 Hz were recorded. After all the data was collected, the

pump unit was turned off by flipping the power switches.

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Uncertainty Analysis

The average results of the uncertainly analysis for pump head (hpump), power (W), and

efficiency (η) be seen in Table 1. All the uncertainties were approximately within 5% of their

corresponding values. A table of the complete uncertainty analysis can be seen in Table 3 of

Appendix II.

Table 1: Uncertainty Analysis Motor Speed [Hz] ε(hpump) [m] ε(W) [Watt] ε(η)

30 0.204 2.232 0.005 40 0.204 3.286 0.004 50 0.204 4.577 0.003

Presentation of Results

Various measurements were taken for three different motor speeds of 30, 40, and 50 Hz.

They were then compared with volumetric flow rate for this experiment. Figure 1 shows the

pressure increase across the pump as a function of flow rate. Figure 2, 3, and 4 show the pump

characteristics, which are head, power, and efficiency, as functions of volumetric flow rate.

Non-dimensionalized pressure increases and flow rates were found and then plotted against each

other to demonstrate self-similarity of the pump. This can be seen in Figure 5.

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Figure 2: Pressure Increase Across Pump vs. Flow Rate

Figure 3: Pump Head vs. Flow Rate

Figure 4: Pump Power vs. Flow Rate

0  20  40  60  80  

100  120  

Pressure  Differen

ce  [k

Pa]  

Flow  Rate  [m3/s]  

Pressure  Increase  vs.  Flow  Rate  

30  Hz  

40  Hz  

50  Hz  

0  2  4  6  8  10  12  

Head

 [m]  

Flow  Rate  [m3/s]  

Head  vs.  Flow  Rate  

30  Hz  

40  Hz  

50  Hz  

0  

50  

100  

150  

Power  [W

a?s]  

Flow  Rate  [m3/s]  

Power  vs.  Flow  Rate  

30  Hz  

40  Hz  

50  Hz  

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Figure 5: Pump Efficiency vs. Flow Rate

Figure 6: Self-Similar Pump Characteristic Chart

0  

10  

20  

30  

40  Effi

cien

cy  [%

]  

Flow  Rate  [m3/s]  

Efficiency  vs.  Flow  Rate  

30  Hz  

40  Hz  

50  Hz  

0  1  2  3  4  

0   0.1   0.2   0.3   0.4   0.5  

Non

-­‐Dim

ension

al  Pressure  

Non-­‐DImensional  Flow  Rate  

Non-­‐Dimensional  Pressure  Rise    vs.  Non-­‐Dimensional  Flow  Rate  

30  Hz  

40  Hz  

50  Hz  

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Analysis and Discussion of Results

When comparing the pressure difference across the pump to flow rate, it can easily be

seen how the pressure difference decreased as the flow rate increased. This trend was expected.

In a constant cross-sectional area pipe, flow rate is directly proportional to velocity, and velocity

is inversely related to pressure. Since flow rate was being decreased, velocity also was

decreasing causing pressure to increase. These trends can be seen in Figure 2.

Figure 3 shows pump head decreasing as flow rate increased. This was an expected

result. It can also be seen how higher motor speeds yield greater pressure heads than lower

motor speeds. Figure 4 represents the pump power as a function of flow rate. It can be seen that

they are directly related to each other. The higher motor speeds resulted in greater power than

the lower motor speeds. Figure 5 shows the efficiency of the pump decreased as flow rate

increased; however, the pump was more efficient at higher motor speeds.

By plotting the non-dimensionalized pressure increase as a function of the non-

dimensionalized flow rate, it can be seen from Figure 6 that the performance characteristics were

self-similar. This proves that for any given flow rate, the pressure increase will be very similar

for set motor speeds.

Conclusions and Recommendations

For this experiment, the trends in the plots demonstrated expected pump characteristics.

Pressure increase, pump head, and efficiency all decreased as flow rate increased. However, the

power increased as flow rate increased. For all the plots, the higher motor speeds resulted in

higher performance characteristics than the lower motor speeds. It is recommended to perform

this experiment at one or two more motor speeds, since the procedure does not take a long time

and the calculations are not tedious. By having results at more motor speeds, one can be even

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more aware of the trends of the performance characteristics and the self-similarity of the pump.

Since there are two pumps on the Armfield Pump Unit, it is also recommended that the

experiment consist of running the pumps in parallel to deliver greater flow or series to deliver

greater head. This would add to the understanding of pumps and being able to choose pumps

based on certain criteria.

Reference Material

[1] Fox, Robert. Pritchard, Philip. McDonald, Alan. Introduction to Fluid Mechanics. 7th Ed.

John Wiley & Sons, Inc. 2009.

[2] ME 4621 Thermal Sciences Laboratory Manual: Experiment B. Louisiana State University.

Baton Rouge, LA. 2011.

[3] http://users.rowan.edu/~hesketh/0906-309/Laboratories/Armfield

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Appendix II: Raw Data Sheet Collected from Lab

Table 3: Raw Data Date: 28th Jun 2011

Orifice Water Pump 1 Motor 1 Motor 1 Volume Pump 1 Pump 1 Overall pressure temp Pressure speed power Flow rate total power efficiency

drop drop rate head output dpo Tw dpp1 n1 Pgr1 Qv Hd P Egr kPa deg C kPa Hz Watts m^3/s m Watts % 6.20 22.0 33.13 30.57 305.1 0.00097 3.47 33.06 10.84 6.04 22.1 32.93 30.13 292.6 0.00096 3.45 32.46 11.09 5.67 22.4 35.25 30.37 276.7 0.00093 3.69 33.61 12.14 5.37 22.2 35.36 30.10 273.6 0.00091 3.70 32.79 11.99 4.58 22.4 37.48 30.10 257.4 0.00084 3.92 32.05 12.45 3.64 22.5 39.30 30.19 237.2 0.00075 4.10 29.92 12.61 3.43 22.6 40.31 30.13 209.8 0.00072 4.21 29.81 14.21 3.00 22.6 40.81 30.40 180.5 0.00068 4.26 28.19 15.62 2.63 22.7 40.00 31.04 161.9 0.00063 4.18 25.88 15.98 2.46 22.7 47.68 30.75 137.3 0.00061 4.96 29.74 21.66 10.03 23.6 55.46 39.98 353.0 0.00124 5.76 69.71 19.75 8.82 24.6 56.47 40.10 338.8 0.00116 5.86 66.55 19.64 8.00 23.8 61.52 40.48 332.7 0.00111 6.38 68.93 20.72 7.24 23.8 70.00 42.15 323.2 0.00105 7.24 74.51 23.06 5.67 24.8 62.83 40.19 305.6 0.00093 6.51 59.29 19.40 5.22 23.9 66.27 40.92 294.3 0.00089 6.86 59.93 20.36 4.53 23.3 70.91 40.39 259.9 0.00083 7.33 59.68 22.96 3.65 17.7 72.63 40.45 242.8 0.00075 7.50 54.86 22.59 2.79 18.6 75.16 40.71 184.9 0.00065 7.76 49.63 26.84 2.34 19.2 77.78 40.65 170.2 0.00060 8.03 46.99 27.60 14.41 22.3 81.62 50.39 417.2 0.00148 8.43 122.33 29.32 13.99 21.0 77.88 50.36 406.7 0.00146 8.04 115.06 28.29 12.74 21.6 87.18 50.24 400.3 0.00139 8.99 122.79 30.67 11.85 26.3 92.73 50.24 393.7 0.00135 9.57 125.95 31.99 10.66 26.4 96.07 50.27 383.0 0.00128 9.91 123.68 32.29 9.17 26.4 99.50 50.03 361.5 0.00118 10.26 118.83 32.87 8.79 26.5 100.92 50.12 353.0 0.00116 10.41 117.95 33.42 7.68 26.7 102.83 50.12 347.1 0.00108 10.61 112.32 32.36 7.17 26.8 106.57 50.18 326.8 0.00105 10.99 112.47 34.41 5.81 26.9 108.69 50.03 305.8 0.00094 11.21 103.22 33.75

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Appendix II: Complete Uncertainty Analysis Table

! ℎ!"#! = !(!!)!"

(Equation 6)

! ! = Δ! ∗ !(!) ! + ! ∗ !(Δ!) ! !/! (Equation 7)

! ! = !(!)!!

!+ !!∗!(!!

!!!! !/!

(Equation 8)

Table 4: Complete Uncertainty Analysis ε(hpump) ε(W) ε(η) 0.204636783

30 Hz

2.353525172 0.003296052

2.329209464 0.003437267

2.335071106 0.003638717

2.297597106 0.003680295

2.245674924 0.003912911

2.165824801 0.004248269

2.167163262 0.004811895

2.120103226 0.005604321

2.04062766 0.006250042

2.266803321 0.007447764 Avgerage 2.232160004 0.004632753

40 Hz

3.324147707 0.002886309

3.239105166 0.003006434

3.307570583 0.003067991

3.501841717 0.003173734

3.127784962 0.003331998

3.195925411 0.003465457

3.288091017 0.003945535

3.266338666 0.004220141

3.277600155 0.005595394

3.332867302 0.00608864 Average 3.286127269 0.003878163

50 Hz

4.411098676 0.00249582

4.271423411 0.002553305

4.465502302 0.002610524

4.582836745 0.002664197

4.612902704 0.00274144

4.631214232 0.0029094

4.654722641 0.002984701

4.64896574 0.003025789

4.749359151 0.003233185

4.738503303 0.003448436 Average 4.57665289 0.00286668