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7/30/2019 Pump PracticeProblems

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Practice Problems on Pumps

C. Wassgren, Purdue University Page 1 of 16 Last Updated: 2010 Oct 29

pump_02

A centrifugal pump with a 12 in. diameter impeller requires a power input of 60 hp when the flowrate is 3200 gpm

against a 60 ft head. The impeller is changed to one with a 10 in. diameter. Determine the expected flowrate, head,

and input power if the pump speed remains the same.

Answer(s):

Q2 = 1850 gpm

H2 = 41.7 ft

2W = 24.1 hp


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pump_05

Data measured during tests of a centrifugal pump at 3500 rpm are given in the table below:

Parameter Inlet Section Outlet Section

gage pressure,p [kPa] 95.2 412

elevation above datum,z [m] 1.25 2.75

avg speed of flow, V[m/s] 2.35 3.62

The working fluid is water. The flow rate is 11.5 m3/hr and the torque applied to the pump shaft is 3.68 Nm.

Evaluate the total heads at the pump inlet and outlet, the hydraulic power input to the fluid, and the pump efficiency.

If the electric motor efficiency is 85%, calculate the electric power requirement.

Answer(s):

Hinlet = 21.6 m

Houtlet = 55.7 m

fluidW = 1.07 kW

pump = 79.4%

requiredfor motor

W = 1.59 kW


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pump_06

A small centrifugal pump, when tested at 2875 rpm with water, delivered a flowrate of 252 gpm and a head of 138 ft

at its best efficiency point (efficiency is 76%). Determine the specific speed of the pump at this test condition.

Sketch the impeller shape you expect. Compute the required power input to the pump.

Answer(s):

Nsd = 1130 rpmgpm1/2/ft3/4Ns = 0.414

shaftW = 11.6 hp


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pump_07

Water is to be pumped from one large open tank to a second large open tank. The pipe diameter throughout is 6 in.

and the total length of the pipe between the pipe entrance and exit is 200 ft. Minor loss coefficients for the entrance,

exit, and the elbow are shown on the figure and the friction factor can be assumed constant and equal to 0.02. A

certain centrifugal pump having the performance characteristics shown is suggested as a good pump for this flow

system.

a. With this pump, what would be the flow rate between the tanks?b. Do you think this pump would be a good choice?

Answer(s):

Q 1600 gpm

The operating efficiency is close to the optimal efficiency of 86% so this is a good pump to use.

pump

Kentrance = 0.5

Kelbow = 1.5

Kexit = 1.0

10 ft

pipe diameter = 6 in

total pipe length = 200 ft


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pump_08

Data measured during tests of a centrifugal pump at 3500 rpm are given in the table below:

Parameter Inlet Section Outlet Section

gage pressure,p [kPa] 85.2 412

elevation above datum,z [m] 1.25 2.75

avg speed of flow, V[m/s] 2.35 3.62

The flow rate is 11.5 m3/hr and the torque applied to the pump shaft is 3.68 Nm. Evaluate the total dynamic heads

at the pump inlet and outlet, the hydraulic power input to the fluid, and the pump efficiency. Specify the electric

motor size needed to drive the pump. If the electric motor efficiency is 85%, calculate the electric power

requirement.

Answer(s):

Hinlet = 10.2 m

Houtlet = 45.4 m

fluid 1100 WW

= 80%

pump 1.8 hpW

motor 2.1 hpW


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pump_10

The pipe system used for a yard sprinkler system is shown below.

The pump performance specifications are given below.

Curve fits to the data in the plot (where [Q] = L/s):

H[m] = (-0.5582 ms2/L2) Q 2 (3.8441 ms/L) Q + 28.011 m

= (-0.0802 s2/L2) Q2 + (0.3459 s/L) Q + 0.0133

NPSHR [m] = (0.3 ms2/L2) Q 2 + 1 m

Determine:

a. Determine the system head curve (i.e. the head the pump must supply in order to have a given flow rate).

b. Determine the operating point for the given conditions.c. Is this a good pump to use for the given conditions? Justify your answer.

d. Will this pump cavitate for the given conditions?

Answer(s):

not available at this time

two 90 regular threaded elbows

gate valve (1/2 closed)

1 m

5 m1 m

1 m

pump

pond

10 m

Upstream of the contraction: 2.5 cm inner diam. galvanized iron pipe

Downstream of the contraction: 1.9 cm inner diam. galvanized iron pipe

Properties of water at given conditions: = 1000 kg/m3, = 1*10-

6m

2/s,

vapor pressure = 2.34 kPa (abs)

sudden contraction

discharge to the atmosphere

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0

5

10

15

20

25

30

0.0 1.0 2.0 3.0 4.0

efficiency

head,

NPSH[m]

flow rate [L/s]

NPSHR

H


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pump_11Consider the pipe/pump system shown below.

The pump performance head curve is approximated as:

H= (3.23*101 m) + (1.65*102 s/m2)Q - (4.82*103 s2/m5)Q 2

where [H] = m and [Q] = m3/s.

a. Determine the system head curve for the pipe system.

b. Determine the operating point for the system.

c. How will the flow rate within the pipe change over time if the pipe carries hard water and lime deposits form

on the interior pipe walls? Explain your answer. You should assume that the deposits do not significantly affect

the pipe diameter.

d. If we wanted to add a valve to control the flow rate in the pipe, would it be better to put the valve upstream or

downstream of the pump? Explain your answer.

Answer(s):

HS= -10 m + (2.07*104 s2/m5)Q2

Q = 4.41*10-2 m3/s

flow rate will decrease over time due to increased roughnessput valve downstream of pump so that it wont affect NPSHA

water

pump

cast iron pipe

diameter = 0.10 m

water density = 1000 kg/m3

water kinematic viscosity = 1.0*10-6 m2/s

10 m

50 m 50 m

0

5

10

15

20

25

30

35

40

0.0E+00 2.0E-02 4.0E-02 6.0E-02 8.0E-02

head,H[m]

flow rate, Q [m3/s]

well-roundedinlet


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pump_12

Consider the pipe/pump system shown in the figure below.

The pump performance head curve is approximated as:H= (3.23*101

m) + (1.65*102

s/m2)Q - (4.82*10

3s

2/m

5)Q

2

where [H] = m and [Q] = m3/s.

a. Determine the system head curve for the pipe system.

b. Determine the operating point for the system.

c. How will the flow rate within the pipe change over time if the pipe carries hard water and lime deposits form

on the interior pipe walls? Explain your answer. You should assume that the deposits do not significantly affect

the pipe diameter.

d. Calculate the net positive suction head available at the pump inlet.

e. If we wanted to add a valve to control the flow rate in the pipe, would it be better to put the valve upstream or

downstream of the pump? Explain your answer.

Answer(s):

HS= 2 m + (5.01*102 s2/m5)Q2

Q = 9.26*10-2

m3/s

flow rate will decrease due to increased roughness

NPSHA = 6.93 m

move the valve downstream of the pump to avoid decreasing NPSHA

H

D

P

h

h = 0.5 m

H = 2 m

D = 0.2 m

L1 = 10 m

L2 = 20 mThe pipe is made of concrete

with a roughness of 3 mm.

90 rounded pipe bend

(equivalent length of 30 pipe diameters)

water with density of 1000 kg/m3, kinematic viscosity of 1.0*10-6 m2/s, and vapor pressure of 2.34 kPa

0

5

10

15

20

25

30

35

40

0.0E+00 2.0E-02 4.0E-02 6.0E-02 8.0E-02

head,

H[m]

flow rate, Q [m3/s]

L1 L2


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pump_13

Consider the pipe system shown in the figure below. The fluid to be pumped is water with a density of 1.0E3 kg/m3,

a kinematic viscosity of 1.0E-6 m2/s, and a vapor pressure of 2.3E3 Pa.

The pump used in this system has the performance plot shown below.

Curve fits to the pump performance data are given below:

H[m] = (-3.25E1 s2/m5) Q2 + (1.23E0 s/m2) Q + (2.78E1 m)

P = (-3.74E0 s2/m6) Q2 + (3.60E0 s/m3) Q

a. Determine the operating volumetric flow rate of the system.

b. Is the given pump a good choice for this system? Explain your answer.c. Determine the NPSHA to the pump for the flow rate determined in part (a).

d. Give one specific modification to the pipe system that could be employed to decrease the likelihood that

cavitation will occur in the pump.

Answer(s):32.85E-1 m /sQ ; this is not a good pump for this system

NPSHA = 6.01E0 m; decrease the elevation, decrease pipe length, use a rounded inlet

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0

5

10

15

20

25

30

0 0.5 1

efficiency

head[m]

flow rate [m3/s]

pump

7.0 mall pipes are comprised of 0.20 m inner

diameter commercial steel pipesharp-edged inlet90 threaded

elbow1.0 m

10. m10. m


10/16



pump_14

Consider the pipe/pump system shown below in which water (with a density of 1.0E3 kg/m3

and dynamic viscosity

of 1.3E-3 Pas) is pumped from tank A to tank B.

The pump to be used in the system has the following pump performance curve.

Curve fits to the pump performance data are given below:

H[m] = (-1.5E3 s2/m5) Q2 + (2.8E1 s/m2) Q + (6.3E1 m)

P = (-5.6E1 s2/m

6) Q

2+ (1.2E1 s/m

3) Q + (2.1E-1)

a. Determine the operating point for the system.

b. Is the given pump efficient for this application? Explain your answer.c. Do you anticipate that cavitation in the pump will be an issue? Explain your answer.

Answer(s):3

1.0E-1 m /sQ ; this is an efficient pump for this application;

cavitation in the pump will most likely not be an issue

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

0.0E+00

1.0E+01

2.0E+01

3.0E+01

4.0E+01

5.0E+01

6.0E+01

7.0E+01

0.0E+00 5.0E-02 1.0E-01 1.5E-01

efficiency

head[m]

flow rate [m3/s]

90 regularthreaded elbow

8.0 m10. m

5.0 m

0.5 m

90 regular

threaded elbow

gate valve

(1/2 open)

pA = 0

(gage)

pB = 200 kPa(gage)

B

A

flow

15 cm diameter pipe with a total length

of 40 m and roughness of 0.9 mm

re-entrant inlet

gravity

pump


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pump_15

Data from tests of a Peerless end suction Type 1440 pump operated at 1750 rpm with a 14.0 in. diameter impeller

are:

flowrate [gpm] total head [ft] power input [hp]

290 204 30

440 203 35

550 200 40

790 187 45

920 175 50

1280 135 60

Plot the performance curves for this pump; include a curve of efficiency versus volume flow rate. Locate the best

efficiency point and specify the pump rating at this point.

Answer(s):

QBEP = 820 gpm

= 83%

HBEP = 185 ft


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pump_16

Typical performance curves for a centrifugal pump, tested with three different impeller diameters in a single casing,

are shown in the figure below. Specify the flow rate and head produced by the pump at its best efficiency point with

a 12 in. diameter impeller. Scale these data to predict the performance of this pump when tested with 11 in. and 13

in. impellers. Comment on the accuracy of the scaling procedure.

Answer(s):

Q12 in.,BEP = 2200 gpm

H12 in.,BEP= 130 ft

UsingD2 = 11 in. andD1 = 12 in., Q1 = 2200 gpm, Q11 in.= 1690 gpm.

UsingD2 = 13 in. andD1 = 12 in., Q1 = 2200 gpm, Q13 in. = 2800 gpm.

From the pump performance diagram, Q11 in.

2000 gpm.

From the pump performance diagram, Q13 in. 2500 gpm.

UsingD2 = 11 in. andD1 = 12 in.,H1 = 130 ft,H11 in.= 109 ft.

UsingD2 = 13 in. andD1 = 12 in.,H1 = 130 ft,H13 in. = 153 ft.

From the pump performance diagram,H11 in. 110 ft.

From the pump performance diagram,H13 in. 150 ft.


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pump_17

A Peerless Model 16A 18B pump is proposed as the supply unit for the Purdue Engineering Mall fountain. The

following requirements have been provided by the architectural firm:

The pump outlet is to be located 3 feet below ground level.

The water flow is to reach a peak height of 30 feet above ground level.

The discharge from the pump is 6 inches in diameter.

The pump characteristics are given in the following plot.

a. What head must be supplied by the pump? Report your answer in ft.

b. What flow rate must be supplied by the pump? Report your answer in gal/min (gpm).

c. What pump impeller diameter should be used? (either 15.00, 16.00, 17.00, or 18.00 inch diameter)

d. What is the pump efficiency? Report your answer in terms of a percentage.

e. What power is required to drive the pump? Report your answer in horsepower (hp).

f. What range of NPSH is acceptable at the pump inlet? Report your answer in ft.

Answer(s):

HS= 33 ft

Q = 9.05 ft3/s = 4060 gpm

15.00 inch

~80%

input intopump

42.4 hpW

> ~9 ft


14/16



pump_18

A pump station is used to fill a tank on a hill using water from a lake. The flow rate is 10.5 L/s and atmospheric

pressure is 101 kPa (abs). The pump is located 4 m above the lake, and the tank surface level is 115 m above the

pump. The suction and discharge lines are 10.2 cm diameter commercial steel pipe. The equivalent length of the

inlet line between the lake and the pump is 100 m. The total equivalent length between the lake and the tank is 2300

m, including all fittings, bends, screens, and valves. The overall efficiency of the pump and motor set is 70%.

What is the net positive suction head available for this pump?

Answer(s):NPSHA = 4.4 m

115 m

4 mlake

tank

pump

water density = 1000 kg/m3

water dynamic viscosity = 1*10-3 Pa.s

water vapor pressure = 1820 Pa (abs)


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pump_19

Brine, with a specific gravity of 1.2, passes through an 85% efficient pump at a flow rate of 125 L/s. The centerlines

of the pumps 300 mm diameter inlet and 200 mm diameter outlet are at the same elevation. The inlet suction gage

pressure is 150 mm of mercury (specific gravity of 13.6) below atmospheric pressure. The discharge pressure is

measured 1.2 m above the centerline of the pumps outlet and indicates 138 kPa (gage). Neglecting losses in the

pipes, what is the input power to the pump?

Answer(s):

into pump 26.4 kWW

pump

inlet diameter =

300 mm

outlet diameter = 200 mm

inlet pressure =

-150 mmHg (gage)

outlet pressure = 138 kPa (gage)

1.2 m


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