Fluid Mechanics: Fundamentals and Applications
Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Textbook Question
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Chapter 14, Problem 47EP

The performance data for a centrifugal water pump are shown in Table P14-47E for water at 77 ° F (gpm= gallons per minute). (a) For each row of data, calculate the pump efficiency (pe1tent). Show all units and unit conwrsions for full credit. (b) Estimate the volume flow rate (gpm) and net head (ft) at the BEP of the pump.

Chapter 14, Problem 47EP, The performance data for a centrifugal water pump are shown in Table P14-47E for water at 77F (gpm=

Expert Solution
Check Mark
To determine

(a)

The pump efficiency for each data tabulated.

Answer to Problem 47EP

The pump efficiency for each data is represented in Table-(2).

    V˙gpmHftbhphpη%
    0.019.00.060.0
    4.018.50.06429.2
    8.017.00.06949.8
    12.014.50.07459.5
    16.010.50.07958.3
    20.06.00.0837.9
    24.00.00.0780.0

Explanation of Solution

Given information:

Table-(1) represents the volume flow rate, height and power of pump.

    V˙gpmHftbhphp
    0.019.00.06
    4.018.50.064
    8.017.00.069
    12.014.50.074
    16.010.50.079
    20.06.00.08
    24.00.00.078

Write the expression for pump efficiency.

  η=(ρgV˙H)bhp  ....(I)

Here, density of water is ρ, acceleration due to gravity is g, volume flow rate is V˙, head developed is H, brake power is bhp.

Calculation:

Refer to Table-A-3E "Properties of saturated water" to obtain density of water as 1.94slug/ft3.

Substitute 1.94slug/ft3for ρ, 32.2ft/s2for g, 0.0gpmfor V˙, 19ftfor Hand 0.06hpfor bhpin Equation (I).

  η=(1.94 slug/ ft3 )(32.2 ft/ s2 )(0.0gpm)(19ft)0.06hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(0.0gpm× 35.315 ft 3/s 15850gpm)(19ft)0.06hp×550 slugft2 / s3 1hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(0.0× 35.315 15850 ft3 /s)(19ft)0.06×550slug ft2/s3×100%=0%

Substitute 1.94slug/ft3for ρ, 32.2ft/s2for g, 4.0gpmfor V˙, 18.5ftfor Hand 0.064hpfor bhpin Equation (I).

  η=(1.94 slug/ ft3 )(32.2 ft/ s2 )(4.0gpm)(18.5ft)0.064hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(4.0gpm× 35.315 ft 3/s 15850gpm)(18.5ft)0.064hp×550 slugft2 / s3 1hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(4.0× 35.315 15850 ft3 /s)(18.5ft)0.064×550slug ft2/s3×100%=29.2%

Substitute 1.94slug/ft3for ρ, 32.2ft/s2for g, 8.0gpmfor V˙, 17ftfor Hand 0.069hpfor bhpin Equation (I).

  η=(1.94 slug/ ft3 )(32.2 ft/ s2 )(8.0gpm)(17ft)0.069hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(8.0gpm× 35.315 ft 3/s 15850gpm)(17ft)0.069hp×550 slugft2 / s3 1hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(8.0× 35.315 15850 ft3 /s)(17ft)0.069×550slug ft2/s3×100%=49.8%

Substitute 1.94slug/ft3for ρ, 32.2ft/s2for g, 12.0gpmfor V˙, 14.5ftfor Hand 0.074hpfor bhpin Equation (I).

  η=(1.94 slug/ ft3 )(32.2 ft/ s2 )(12.0gpm)(14.5ft)0.074hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(12.0gpm× 35.315 ft 3/s 15850gpm)(14.5ft)0.074hp×550 slugft2 / s3 1hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(12.0× 35.315 15850 ft3 /s)(14.5ft)0.074×550slug ft2/s3×100%=59.5%

Substitute 1.94slug/ft3for ρ, 32.2ft/s2for g, 16.0gpmfor V˙, 10.5ftfor Hand 0.079hpfor bhpin Equation (I).

  η=(1.94 slug/ ft3 )(32.2 ft/ s2 )(16.0gpm)(10.5ft)0.079hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(16.0gpm× 35.315 ft 3/s 15850gpm)(10.5ft)0.079hp×550 slugft2 / s3 1hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(16.0× 35.315 15850 ft3 /s)(10.5ft)0.079×550slug ft2/s3×100%=53.8%

Substitute 1.94slug/ft3for ρ, 32.2ft/s2for g, 20.0gpmfor V˙, 6ftfor Hand 0.08hpfor bhpin Equation (I).

  η=(1.94 slug/ ft3 )(32.2 ft/ s2 )(20.0gpm)(6ft)0.08hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(20.0gpm× 35.315 ft 3/s 15850gpm)(6ft)0.08hp×550 slugft2 / s3 1hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(20.0× 35.315 15850 ft3 /s)(6ft)0.08×550slug ft2/s3×100%=37.9%

Substitute 1.94slug/ft3for ρ, 32.2ft/s2for g, 24.0gpmfor V˙, 0ftfor Hand 0.78hpfor bhpin Equation (I).

  η=(1.94 slug/ ft3 )(32.2 ft/ s2 )(24.0gpm)(0ft)0.078hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(24.0gpm× 35.315 ft 3/s 15850gpm)(0ft)0.078hp×550 slugft2 / s3 1hp×100%=(1.94 slug/ ft3 )(32.2 ft/ s2 )(24.0× 35.315 15850 ft3 /s)(0ft)0.078×550slug ft2/s3×100%=0%

Table-(2) represents the efficiency of pump for different head, volume flow rate and power.

Table-(2)

    V˙gpmHftbhphpη%
    0.019.00.060.0
    4.018.50.06429.2
    8.017.00.06949.8
    12.014.50.07459.5
    16.010.50.07958.3
    20.06.00.0837.9
    24.00.00.0780.0
Expert Solution
Check Mark
To determine

(b)

The volume flow rate for BEP of the pump.

The net head for BEP of the pump.

Answer to Problem 47EP

The volume flow rate for BEP of the pump is 12gpm.

The net head for BEP of the pump is 14.5ft.

Explanation of Solution

Given information:

Table-(2) represents the efficiency of pump for different head, volume flow rate and power.

Table-(2)

    V˙gpmHftbhphpη%
    0.019.00.060.0
    4.018.50.06429.2
    8.017.00.06949.8
    12.014.50.07459.5
    16.010.50.07958.3
    20.06.00.0837.9
    24.00.00.0780.0

Here, from the Table-(2) the maximum efficiency of pump is 59.5%at the volume flow rate of 12gpmand head of 14.5ft.

Conclusion:

The volume flow rate for BEP of the pump is 12gpm.

The net head for BEP of the pump is 14.5ft.

Expert Solution
Check Mark
To determine

(b)

The volume flow rate for BEP of the pump.

The net head for BEP of the pump.

Answer to Problem 47EP

The volume flow rate for BEP of the pump is 12gpm.

The net head for BEP of the pump is 14.5ft.

Explanation of Solution

Given information:

Table-(2) represents the efficiency of pump for different head, volume flow rate and power.

Table-(2)

    V˙gpmHftbhphpη%
    0.019.00.060.0
    4.018.50.06429.2
    8.017.00.06949.8
    12.014.50.07459.5
    16.010.50.07958.3
    20.06.00.0837.9
    24.00.00.0780.0

Here, from the Table-(2) the maximum efficiency of pump is 59.5%at the volume flow rate of 12gpmand head of 14.5ft.

Conclusion:

The volume flow rate for BEP of the pump is 12gpm.

The net head for BEP of the pump is 14.5ft.

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Chapter 14 Solutions

Fluid Mechanics: Fundamentals and Applications

Ch. 14 - There are three main categories of dynamic pumps....Ch. 14 - For each statement about cow cetrifugal the...Ch. 14 - Prob. 13CPCh. 14 - Consider flow through a water pump. For each...Ch. 14 - Write the equation that defines actual (available)...Ch. 14 - Consider a typical centrifugal liquid pump. For...Ch. 14 - Prob. 17CPCh. 14 - Consider steady, incompressible flow through two...Ch. 14 - Prob. 19CPCh. 14 - Prob. 20PCh. 14 - Suppose the pump of Fig. P1 4-19C is situated...Ch. 14 - Prob. 22PCh. 14 - Prob. 23EPCh. 14 - Consider the flow system sketched in Fig. PI 4-24....Ch. 14 - Prob. 25PCh. 14 - Repeat Prob. 14-25, but with a rough pipe-pipe...Ch. 14 - Consider the piping system of Fig. P14—24. with...Ch. 14 - The performance data for a centrifugal water pump...Ch. 14 - For the centrifugal water pump of Prob. 14-29,...Ch. 14 - Suppose the pump of Probs. 14-29 and 14-30 is used...Ch. 14 - Suppose you are looking into purchasing a water...Ch. 14 - The performance data of a water pump follow the...Ch. 14 - For the application at hand, the flow rate of...Ch. 14 - A water pump is used to pump water from one large...Ch. 14 - For the pump and piping system of Prob. 14-35E,...Ch. 14 - A water pump is used to pump water from one large...Ch. 14 - Suppose that the free surface of the inlet...Ch. 14 - Calculate the volume flow rate between the...Ch. 14 - Comparing the results of Probs. 14-39 and 14-43,...Ch. 14 - Prob. 45PCh. 14 - The performance data for a centrifugal water pump...Ch. 14 - Transform each column of the pump performance data...Ch. 14 - 14-51 A local ventilation system (a hood and duct...Ch. 14 - Prob. 52PCh. 14 - Repeat Prob. 14-51, ignoring all minor losses. How...Ch. 14 - Suppose the one- way of Fig. P14-51 malfunctions...Ch. 14 - A local ventilation system (a hood and duct...Ch. 14 - For the duct system and fan of Prob. 14-55E,...Ch. 14 - Repeat Prob. 14-55E, ignoring all minor losses....Ch. 14 - A self-priming centrifugal pump is used to pump...Ch. 14 - Repeat Prob. 14-60. but at a water temperature of...Ch. 14 - Repeat Prob. 14-60, but with the pipe diameter...Ch. 14 - Prob. 63EPCh. 14 - Prob. 64EPCh. 14 - Prob. 66PCh. 14 - Prob. 67PCh. 14 - Prob. 68PCh. 14 - Prob. 69PCh. 14 - Two water pumps are arranged in Series. The...Ch. 14 - The same two water pumps of Prob. 14-70 are...Ch. 14 - Prob. 72CPCh. 14 - Name and briefly describe the differences between...Ch. 14 - Discuss the meaning of reverse swirl in reaction...Ch. 14 - Prob. 75CPCh. 14 - Prob. 76CPCh. 14 - Prob. 77PCh. 14 - Prob. 78PCh. 14 - Prob. 79PCh. 14 - Prob. 80PCh. 14 - Wind ( =1.204kg/m3 ) blows through a HAWT wind...Ch. 14 - Prob. 82PCh. 14 - Prob. 84CPCh. 14 - A Francis radial-flow hydroturbine has the...Ch. 14 - Prob. 87PCh. 14 - Prob. 88PCh. 14 - Prob. 89PCh. 14 - Prob. 90CPCh. 14 - Prob. 91CPCh. 14 - Discuss which dimensionless pump performance...Ch. 14 - Prob. 93CPCh. 14 - Prob. 94PCh. 14 - Prob. 95PCh. 14 - Prob. 96PCh. 14 - Prob. 97PCh. 14 - Prob. 98PCh. 14 - Prob. 99PCh. 14 - Prob. 100EPCh. 14 - Prob. 101PCh. 14 - Calculate the pump specific speed of the pump of...Ch. 14 - Prob. 103PCh. 14 - Prob. 104PCh. 14 - Prob. 105PCh. 14 - Prob. 106PCh. 14 - Prob. 107EPCh. 14 - Prob. 108PCh. 14 - Prob. 109PCh. 14 - Prob. 110PCh. 14 - Prove that the model turbine (Prob. 14-109) and...Ch. 14 - Prob. 112PCh. 14 - Prob. 113PCh. 14 - Prob. 114PCh. 14 - Prob. 115CPCh. 14 - Prob. 116CPCh. 14 - Prob. 117CPCh. 14 - Prob. 118PCh. 14 - For two dynamically similar pumps, manipulate the...Ch. 14 - Prob. 120PCh. 14 - Prob. 121PCh. 14 - Prob. 122PCh. 14 - Calculate and compare the turbine specific speed...Ch. 14 - Prob. 124PCh. 14 - Prob. 125PCh. 14 - Prob. 126PCh. 14 - Prob. 127PCh. 14 - Prob. 128PCh. 14 - Prob. 129PCh. 14 - Prob. 130PCh. 14 - Prob. 131PCh. 14 - Prob. 132PCh. 14 - Prob. 133PCh. 14 - Prob. 134PCh. 14 - Prob. 135PCh. 14 - A two-lobe rotary positive-displacement pump moves...Ch. 14 - Prob. 137PCh. 14 - Prob. 138PCh. 14 - Prob. 139PCh. 14 - Prob. 140PCh. 14 - Which choice is correct for the comparison of the...Ch. 14 - Prob. 142PCh. 14 - In a hydroelectric power plant, water flows...Ch. 14 - Prob. 144PCh. 14 - Prob. 145PCh. 14 - Prob. 146PCh. 14 - Prob. 147PCh. 14 - Prob. 148PCh. 14 - Prob. 149PCh. 14 - Prob. 150PCh. 14 - Prob. 151P
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