Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 14, Problem 78P
To determine

The power input to the pump.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

Temperature of water is 70°F.

Velocity of water is 6ft/min.

Diameter of the pipe is 5 in.

Length of the pipe is 125 ft.

The elevation difference is 12 ft.

Flow rate of water is 1.5ft3/s.

Pump efficiency is 70%.

Calculation:

Applying energy equation at points 1 at the free surface of water in the river and point 2 at the free surface of water in the tank.

  P1ρg+α1V122g+z1+hpump=P2ρg+α2V222g+z2+hturbine+hLα1V122g+hpump=z2+hLhpump=z2+hLα1V122g        (I)

Refer Table A-15E “Properties of saturated water” from Appendix 2 and obtain the following properties of water:

  Density, ρ=62.3lbm/ft3Dynamic viscocity, μ=6.556×104lbm/fts

Calculate the velocity of flow.

  V=V˙Ac=(1.5ft3/s)π4(512 ft)2=11.0ft/s

The Reynolds number is,

  Re=ρVDμ=(62.3lbm/ft3)(11.0ft/s)(512 ft)(6.556×104lbm/fts)=435500

Since the Reynolds number is greater than 4000, the flow is turbulent. Hence, the friction factor is determined from the Moody chart as follows:

  1f=2.0log(ε/D3.7+2.51Ref)1f=2.0log(0.0005 ft/(5/12ft)3.7+2.51435500f)

Solving the above equation, f=0.0211.

Calculate the total minor loss coefficient.

  KL=KL,entrance+3KL,elbow+KL,exit=0+3(0.3)+1.0=1.9

Calculate the head loss.

  hL=(fLD+KL)V22g=[(0.0211)125 ft(5/12) ft+1.9](11ft/s)22(32.2ft/s2)=15.5ft

Calculate hpump form Equation (I).

  hpump=z2+hLα1V122g=12 ft+15.5ft(6ft/s)22(32.2ft/s2)=26.9ft

Calculate the power required by the pump.

  W˙pump=V˙ρghpumpηpump=(1.5ft3/s)(62.3lbm/ft3)(32.2ft/s2)(26.9 ft)0.70(1 lbf32.2 lbmft/s2)(1 kW737lbfft/s)=4.87 kW

Thus, the power input to the pump is 4.87 kW.

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Chapter 14 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 14 - Shown here is a cool picture of water being...Ch. 14 - Someone claims that the volume flow rate in a...Ch. 14 - Someone claims that the average velocity in a...Ch. 14 - Someone claims that the shear stress at the center...Ch. 14 - Someone claims that in fully developed turbulent...Ch. 14 - How does the wall shear stress τw vary along the...Ch. 14 - In the fully developed region of flow in a...Ch. 14 - How is the friction factor for flow in a pipe...Ch. 14 - Discuss whether fully developed pipe flow is one-,...Ch. 14 - Consider fully developed flow in a circular pipe...Ch. 14 - Consider fully developed laminar flow in a...Ch. 14 - Explain why the friction factor is independent of...Ch. 14 - What is turbulent viscosity? What causes it? Ch. 14 - Consider fully developed laminar flow in a...Ch. 14 - How is head loss related to pressure loss? For a...Ch. 14 - Consider laminar flow of air in a circular pipe...Ch. 14 - What is the physical mechanism that causes the...Ch. 14 - The velocity profile for the fully developed...Ch. 14 - Water flows steadily through a reducing pipe...Ch. 14 - Water at 10°C (ρ = 999.7 kg/m3 and μ = 1.307 ×...Ch. 14 - Consider an air solar collector that is 1 m wide...Ch. 14 - Heated air at 1 atm and 100°F is to be transported...Ch. 14 - In fully developed laminar flow in a circular...Ch. 14 - The velocity profile in fully developed laminar...Ch. 14 - Repeat Prob. 14–34 for a pipe of inner radius 7...Ch. 14 - Water at 15°C (ρ = 999.1 kg/m3 and μ = 1.138 ×...Ch. 14 - Consider laminar flow of a fluid through a square...Ch. 14 - Repeat Prob. 14–37 for turbulent flow in smooth...Ch. 14 - Air enters a 10-m-long section of a rectangular...Ch. 14 - Water at 70°F passes through...Ch. 14 - Oil with ρ = 876 kg/m3 and μ = 0.24 kg/m·s is...Ch. 14 - Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27...Ch. 14 - Air at 1 atm and 60°F is flowing through a 1 ft ×...Ch. 14 - Prob. 44PCh. 14 - Prob. 45PCh. 14 - Oil with a density of 850 kg/m3 and kinematic...Ch. 14 - Prob. 47PCh. 14 - Prob. 48PCh. 14 - Prob. 50PCh. 14 - Prob. 51PCh. 14 - Prob. 52PCh. 14 - Prob. 53PCh. 14 - Prob. 54PCh. 14 - Prob. 55PCh. 14 - Prob. 56PCh. 14 - Prob. 57PCh. 14 - Water is to be withdrawn from an 8-m-high water...Ch. 14 - Prob. 59PCh. 14 - Prob. 60PCh. 14 - Prob. 61PCh. 14 - Prob. 62PCh. 14 - Prob. 63PCh. 14 - Prob. 64PCh. 14 - Consider two identical 2-m-high open tanks filled...Ch. 14 - A piping system involves two pipes of different...Ch. 14 - Prob. 67PCh. 14 - Prob. 68PCh. 14 - Prob. 69PCh. 14 - Prob. 70PCh. 14 - The water needs of a small farm are to be met by...Ch. 14 - Prob. 72PCh. 14 - Prob. 73PCh. 14 - Prob. 74PCh. 14 - Prob. 75PCh. 14 - Prob. 76PCh. 14 - Prob. 77PCh. 14 - Prob. 78PCh. 14 - Prob. 80PCh. 14 - Prob. 81PCh. 14 - A vented tanker is to be filled with fuel oil with...Ch. 14 - Two pipes of identical length and material are...Ch. 14 - Prob. 84PCh. 14 - Prob. 85PCh. 14 - Prob. 86PCh. 14 - Prob. 87PCh. 14 - Prob. 88PCh. 14 - Prob. 90PCh. 14 - Prob. 91PCh. 14 - Prob. 92PCh. 14 - Prob. 93PCh. 14 - Prob. 94RQCh. 14 - Prob. 95RQCh. 14 - Prob. 96RQCh. 14 - Prob. 97RQCh. 14 - Prob. 98RQCh. 14 - Prob. 99RQCh. 14 - Repeat Prob. 14–99E assuming the pipe is inclined...Ch. 14 - Prob. 101RQCh. 14 - Prob. 102RQCh. 14 - Prob. 103RQCh. 14 - Prob. 104RQCh. 14 - Two pipes of identical diameter and material are...Ch. 14 - Prob. 106RQCh. 14 - Prob. 107RQCh. 14 - Prob. 108RQCh. 14 - Prob. 109RQCh. 14 - Prob. 110RQCh. 14 - Prob. 111RQCh. 14 - Prob. 112RQCh. 14 - Prob. 114RQCh. 14 - Prob. 115RQCh. 14 - Prob. 116RQCh. 14 - Prob. 118RQ
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