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 107RQ
To determine

The flow rate through the pipes.

Expert Solution & Answer
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Explanation of Solution

Given:

Temperature of water is 100°C.

Length of the pipe A is 500 m.

Length of pipe B is 800 m.

Diameter of the pipe A is 30cm.

Diameter of the pipe B is 45cm.

Flow rate is 3m3/s.

Calculation:

Refer Table 15 “Properties of saturated water” from Appendix 1 and obtain the following properties of water at 100°C:

  Density,ρ=957.9kg/m3Dynamic viscosity,μ=0.282×103kg/ms

From the rate of flow through the pipes,

  V˙1=V1A1V˙1=V1[π4(0.3 m)2]        (I)

  V˙2=V2A2V˙2=V2[π4(0.45 m)2]        (II)

The Reynolds number in the first pipe is,

  Re1=ρV1D1μ=(957.9kg/m3)V1(0.3 m)(0.282×103kg/ms)        (III)

The Reynolds number in the second pipe is,

  Re2=ρV2D2μ=(957.9kg/m3)V2(0.45 m)(0.282×103kg/ms)        (IV)

The friction factor is determined from the Moody chart as follows:

  1f1=2.0log(ε/D3.7+2.51Ref1)1f1=2.0log(0.000045m/0.3m3.7+2.51Re1f1)        (V)

  1f2=2.0log(0.000045m/0.45m3.7+2.51Re2f2)        (VI)

The head loss is,

  hL=hL,1=hL,2        (VII)

The head loss in pipe 1 is,

  hL,1=f1L1D1V122ghL,1=f1(500 m0.3 m)[V122(9.81m/s2)]        (VIII)

The head loss in pipe 2 is,

  hL,2=f2L2D2V222ghL,2=f2(800 m0.45 m)[V222(9.81m/s2)]        (IX)

The total flow rater between the reservoirs is,

  V˙=V˙1+V˙2        (X)

We have 10 equations with 10 unknowns. Solving the system of simultaneous equations, we get;

  V˙1=0.919m3/sV˙2=2.081m3/sV1=13.0m/sV2=13.1m/shL=187 mRe1=1.324×107Re2=2.00×107f1=0.0131f2=0.0121

Thus, the flow rate through pipe A and pipe B is 0.919m3/s and 2.081m3/s respectively.

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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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