Fundamentals Of Thermal-fluid Sciences In Si Units
Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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Chapter 14, Problem 77P
To determine

The discharge rate of water.

Expert Solution & Answer
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Explanation of Solution

Given:

Temperature of water is 15°C.

Diameter of the first pipe is 10cm.

Length of the first pipe is 20 m.

Diameter of the second pipe is 4cm.

Length of the second pipe is 35 m.

Level of water in the reservoir is 18 m.

Calculation:

Refer Table A-15 “Properties of saturated water” from Appendix 1 to obtain the following properties of water:

  Density,ρ=999.1kg/m3Dynamic viscosity,μ=1.138×103kg/ms

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

  P1ρg+α1V122g+z1+hpump=P2ρg+α2V222g+z2+hturbine+hLz1=α2V222g+hL18m=V222(9.81m/s2)+hL        (I)

From the continuity equation,

  V1A1=V2A2V1=A2A1V2V1=(D2D1)2V2V1=(4 cm10 cm)2V2V1=0.16V2        (II)

The head loss is,

  hL=(f1L1D1+KL,entrance)V122g+(f2L2D2+KL,contraction)V222ghL=(f120 m0.10 m+0.5)V122(9.81m/s2)+(f235 m0.04 m+0.46)V222(9.81m/s2)        (III)

The flow rate is,

  V˙=V2A2=π4(0.04m2)V2        (IV)

The Reynolds number in the first pipe is,

  Re1=ρV1D1μ=(999.1kg/m3)V1(0.10 m)(1.38×103kg/ms)        (V)

The Reynolds number in the second pipe is,

  Re2=ρV2D2μ=(999.1kg/m3)V2(0.04 m)(1.38×103kg/ms)        (VI)

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

  1f1=2.0log(ε/D3.7+2.51Ref1)1f1=2.0log(2.51Re1f1)        (VII)

  1f2=2.0log(2.51Re2f2)        (VII)

We have 8 equations with 8 unknowns. Solving the system of simultaneous equations, we get;

  V˙=0.00595m3/sV1=0.757m/sV2=4.73m/shL=16.86 mRe1=66500Re2=166200f1=0.0196f2=0.0162

Thus, the discharge rate of water is 0.00595m3/s.

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Chapter 14 Solutions

Fundamentals Of Thermal-fluid Sciences In Si Units

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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