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 12, Problem 63P

a)

To determine

The maximum flow of water.

a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The efficiency of the pump (ηpump) is 78%.

The input power (W˙pump.in) is 5kW.

Height of the pool from the underwater surface (h) is 30 m.

The diameter of the intake pipe (d1) is 0.07 m.

The diameter of the discharge side pipe (d2) is 0.05 m.

Calculation:

Draw the free body diagram of the system as in Figure 1.

Fundamentals of Thermal-Fluid Sciences, Chapter 12, Problem 63P , additional homework tip  1

Consider the acceleration due to gravity (g) as 9.81m/s2.

Calculate the work done by the pump (W˙pump,out) using the relation;

  ηpump=W˙pump,outW˙pump,inW˙pump,out=ηpumpW˙pump,in=0.78(5)=3.9kW

Write the Bernoulli’s equation between the points 1 and 2 as follows;

  m˙(P1ρ+α1V122+gz1)+W˙pump,out=m˙(P2ρ+α2V222+gz2)+W˙turbine,e+Emech,loss

    m˙(P1ρ+α1V122+gz1)+W˙pump,out=m˙(P2ρ+α2V222+gz2)+0+Emech,lossm˙(Patmρ+0+0)+W˙pump,out=m˙(Patmρ+0+9.81(30))+Emech,lossW˙pump,out=9.81(30)m˙+Emech,loss

Substitute m˙ghL for Emech,loss.

  W˙pump,out=9.81(30)m˙+m˙ghL3.9×103=m˙(9.81(30)+9.81(4))m˙=3.9×1039.81(30)+9.81(4)=11.69kg/s

Calculate the maximum flow of water through the pump (Q) using the relation;

  Q=m˙ρ=11.691000=0.01169m3/s

Thus, the maximum flow of water through the pump is 0.01169m3/s_.

b)

To determine

The Pressure difference across the pump.

b)

Expert Solution
Check Mark

Explanation of Solution

Given:

The efficiency of the pump (ηpump) is 78%.

The input power (W˙pump.in) is 5kW.

The datum head at point 2 (z2) is 30 m.

The diameter of the intake pipe (d1) is 7 cm.

The diameter of the discharge side pipe (d2) is 5 cm.

Calculation:

Draw the free body diagram of the system as in Figure 1.

Fundamentals of Thermal-Fluid Sciences, Chapter 12, Problem 63P , additional homework tip  2

Calculate the area of intake pipe using the formula;

  A1=πd124=π(0.07)24=3.848×103m2

Calculate the discharge of water through the pipe at the intake side using the expression;

  V1=QA1=0.011693.848×103=3.038m/s

Calculate the area of intake pipe using the formula;

  A2=πd224=π(0.05)24=1.963×103m2

Calculate the discharge of water through the pipe at the intake side using the expression;

  V2=QA2=0.011691.963×103=5.955m/s

Write the Bernoulli’s equation between the intake side and discharge side as follows;

  P1ρg+α1V122g+z1+hpump,out=P2ρg+α2V222g+z2+hturbine,e+hLP1ρg+(1)V122g+0+hpump,out=P2ρg+(1)V222g+0+0+0P1P2ρg=V22V122ghpump,outP1P2ρg=V22V122gW˙pump,outm˙g

  P1P2ρg=1g(V22V122W˙pump,outm˙)P1P2=ρ(V22V122W˙pump,outm˙)P2P1=ρ(W˙pump,outm˙V22V122)

Substitute 11.69 kg/s for m˙, 3.9 kW for W˙pump,out, 5.955 m/s for V2, 3.038 m/s for V1 and 1000kg/m3 for ρ.

  P2P1=1000(3.9×10311.695.95523.03822)=1000(333.6213.12)=320503.7 Pa=320.5kPa

Thus, the Pressure difference across the pump is 320.5kPa_.

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Chapter 12 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 12 - A glass manometer with oil as the working fluid is...Ch. 12 - The velocity of a fluid flowing in a pipe is to be...Ch. 12 - The water level of a tank on a building roof is 20...Ch. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - Prob. 16PCh. 12 - Prob. 17PCh. 12 - Prob. 18PCh. 12 - A piezometer and a Pitot tube are tapped into a...Ch. 12 - The diameter of a cylindrical water tank is Do and...Ch. 12 - Prob. 21PCh. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - An airplane is flying at an altitude of 12,000 m....Ch. 12 - While traveling on a dirt road, the bottom of a...Ch. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - Air at 105 kPa and 37°C flows upward through a...Ch. 12 - A handheld bicycle pump can be used as an atomizer...Ch. 12 - Prob. 31PCh. 12 - The water pressure in the mains of a city at a...Ch. 12 - Prob. 33PCh. 12 - Air is flowing through a venturi meter whose...Ch. 12 - The water level in a tank is 15 m above the...Ch. 12 - What is useful pump head? How is it related to the...Ch. 12 - Prob. 38PCh. 12 - What is irreversible head loss? How is it related...Ch. 12 - Consider the steady adiabatic flow of an...Ch. 12 - Prob. 41PCh. 12 - Prob. 42PCh. 12 - Prob. 43PCh. 12 - Prob. 44PCh. 12 - In a hydroelectric power plant, water flows from...Ch. 12 - Reconsider Prob. 12–45E. Determine the flow rate...Ch. 12 - Prob. 47PCh. 12 - Water is being pumped from a large lake to a...Ch. 12 - A 15-hp (shaft) pump is used to raise water to a...Ch. 12 - Prob. 51PCh. 12 - The water level in a tank is 20 m above the...Ch. 12 - Prob. 53PCh. 12 - Prob. 54PCh. 12 - Water flows at a rate of 20 L/s through a...Ch. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61PCh. 12 - Prob. 62PCh. 12 - Prob. 63PCh. 12 - A 73-percent efficient 12-hp pump is pumping water...Ch. 12 - Prob. 65PCh. 12 - Air flows through a pipe at a rate of 120 L/s. The...Ch. 12 - Air at 100 kPa and 25°C flows in a horizontal duct...Ch. 12 - Prob. 68RQCh. 12 - Prob. 69RQCh. 12 - Prob. 70RQCh. 12 - A 3-m-high large tank is initially filled with...Ch. 12 - Prob. 73RQCh. 12 - Prob. 74RQ
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