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 47P
To determine

The mechanical efficiency of the pump.

Expert Solution & Answer
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Explanation of Solution

Given:

The electric power generated by the pump is W˙electric=25kW.

The density of the oil is ρ=860kg/m3.

The rate of pumping is V˙=0.1m3/sec.

The inlet diameter of the pipe is D1=8cm.

The outlet diameter of the pipe is D2=12cm.

The pressure rise in the oil is ΔP=P2P1=250kPa.

The efficiency of the motor is ηmotor=90%.

The kinetic energy correction factor is α=1.05.

Calculation:

Consider the point 1 is the inlet of the pump and the point 2 is the outlet of the pump.

The elevation difference at the point 1 and point 2 are same. Therefore, z1=z2.

Consider the acceleration due to gravity (g) as 9.81m/sec2.

Find the velocity at point 1 (V1) using the equation;

  V1=V˙A1=4V˙πD12

Substitute V˙=0.1m3/s and D1=8cm in the above equation;

  V1=4×0.1π×(8cm×1m100cm)2=19.894m/sec

Find the velocity at point 2 (V2) using the equation;

  V2=V˙A2=4V˙πD22

Substitute V˙=0.1m3/s and D2=12cm in the above equation;

  V2=4×0.1π×(12cm×1m100cm)2=8.842m/sec

Write the Energy equation in terms of the heads between the points 1 and 2 as follows;

  P1ρg+αV122g+z1+hpump,u=P2ρg+αV222g+z2+hturbine,e+hLP1ρg+αV122g+z1+hpump,u=P2ρg+αV222g+z1+0+0hpump,u=P2ρg+αV222gP1ρgαV122g=P2P1ρg+αV22V122g

Substitute P2P1=250kPa, ρ=860kg/m3, g=9.81m/sec2, α=1.05, V2=8.842m/sec, and V1=19.894m/sec in the above equation;

  hpump,u=250kPa×1,000N/m21kPa×1kgm/sec21N860×9.81+1.05×(8.842219.8942)2×9.81=12.634m

Find the useful pumping power (W˙pumps,u) using the relation;

  W˙pumps,u=ρV˙ghpump,u

Substitute ρ=860kg/m3, V˙=0.1m3/s, g=9.81m/sec2, and hpump,u=12.634m in the above equation;

  W˙pumps,u=860×0.1×9.81×12.634=10.659×103W×1kW1,000W=10.659kW

Find the shaft pumping power (W˙pump,shaft) using the equation;

  W˙pump,shaft=ηmotorW˙electric

Substitute ηmotor=90% and W˙electric=25kW in the above equation;

  W˙pump,shaft=90100×25=22.5kW

Find the mechanical efficiency of the pump (ηpump) using the relation;

  ηpump=W˙pump,uW˙pump,shaft×100%

Substitute W˙pump,u=10.6kW and W˙pump,shaft=22.5kW in the above equation;

  ηpump=10.622.5×100%=47.1%

Therefore, the mechanical efficiency of the pump is 47.1%_.

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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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