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 31P

(a)

To determine

The minimum flow rate required for not occurring the cavitation in the given piping system.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The temperature (T) of the water in the siphon is 20°C.

The diameter (d) of the small pipe is 10 cm.

The diameter (D) of the large pipe is 16 cm.

Calculation:

The vapor pressure (PV) of water at T=20°C is 2.338 kPa.

Consider the atmospheric pressure as 101.325 kPa.

Consider the density (ρ) of the water as 1,000kg/m3.

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

Write the Bernoulli’s equation between the points 1 and 4 as follows;

  P1ρg+V122g+z1=P4ρg+V422g+z4Patmρg+022g+z1=Patmρg+V422g+0z1=V422gV4=2gz1

Substitute g=9.81m/s2 and z1=(1+4)m in the above equation.

  V4=2×9.81×(1+4)=9.905m/sVD=V4=9.905m/s

Write the continuity equation for the small and large pipes as follows;

  AdVd=ADVDπd24×Vd=πD24×VDd2Vd=D2VD        (I)

Substitute d=10cm, D=16cm, and VD=9.905m/s in the equation (I).

  102×Vd=162×9.905Vd=25.357m/sV2=Vd=25.357m/s

Check the possibility of the velocity 25.357 m/s.

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

  P1ρg+V122g+z1=P2ρg+V222g+z2101.325kPa×1,000Pa1kPa1,000×9.81+022×9.81+(1+4)=P2ρg+25.35722×9.81+210.329+5=P2ρg+32.772+2P2ρg=19.443<0

Therefore, the velocity 25.357m/s cannot be maximum.

Use the Bernoulli’s equation for the points 1 and 2 to find the maximum velocity. Consider the vapor pressure at point 2.

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

  P1ρg+V122g+z1=P2ρg+V222g+z2101.325kPa×1,000Pa1kPa1,000×9.81+022×9.81+(1+4)=2.338kPa×1,000Pa1kPa1,000×9.81+Vmax22×9.81+210.329+5=0.238+Vmax22×9.81+2Vd=Vmax=16m/s

Find the maximum flowrate (V˙)  using the relation;

  V˙=AdVd=πd24Vd=π×(10cm×1m100cm)24×16=0.125m3/s

Thus, the minimum flow rate required for not occurring the cavitation in the given piping system is 0.125m3/s_.

(b)

To determine

The maximum elevation of the highest point to avoid cavitation.

(b)

Expert Solution
Check Mark

Explanation of Solution

Find the velocity in the large pipe using the Equation (I).

Substitute d=10cm, D=16cm, and Vd=16m/s in the equation (I).

  102×16=162×VDVD=6.25m/sV3=VD=6.25m/s

The maximum pressure occurs at point 3, and the atmospheric pressure at point 3 is P3=2.338kPa.

Write the Bernoulli’s equation between the points 1 and 3 as follows;

  P1ρg+V122g+z1=P3ρg+V322g+z3101.325kPa×1,000Pa1kPa1,000×9.81+022×9.81+(1+4)=2.338kPa×1,000Pa1kPa1,000×9.81+6.2522×9.81+z310.329+5=0.238+2+z3zmax=z3=13m

Thus, the maximum elevation of the highest point to avoid cavitation is 13m_.

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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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