Water at 20°C is siphoned from a reservoir as shown in Fig. P5-53. For d = 8 cm and D = 16 cm, determine (a) the minimum flow rate that can be achieved without cavitation occurring in the piping system and (b) the maximum elevation of the highest point of the piping system to avoid cavitation. (c) Also, discuss the ways of increasing the maximum elevation of the highest point of the piping system to avoid cavitation.
(a)
The minimum flow rate in the piping system.
Answer to Problem 53P
The minimum flow rate in the piping system is
Explanation of Solution
Given information:
The diameter of smaller the pipe is
The figure below shows the different sections in the piping system.
Figure-(1)
Write the expression for Bernoulli's equation between section
Here, the atmospheric pressure is
Write the expression for discharge of fluid from the pipe.
Here, the area of the section
Write the expression for the area of the section
Here, the diameter of the larger pipe is
Write the expression for velocity of the fluid at section
Here, the diameter of smaller the pipe is
Write the expression for Bernoulli's equation between section
Here, the datum head at section
Write the expression for minimum flow rate in the pipe.
Here, the area of the section
Write the expression for area of the section
Calculation:
The velocity at section
The line
Substitute
Substitute
Substitute
Substitute
Refer to the Table A-3 "Properties of saturated water" to obtain the value of absolute pressure as
The density of the water is
Substitute
The value of pressure at section
Substitute
Substitute
Substitute
Conclusion:
The minimum flow rate in the piping system is
(b)
The maximum elevation of the highest point of the piping system.
Answer to Problem 53P
The maximum elevation of the highest point of the piping system is
Explanation of Solution
Write the expression for the velocity at section
Here, the diameter of the larger pipe is
Write the expression for Bernoulli's equation between section
Here, the datum head at section
Calculation Substitute
Substitute
Conclusion:
The maximum elevation of the highest point of the piping system is
(c)
The way of increasing the maximum elevation of the highest point of the piping system to avoid cavitation.
Explanation of Solution
By increasing the diameter of the siphoned pipe, the elevation of the highest point of the piping system can be increased because the value of pressure at section is greater than absolute pressure, hence cavitation can be avoided in the pipe.
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Chapter 5 Solutions
Fluid Mechanics: Fundamentals and Applications
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