Water is siphoned from a reservoir open to the atmosphere by a pipe with diameter D. total length L. and friction factor f as shown in Fig. 8-159. Atmospheric pressure is 99.27 kPa. Minor losses may be ignored. (a) Verify the following equation for the ratio of exit velocity for the siphon with nozzle to the e>it velocity for the siphon without the nozzle. VD/VC
Calculate its value for L = 28 m. h1 = 1.8 m, h2 = 12m. D = l2 cm, d = 3 cm, and f= 0.02.
(b) Show that static pressure at B in the siphon with the nozzle is greater and the velocity is smaller with respect to the siphon without the nozzle. Explain how this situation can be useful with respect to flow physics.
(e) Determine the maximum value of h2 in the piping system to avoid cavitation. The density and vapor pressure of water are p = 1000 kg/m3 and Pv = 4.25 kPa, and L1 = 4 in.
(a)
The verification of relation
The value of
Answer to Problem 159P
The relation
The value of
Explanation of Solution
Given information:
The length of pipe is
Write the expression for the Bernoulli Equation.
Here, pressure at point
Write the expression for conservation of mass in nozzle.
Here, diameter of nozzle is
Write the expression for head loss.
Here, head loss is
Calculation:
Substitute
Substitute
Substitute
From Equation (IV) and (VI).
Substitute
Conclusion:
The relation
The value of
(b)
The static pressure at
The velocity at
Answer to Problem 159P
The static pressure at
The velocity at
Explanation of Solution
Calculation:
Substitute
Substitute
Substitute
From Equation (VIII) and (X), since
Since the pipe diameter is greater than nozzle diameter, therefore ratio of pipe diameter to nozzle diameter will be greater than one. Thus the static pressure at
From equation (VIII).
From equation (X).
From Equation (XI) and (XII), since
Since the static pressure at
Conclusion:
The static pressure at
The velocity at
(c)
The maximum value of
Answer to Problem 159P
The maximum value of
Explanation of Solution
Given information:
The density of water is
Calculation:
Substitute
Substitute
Conclusion:
The maximum value of
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Chapter 8 Solutions
Fluid Mechanics: Fundamentals and Applications
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