Concept explainers
(a)
The rate of discharge through the slit.
Answer to Problem 94P
The rate of discharge through the slit is
Explanation of Solution
Given information:
The length of the slit is
Write the expression for velocity based on parabolic profile.
Here, the first constant is
Write the expression for flow rate of water.
Here, the elemental area is
Write the expression of elemental area.
Here, the width of the rectangular slit is
Write the expression of elemental flow rate of water.
Here, the elemental area is
Write the expression of the force acting on the element.
Here, the density of the fluid is
Calculation:
At the starting of the jet.
Substitute
At the end of the jet.
Substitute
Substitute
Substitute
Substitute
Substitute
Integrate Equation (VII) on both sides the change in length is
Conclusion:
The rate of discharge through the slit is
(b)
The vertical force acting on the pipe due to discharge process.
Answer to Problem 94P
The vertical force acting on the pipe due to discharge process is
Explanation of Solution
Calculation:
Substitute
Integrate equation (VIII) on both sides the change in length of the element is
Conclusion:
The vertical force acting on the pipe due to discharge process is
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Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
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