For a gate width of 2 m into the paper (Fig. P3-78), determine the force required to hold the gate K at its location.
The force required to hold the gate.
Answer to Problem 78P
The force required to hold the gate is
Explanation of Solution
Given:
In the following figure all the parameter is given.
b
Figure-(1)
Write the expression for the density of fluid in the top portion.
Here, the density of the fluid situated at top is
Write the expression for the density of fluid in the lower portion.
Here, the density of the fluid situated at lower portion is
Draw free body diagram for the portion AB.
Figure-(2)
In Figure-(2) hydrostatic are shown as
Write the expression for the hydrostatic force acting in top portion.
Here, force is
Write the expression for the depth from surface at which the force
Write the expression for the hydrostatic force acting in lower portion.
Here, force is
Write the expression for the depth from surface at which the force
The below figure shows the free body diagram of portion BC.
Figure (3)
Write the expression for force acting on the portion BC.
Here, force is
The below figure shows the free body diagram for all portions.
Figure (4)
Write the expression for the distance of force
Here, the distance of force
Write the expression for the distance of force
Here, the distance of force
Write the expression for the moment equilibrium condition about the point A.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The force required is
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Chapter 3 Solutions
Fluid Mechanics: Fundamentals and Applications
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