
The force

Answer to Problem 2.83P
The force
Explanation of Solution
Write the expression for horizontal component of hydrostatic force.
Here, the specific weight of water is
Write the area of projected plane.
Substitute
Write the moment of inertia of projected plane.
Here, the radius of the curve is
Write the position of the horizontal force.
Write the height of centre of gravity.
Substitute
The vertical force is the difference of the hydrostatic force of the square part and hydrostatic force of quarter circle part.
Write the expression for vertical force.
Here, the volume of the square part is
Write the expression for volume of the square part.
Write the expression for volume of the quarter circle part.
Substitute
Write the moment about
The weight of the gate acts at its centre of gravity.
Write the center of gravity of the quarter circle from
The following diagram shows the forces on the gate.
Figure-(1)
In Figure-(1), the weight of the gate is
Write the moment about
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the force
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Chapter 2 Solutions
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