A 4-m-long quarter-circular gate of radius 3 m and of negligible weight is hinged about its upper edge A, as shown in Fig. P3-90. The gate controls the flow of water over the ledge at B, where the gate is pressed by a spring. Determine the minimum spring force required to keep the gate closed when the water level rises to A at the upper edge of the gate.
The minimum spring force required to keep the gate closed when the water level rises to A at the upper edge of the gate.
Answer to Problem 90P
The minimum spring force required to keep the gate closed when the water level rises to
Explanation of Solution
Given information:
The radius of quarter circle is
The Figure below shows the free body diagram of gate with all forces acting on it.
Figure-(1)
Due to hydrostatic force there is horizontal and vertical force on the gate.
Write the expression for the horizontal force on gate.
Here, the horizontal force acting on the gate is
The area of projected portion of the gate is in the shape of rectangle whose length is
Write the expression for area of gate
Write the expression the height of center of gravity of the projected portion of the gate from its base.
Write the expression of the vertical force on gate.
Here, the vertical force acting on the gate is
Write the expression for weight of fluid.
Here, the weight of fluid is
Write the expression for volume of fluid block.
Substitute
Write the expression to resolve the force in vertical direction.
Here, the vertical reaction at
Write the expression for centre of gravity of fluid element.
Write the expression for moments of all the forces about hinge
Here, the perpendicular distance from the force
Calculation:
Substitute,
Substitute,
Substitute
Substitute
Substitute,
Substitute
Substitute
Substitute
Conclusion:
The minimum spring force required is
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Chapter 3 Solutions
Fluid Mechanics: Fundamentals and Applications
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L