The horizontal force (P) required to hold the gate.
Answer to Problem 2.86P
The force P =
Explanation of Solution
Given information:
The quarter circle BC is hinged at point C.
The weight of the gate is neglected.
To find force P, the moment for the above system needs to be taken from point C. Therefore, the horizontal and the vertical water forces acting on the gate needs to be found with their respective point of action.
The width of the gate into the paper is not mentioned. Therefore, consider that as 3m.
Assume that the horizontal force acting on the panel is
In above equation,
Assume that the vertical force acting on the panel is
In above equation,
The below equation is used to find the line of action of horizontal force
In above equation,
Calculation:
To find horizontal force,
According to the above mentioned explanation,
Therefore, the horizontal component of the hydrostatic force =
To find the line of action,
In this case, the inertia of the rectangular plane is equal to,
Therefore,
The horizontal force is acting at a distance
To find vertical force,
According to the above mentioned explanation,
The vertical force acts at a distance equals to
Therefore,
The above values can be represented as below,
To find the magnitude of force P, take moment for the above system from point C in clockwise direction.
The force P required to hold the gate stationary is equals to
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Chapter 2 Solutions
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