A rectangular gate with height L and width b (out of the page) is hinged about its midpoint as shown below. The depth of the water above the hinge is

h.    The pressure on the back side of the gate is atmospheric.

 

 

 

 

 

 

 

 

 

 

 

 

P

 

 

 

I.    Carefully sketch the gage pressure distribution acting on the gate. Also show the approximate location of the discrete resultant force FR.

 

II.     Determine analytical expressions for the magnitude FR and location yR of the force of the water on the gate. Your answer should only be in terms of γ, h, L, and  b.

 

III.     Determine an analytical expression for the magnitude of the force P required to keep the gate closed. Your answer should only be in terms of γ, L, and b.

 

IV.     In part III, you should have found that P does not depend on h. Give a physical (not just mathematical) explanation for why this is true. Hint: Use your answer to part I. Pictures may be useful in your answer.

 

V.       At what depth should the hinge be located so that P “ 0?

 

 

 

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