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Pressure in a fluid-mechanical properties of fluids

Question

A rectangular gate  3×1m2 stands vertical with water on one side of it hinged at middle. The force F required to be applied at the bottom to keep the gate in equilibrium is K×103N . ρwater=1×103  kg/m3  and   g=10  m/s2 . Find K

Moderate
Solution

The equivalent thrust force is

Fth=12ρgH2=1.5×104N

And it acts at a distance of 13m from bottom as shown in figure.
Taking torque about hinge to be zero gives 
F=0.5×104N



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