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  • Find torque of pressure force on the vertical wall of an open cubical vessel of side a filled with a liquid about lower edge of the same wall

Density of liquid is d 

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You can calculate the total force on the container from the pressure by integrating the pressure over the height of the container as follows: F=\int PdA

In this case, the area element dA will be equal to a differential height element dh times the circumference of the rectangle 2*(Len +breadth) ,which gives

F=2(l+b)* \rho g \int_{0}^{h}hdh=(l+b) \rho gh^2

You can note that since the pressure is linear in height, you get average pressure by taking the pressure to be at the mid-point of the tank. Therefore Torque \tau =(l+b) \rho gh^2 *h/2

 

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Harsh

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