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  4. To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid pressure on the sides of the vessel equal to the force exerted by the liquid on the bottom of the vessel?

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Q. To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid pressure on the sides of the vessel equal to the force exerted by the liquid on the bottom of the vessel?

Mechanical Properties of Fluids

Solution:

Let $h$ be the desired height of liquid in cylinder for which the force on the bottom and sides of the vessel is equal
Force on bottom =$\rho gh \times\pi R^{2}$
Force on walls of vessel $=\rho g \left(h /2\right)\times2\pi Rh$
According to question,
$\rho gh\pi R^{2} = \rho g \pi Rh^{2} $
or $R=h$