The height to which a cylindrical vessel must | vedclass

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(B) Let the height of the liquid be $h$ and the radius of the cylindrical vessel be $r$. The density of the liquid is $\rho$.$1$. The pressure at the

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Radius of the vessel

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(B) Let the height of the liquid be $h$ and the radius of the cylindrical vessel be $r$. The density of the liquid is $ho$.$1$. The pressure at the bottom of the vessel is $P_{bottom} = hho g$. The force exerted on the bottom is $F_{bottom} = P_{bottom} 	imes A_{bottom} = (hho g)(\pi r^2)$.$2$. The pressure varies linearly with depth along the vertical side. The average pressure on the side wall is $P_{avg} = \frac{0 + hho g}{2} = \frac{1}{2}hho g$. The area of the side wall is $A_{side} = 2\pi rh$. Thus,the force on the side wall is $F_{side} = P_{avg} 	imes A_{side} = (\frac{1}{2}hho g)(2\pi rh) = \pi ho g r h^2$.$3$. According to the problem,$F_{bottom} = F_{side}$.Therefore,$hho g \pi r^2 = \pi ho g r h^2$.$4$. Simplifying the equation: $h r^2 = r h^2$,which gives $h = r$.

The height to which a cylindrical vessel must be filled with a homogeneous liquid,such that the average force with which the liquid presses the side of the vessel is equal to the force exerted by the liquid on the bottom of the vessel,is equal to:

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