Question

a large vessel of height H ,is filled with a liquid of density D ,upto the brim .a small hole of radius r is made at the side verticle face ,close to the base .the horizontal force is required to stop the gushing of liquid ??????????????????

Answer 1

A large vessel of height $H$, is filled with a liquid of density $D$, up to the brim. A small hole of radius $r$ is made at the side vertical face, close to the base. The horizontal force is required to stop the gushing of liquid?

Force equals:

$$F = pS$$

where $p$ – pressure, $S$ – area of the hole.

The pressure of liquid at the height $H$ equals:

$$p = DgH$$

where $D$ – density of liquid, $g$ – acceleration due to gravity

Area of the hole equals:

$$S = \pi r^2$$

Therefore:

$$F = DgH\pi r^2$$

Answer: $F = DgH\pi r^2$