The vertical component of pressure force on a submerged curved surface is equal to

Concept:

The hydrostatic force on the curved surface on horizontal direction:

\(F_H=ρ g {\bar h}A\)

where

\(ρ=\) the density of the fluid

g = acceleration due to gravity

\(\bar h=\) the distance of the center of gravity of the body from the free surface level

A = vertical projection of the area

The hydrostatic force on the curved surface on vertical direction:

V = volume of the above-curved surface up to the free surface level

Note:

The vertical component of hydrostatic force on a submerged curved surface is equal to the weight of the liquid above-curved surface up to the free surface level (ρgV). 

Important Points

Hydrostatic force on a plane's submerged surface is given by

F = Pressure at the centroid × Area of the surface acts on the center of pressure

F = ρgh̅A 

For a plane surface of arbitrary shape immersed in a liquid in such a way that the plane of the surface makes an angle θ with the free surface of the liquid:

Center of pressure, \({h^*} = \frac{{{I_G}{{\sin }^2}\theta }}{{A̅ h}} + \bar h\)

A = Total area of an inclined surface

h̅ = Depth of center of gravity of inclined area from a free surface

h* = Distance of center of pressure from the free surface of a liquid