The point in the immersed body through which the resultant pressure of the liquid be taken to act is known as

Concept:

Pascal’s Law:

According to Pascal’s Law, the pressure or intensity of pressure at a point in a static fluid is equal in all directions.

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

where

A = Total area of an inclined surface,

h̅ = Depth of centre of gravity of inclined area from a free surface,

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

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

For vertical plane surface: θ = 90°

\({h^*} = \frac{{{I_G}}}{{A \bar h}} + \bar h\)

The following facts can be concluded from the above equations:

• Centre of pressure lies below the centroid because for any plane surface, the factor IG/Ah̅ is always positive.
• The deeper the surface is lowered into the liquid (i.e. greater is the value of h̅), closer comes the centre of pressure to the centroid of the area.
• Depth of the center of pressure is independent of the specific weight of the liquid and is consequently the same for all liquids.
• The point in the immersed body through which the resultant pressure of the liquid be taken to act is known as the Centre of pressure.

Additional Information 

Total Pressure:

\(F_h=\omega ∫ydA \cos \theta\)

\(F_y=\omega ∫ydA \sin \theta\)

The total pressure on a surface immersed in a liquid depends on its inclination to the liquid surface.