•    The force exerted by the static fluid on the surface in contact with the fluid is called as total pressure. It is denoted by ‘P’.
•    It is always normal to the contact surface.
•    The surface may be horizontal, vertical, inclined or curved.

P = γ ¯XA

Te point at which the total pressure is supposed to act is called as centre of pressure. It is denoted by ¯h.

¯h = ¯x + I_Gsin² θ / A ¯X

Consider a plate AB vertically submerged in fluid.
Now consider small strip of area dA lying at a depth of x from ‘O’.

Pressure intensity on the strip,

dp = γ . x


Total pressure force on strip,

dp = Pressure x Area

= γ . x . dA

Total pressure force on the whole area.
Integrate Equation

∫ dp = ∫ γ . x . dA

= γ . ∫ x . dA

But ( ) xdA is the sum of moments of the area of the strip, which is equal to A ¯x.

P = γ . A ¯x

Centre of pressure can be calculated by using law of moment.

Law of moment states, “Sum of moment of all such pressure forces on strip about free surface is equal to the moment of whole body about free surface.

Total pressure force on strip,

dp = γ . x. dA

Moment of force on strip,

dM = dp. x

= (γ.x .dA) x

= γ . x² dA

Now sum of moment of all such pressure forces on strip about free surface.

Integrate Equation

∫ dM = ∫ γ . x² dA

= ∫ γ . x² dA

But we know         ∫ X² dA  =  I_O = moment of inertia about free surface

M = γ . I_O

But moment of whole body about free surface,

M = P ¯h

Equate the Equations and

P ¯h = γ  . I_O

by parallel axis theorem     I_O = I_G + A (¯x)²

γ (A. ¯x) ¯h = γ (I_G + A(¯x)² )

¯h =  I_{G /} A¯x + A(¯x)² / A¯x

¯h  =  I_G / A¯x + ¯x

The centre of pressure always lies below the centre of gravity by  I_G / A¯x . If I_G / A¯x > 0.

For greater depths, centre of pressure approaches centre of gravity as ¯x is larger and I_G / ¯x becomes smaller.

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