The Centre of Pressure for a Rectangular Lamina Immersed Vertically in Water

Definition of Centre of Pressure:
The Centre of Pressure is a point through which the total force on an immersed surface can be assumed to act.

Finding the Depth of Centre of Pressure:
For a rectangular lamina immersed vertically in water up to height h, the depth of centre of pressure can be found as follows:

- The Centre of Pressure lies at a distance d from the top edge of the lamina.
- Let AB be the top edge of the lamina and CD be the bottom edge of the lamina.
- Consider an elemental strip EF of width dx at a distance x from the left edge of the lamina.
- Let P be the point where the elemental strip EF intersects the surface of water.
- The pressure at point P is given by P = ρgh, where ρ is the density of water and g is the acceleration due to gravity.
- The elemental force acting on the strip EF is dF = P * (dx).
- The moment of this elemental force about the top edge AB of the lamina is given by dM = dF * (d - x) = ρgh * (dx) * (d - x).
- The total moment of all such elemental forces about the top edge AB of the lamina is given by M = ∫dM = ∫ρgh * (dx) * (d - x).
- Simplifying the integral, we get M = ρgh * [(d^2)/2 - (d^3)/(3l)].
- The total force acting on the lamina is given by F = ρgh * (l * b), where l and b are the length and breadth of the lamina respectively.
- The depth of centre of pressure is given by dcp = M / F = [(d^2)/2 - (d^3)/(3l)] / (l * b).

Solving for dcp, we get dcp = 2h/3.

Therefore, the correct answer is option 'C'.