Centre of pressure vs centroid – vertical immersed surface For a vertically immersed plane surface in a static liquid, the centre of pressure (point of action of the resultant hydrostatic force) lies __________ the surface’s centre of gravity (centroid).

Introduction:
The distribution of hydrostatic pressure on submerged surfaces is linear with depth, pulling the resultant force toward the deeper parts of the surface. Recognizing the relative position of the centre of pressure to the centroid is essential for gate and wall design to ensure correct moment calculations.

Given Data / Assumptions:

• Liquid at rest, constant density, uniform gravity.
• Plane surface is vertical and fully or partially submerged.
• Free-surface pressure is uniform (usually atmospheric).

Concept / Approach:

For a vertical plane, pressure increases linearly with depth. The resultant hydrostatic force acts at depth y_cp = ȳ + I_G / (A * ȳ), where ȳ is centroid depth, A is area, and I_G is the second moment of area about the centroidal axis parallel to the free surface. Because I_G/(Aȳ) is positive, y_cp is deeper than ȳ; thus, the centre of pressure lies below the centroid when referenced to the free surface.

Step-by-Step Solution:

Verification / Alternative check:

For a horizontal surface, the pressure is uniform and y_cp = ȳ; this limiting case reinforces that the downward shift arises from the depth gradient in a vertical surface.

Why Other Options Are Wrong:

At/above: Would contradict the increasing pressure with depth.Indeterminate/“midway”: Location depends on geometry (I_G, A, ȳ), not just fluid density.

Common Pitfalls:

Equating centroid and centre of pressure in all cases; they coincide only when pressure is uniform across the surface.

Final Answer:

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