Centre of pressure – Vertical plane surface in a liquid For a vertically immersed plane surface, the centre of pressure lies, relative to the surface's centre of gravity (centroid), at a position:

Introduction:
The centre of pressure is the point of action of the resultant hydrostatic force on a submerged plane surface. Due to the linear increase of pressure with depth, the resultant acts below the geometric centroid when the surface is vertical or inclined, a fact vital for the design of gates and retaining walls.

Given Data / Assumptions:

• Static liquid, constant density.
• Plane surface is vertical (or inclined but not horizontal).
• Free surface pressure is uniform (often atmospheric).

Concept / Approach:

Because pressure increases with depth, the lower part of the surface experiences greater pressure than the upper part, pulling the resultant downward relative to the centroid. Quantitatively, for an inclined surface the depth of the centre of pressure is y_cp = ȳ + I_G / (A * ȳ), where ȳ is the depth of the centroid, A is area, and I_G is the second moment of area about the centroidal axis parallel to the free surface. Since I_G / (A * ȳ) is positive, y_cp exceeds ȳ (deeper), i.e., the centre of pressure lies below the centroid.

Step-by-Step Solution:

Verification / Alternative check:

For a horizontal plane surface, pressure is uniform and the centre of pressure coincides with the centroid; this special case confirms that the downward shift for vertical surfaces arises from the pressure gradient with depth.

Why Other Options Are Wrong:

Above / same level: Would require an inverse pressure gradient, which does not occur in normal hydrostatics.Depends only on density or needs flow velocity: Location also depends on geometry (I_G, A, ȳ) and does not require flow.

Common Pitfalls:

Forgetting that the centre of pressure moves closer to the deeper edge as the surface becomes more inclined, and that for horizontal surfaces it coincides with the centroid.

Final Answer:

below