Hydrostatics – location of the centre of pressure for an inclined plane surface For a plane surface immersed in a liquid and inclined at an angle θ to the free surface, the depth of the centre of pressure, measured from the free surface, lies __________ the depth of the surface’s centre of gravity (centroid).

Introduction:
When a plane surface is submerged, hydrostatic pressure increases linearly with depth, producing a distributed force. The resultant acts at the centre of pressure, which is not at the centroid except in special cases. This question checks the qualitative position of that point for surfaces not horizontal.

Given Data / Assumptions:

• Liquid is at rest; density is constant; gravity uniform.
• Plane surface fully or partially submerged and inclined by angle θ.
• Free-surface pressure uniform (e.g., atmospheric).

Concept / Approach:

The depth of the centre of pressure is 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 an axis through the centroid parallel to the free surface. Since I_G, A, and ȳ are positive, the additional term is positive, making y_cp > ȳ. Thus the centre of pressure lies deeper than the centroid, i.e., below it when referenced to the free surface.

Step-by-Step Solution:

Verification / Alternative check:

For a horizontal plane (no depth gradient), I_G/(A*ȳ) → 0 for the relevant axis and centre of pressure coincides with the centroid, the expected special case.

Why Other Options Are Wrong:

Above / same depth: Would contradict the positive moment shift caused by increasing pressure with depth.Indeterminate/depends only on density: Location also depends on geometry via I_G and A.

Common Pitfalls:

Confusing centroid with centre of pressure; they coincide only when pressure is uniform across the surface.

Final Answer:

below