Hydrostatics – Definition of the point of action of resultant pressure The point at which the resultant hydrostatic force acts on an immersed plane surface is called the what?

Introduction:
In hydrostatics, pressure on an immersed plane surface varies linearly with depth, leading to a distributed force that can be replaced by a single resultant. Knowing where this resultant acts is crucial for gate design, slab stability, and retaining structures. The term for that point is tested here.

Given Data / Assumptions:

• Static fluid, constant density, uniform gravity.
• Plane surface (vertical, inclined, or horizontal) fully or partially submerged.
• No dynamic effects (no flow-induced shear).

Concept / Approach:

The intensity increases with depth, so the resultant acts below the geometric centroid (for surfaces not horizontal). The exact location is the centre of pressure, where the moment of the resultant about any axis equals the moment of the distributed pressure about that axis: y_cp = I_G / (A * ȳ) + ȳ for an inclined plate, where I_G is second moment of area about the centroidal axis parallel to the free surface, A is area, and ȳ is centroid depth.

Step-by-Step Solution:

Verification / Alternative check:

For a horizontal surface, pressure is uniform and the centre of pressure coincides with the centroid; for vertical surfaces, it lies below the centroid—matching textbook results.

Why Other Options Are Wrong:

Centre of gravity / centroid of volume: Refer to mass or volume distribution, not pressure resultants.Centre of depth / centre of immersed surface: Nonstandard or imprecise terms for this context.

Common Pitfalls:

Assuming the resultant always passes through the centroid; this happens only when pressure is uniform (e.g., horizontal surfaces).

Final Answer:

centre of pressure