Hydrostatics: through which point does the resultant hydrostatic force act on a submerged plane surface? In fluid mechanics and civil engineering hydraulics, identify the point through which the single resultant of distributed hydrostatic pressure on a plane surface always acts.

Introduction / Context:The fluid pressure on a submerged plane surface increases linearly with depth, producing a distributed load. To replace this distribution with a single equivalent force for design and analysis (e.g., gates, dams, tank covers), we use the concept of the resultant hydrostatic force and its line of action.

Given Data / Assumptions:

• Incompressible, static fluid.
• Plane surface fully or partially submerged.
• Atmospheric effects uniform and thus cancel for force location.

Concept / Approach:Resultant magnitude on a plane area A is F = rho * g * ȳ * A, where ȳ is depth of area centroid below free surface. However, the line of action is not through the centroid unless pressure is uniform. The correct point is the centre of pressure, located below the centroid because pressure increases with depth.

Step-by-Step Solution:

Verification / Alternative check:Compute moments of pressure diagram; the centroid of a triangular (or trapezoidal) pressure diagram lies below the centroid of the area, consistent with y_cp > ȳ.

Why Other Options Are Wrong:

• Centre of top/bottom edge: generally not the correct line of action.
• Metacentre: relates to floating body stability, not fixed plane surfaces.
• None of these: incorrect because “centre of pressure” is the standard answer.

Common Pitfalls:Confusing force magnitude point (centroid depth for F) with force location (centre of pressure). Assuming uniform pressure leads to centroid, which is not valid for varying pressure.

Final Answer:centre of pressure