Hydrostatics – total pressure on a horizontal plane area at depth x For a plane surface of area A immersed horizontally in a liquid of specific weight w with its centroid at depth x from the free surface, the total pressure on the surface equals:

Introduction:Total hydrostatic force on a plane surface equals the pressure at the centroid times the area when the surface is horizontal, because pressure is uniform over that surface at a given depth.

Given Data / Assumptions:

• Surface is horizontal; its entire area is at the same depth x.
• Fluid is incompressible with specific weight w.
• Gravity is constant; edge effects are negligible.

Concept / Approach:Pressure at depth x is p = w * x. For a horizontal plane at constant depth, pressure is uniform; hence total force F is pressure times area.

Step-by-Step Solution:1) Compute pressure: p = w * x.2) Multiply by area: F = p * A.3) Therefore, F = (w * x) * A = w * A * x.

Verification / Alternative check:Integrating pressure over the area yields the same result because p is constant over a horizontal plane at given depth: F = ∬ p dA = p ∬ dA = p * A.

Why Other Options Are Wrong:

• w.A: missing the depth factor x.
• w x: missing the area A.
• w A / x: incorrect inverse dependence on depth.

Common Pitfalls:Confusing horizontal with vertical surfaces (where pressure varies with depth and centroid/center-of-pressure concepts differ).

Final Answer:w A x