Hydrostatics: depth of centre of pressure for a vertical rectangular gate 4 m wide and 3 m high with its top at the free surface (water up to the top) is

Introduction / Context:The centre of pressure is the point of action of the resultant hydrostatic force on a submerged plane surface. For vertical gates, correctly locating this point is crucial for hinge design, anchor sizing, and stress checks.

Given Data / Assumptions:

• Vertical rectangular plate: width b = 4 m, height h = 3 m.
• Top edge at the free surface; hydrostatic pressure due to water only.
• Uniform gravitational acceleration and density.

Concept / Approach:

The depth to the centroid (centre of area) from the free surface is y_bar = h/2. The centre of pressure depth y_cp for a vertical plane surface with top at the free surface is y_cp = y_bar + (I_G / (A * y_bar)), where I_G is the second moment of area about the horizontal centroidal axis and A is the area.

Step-by-Step Solution:

Verification / Alternative check:

Centre of pressure should lie below the centroid (because pressure increases with depth). The value 2.0 m > 1.5 m satisfies this physical expectation.

Why Other Options Are Wrong:

(a) and (b) place the resultant above the centroid, impossible here. (d) and (e) are deeper than warranted by the area moment ratio and overestimate lever arms and moments.

Common Pitfalls:

Using I about the free surface instead of about the centroid; forgetting that the top is at the surface, which simplifies the formula.

Final Answer:

2.0 m