Center of pressure for a vertical plane surface fully submerged Where is the center of pressure located relative to the area for a vertical plane surface immersed in a liquid (with its centroid below the free surface)?

Introduction / Context:
Hydrostatic forces on submerged gates and plates act at a point called the center of pressure, which is not generally the centroid because pressure increases linearly with depth. Correctly locating this point is essential for computing moment and designing supports.

Given Data / Assumptions:

• Plane, vertical surface fully submerged in a static liquid.
• Centroid of the area is at depth y_c below the free surface.
• Liquid is incompressible; hydrostatic pressure varies as p = γ y.

Concept / Approach:

The resultant hydrostatic force on a plane surface equals F = γ A y_c. The center of pressure depth for a vertical surface is y_cp = y_c + I_G / (y_c A), where I_G is the second moment of area about a horizontal axis through the centroid. Because I_G, y_c, and A are all positive, y_cp > y_c; i.e., the center of pressure lies below the centroid but not at any special edge point.

Step-by-Step Solution:

Verification / Alternative check:

For a rectangle of height h, I_G = b h^3/12. With y_c known, y_cp evaluates to a value below y_c but above the lower edge unless very shallow submergence.

Why Other Options Are Wrong:

(a) Centroid is not the center of pressure under linear pressure variation. (b) and (c) tie the point to edges, which is incorrect. (e) A fixed fraction independent of geometry is not valid.

Common Pitfalls:

Confusing magnitude (F) with location (y_cp); overlooking the effect of shape via I_G.

Final Answer:

none of these