Hydrostatics in dam engineering: The total hydrostatic pressure on a dam primarily depends on which geometric/physical factors?

Introduction / Context:

Design of gravity and arch dams requires accurate estimation of hydrostatic forces. Hydrostatic pressure increases linearly with depth (p = rho * g * h) and produces resultant forces whose magnitude and line of action depend on the submerged area’’s geometry (shape) and its depth below the free surface.

Given Data / Assumptions:

• Incompressible fluid with constant specific weight gamma = rho * g.
• Still water (no dynamic pressure components).
• Plane surfaces of the dam face in contact with water.

Concept / Approach:

The pressure at a point depends solely on depth below the free surface. The total hydrostatic force on a plane area equals pressure at the centroid times area (F = p_c * A), independent of orientation, while the center of pressure location depends on second moment of area about the horizontal axis. Thus, total force depends on depth (through p_c) and on shape/area distribution (through A and moments), not on dam material. The “length” in plan only scales force if we consider a strip of given width; conceptually, per unit length analysis makes length irrelevant to intensity.

Step-by-Step Solution:

Verification / Alternative check:

For a vertical rectangular face of height H and unit width, A = H * 1 and h_c = H/2, giving F = gamma * H^2 / 2. Changing shape or inclination modifies A and h_c, altering F and its line of action, confirming dependence on depth and shape.

Why Other Options Are Wrong:

• Length (alone) is not a governing variable per unit-width formulations.
• Material of the dam does not affect water pressure (a fluid property), though it affects structural capacity.

Common Pitfalls:

• Confusing hydrostatic pressure (fluid side) with stress distribution inside the dam (material dependent).

Final Answer:

Both (b) and (c)