Dam Hydrostatic Pressure Calculator

The pressure at depth h in a fluid is P = rho * g * h, where rho is water density (1,000 kg/m3), g is 9.81 m/s2, and h is depth. The total hydrostatic force on a vertical flat wall of width W and water depth H is F = 0.5 * rho * g * H^2 * W. This is because pressure varies linearly from 0 at the surface to rho*g*H at the base, giving an average pressure of rho*g*H/2.

The resultant force acts at one-third of the water depth from the base (H/3 from the bottom) on a vertical flat wall. This point is called the centre of pressure. It is lower than the centroid of the water depth (H/2) because pressure increases with depth, shifting the resultant force toward the base.

Hydrostatic pressure (Pa or kPa) is a local quantity at a specific point at a given depth. Hydrostatic force (N or kN) is the total integrated pressure over the entire submerged area of the wall. Force = Pressure * Area, but because pressure varies with depth, an integral is required. For a rectangular vertical wall, Force = 0.5 * rho * g * H^2 * W.

This formula applies to vertical flat walls. For inclined or curved walls, the horizontal component of force is calculated the same way (projected vertical area), while the vertical component equals the weight of water above the curved surface. Complex curved structures require integration over the surface geometry, which is typically done by engineers using CAD or finite element software.

Dam and retaining wall design uses factors of safety typically of 1.5 to 2.0 against sliding, 2.0 against overturning, and 3.0 for structural strength. These are specified by standards bodies such as the US Army Corps of Engineers (EM 1110-2-2100) and FEMA (NRCS Dam Safety guidelines). This calculator gives the theoretical hydrostatic force; actual design must include factor-of-safety calculations by a licensed engineer.