Hydrostatic Pressure Force on a Plane Surface

The resultant force on a horizontal submerged surface equals the fluid pressure at that depth multiplied by the surface area. Since depth remains constant across a horizontal surface, the pressure is uniform. This resultant force acts through the centroid of the surface area.

On horizontal surfaces, depth is constant, so pressure remains uniform. On vertical surfaces, pressure increases with depth as distance from the fluid's free surface increases. This varying pressure distribution requires integrating pressure contributions across the surface to find the total resultant force.

The center of pressure is the point where the total hydrostatic pressure acts on a submerged surface. Although the resultant force may appear to act through the centroid, it actually acts through the center of pressure, which is located below the centroid due to the varying pressure distribution with depth.

For an inclined surface, the force on each small element depends on its depth and the fluid's specific weight. To find the total resultant force, integrate the contributions from all surface elements. The resulting force acts through the center of pressure, not the geometric centroid.

Specific weight is a key parameter in hydrostatic force calculations. For vertical and inclined surfaces, the resultant force is computed as the product of the fluid's specific weight, the surface area, and the depth of the centroid from the fluid surface. It directly determines the magnitude of pressure at any depth.

Integrating pressure contributions across an inclined surface accounts for varying depths of each element. This integration determines both the magnitude and location of the resultant force. The resultant acts through the center of pressure, which lies below the centroid due to the non-uniform pressure distribution.

Plane surfaces experience hydrostatic forces based on uniform or linearly varying pressure depending on orientation. Understanding plane surface analysis provides the foundation for analyzing hydrostatic pressure force on a curved surface, where pressure varies in multiple directions and requires component analysis.