Hydrostatic Force Formula |
||
|
\( F_h \;=\; \rho \cdot g \cdot h \cdot A \) (Hydrostatic Force) \( \rho \;=\; \dfrac{ F_h }{ g \cdot h \cdot A } \) \( g \;=\; \dfrac{ F_h }{ \rho \cdot h \cdot A } \) \( h \;=\; \dfrac{ F_h }{ \rho \cdot g \cdot A } \) \( A \;=\; \dfrac{ F_h }{ \rho \cdot g \cdot h } \) |
||
| Symbol | English | Metric |
| \( F_h \) = Hydrostatic Force | \(lbf\) | \(N\) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \(lbm \;/\; ft^3\) | \(kg \;/\; m^3\) |
| \( g \) = Gravitational Acceleration | \(ft \;/\; sec^2\) | \(m \;/\; s^2\) |
| \( h \) = Vertical Depth of the Free Surface of the Fluid to the Centroid of the Submerged Area | \(ft\) | \(m\) |
| \( A \) = Area of the Submerged Surface | \(ft^2\) | \(m^2\) |
Hydrostatic force, abbreviated as \(HF\) is the force exerted by a fluid at rest on a submerged surface due to the pressure of the fluid acting perpendicularly to that surface. Since the fluid is stationary, its pressure at any point depends only on the depth below the free surface, the fluid's density, and gravitational acceleration. This pressure is uniform in all directions at a given depth and acts normally (perpendicularly) to any surface it contacts. The net hydrostatic force on a surface is found by integrating this varying pressure over the entire area; for plane surfaces, it equals the pressure at the centroid of the area multiplied by the total area. The point where this resultant force acts is called the center of pressure, which lies below the centroid for inclined or vertical surfaces because pressure increases with depth.
Hydrostatic forces are responsible for phenomena such as the buoyant force on submerged objects (Archimedes’ principle), the outward push on dam walls, the lift on submarine hulls, and the pressure felt by divers at depth. In engineering, accurately calculating these forces is used for designing safe dams, tanks, gates, ships, and underwater structures.
