Load Distributed over a Area

Previously, it was determined that the resultant force F_R for a distributed load over a line is,

It was also shown that the location of the line of action of F_R is given by

Similarly, if the load is distributed over an area as shown, then the resultant is found by

The line of action of F_R passes through the point defined by

Pressure on a Submerged Surface

When a body is submerged in a fluid, either a liquid or a gas, then the fluid exerts a pressure normal or perpendicular to the surface. This pressure, called hydrostatic pressure, depends on the depth and density of the fluid, the acceleration of gravity, and the pressure at the surface of the liquid. The pressure at any point is

     p = p_o + ρgd

Here p_o is the pressure at the surface of the liquid, ρ is the density of the fluid, g is the acceleration of gravity, and d is the depth at that point.

Generally, devices that measure pressure actually measure the amount above some reference pressure; this is called gage pressure. If the reference pressure is the pressure at the surface of the liquid, then the gage pressure at a point is simply

     p = ρgd