To determine the force exerted by a fluid. at a given point, a fluid at rest exerts a pressure, p, that is the same in all directions. the magnitude of p can be determined from the following relationship:

p=γz=rhogz

where rho is the fluid's mass density, γ is the fluid's specific weight, z is the point's depth (measured from the fluid's surface), and g is the acceleration due to gravity. this pressure creates a linear distributed load on a flat vertical or inclined surface and a uniform distributed load on a horizontal surface. the resultants of these loadings can be determined by finding the volume under the loading curves.

a gate rotates at point a and releases water when the water's depth, d, exceeds a certain value. (figure 1) the gate's width (perpendicular to the image) is b = 2.05 ft , the water's depth is d = 3.66 ft , and point a is located at h = 1.83 ft . what is f, the magnitude of the horizontal force exerted on the gate by the water? the water's specific weight is γw = 62.4 lb/ft3