Understanding Hydrostatic Forces on Plain and Curved Surfaces

What you’ll learn

Hydrostatics provides fundamental insights key to some aspects of fluid mechanics, particularly in understanding Fluid Mechanics equations. Static fluids exert force on any submerged surface, and grasping this concept is crucial in the field of hydrostatics. In particular, professionals in civil and hydraulic engineering focus on these forces while constructing structures such as dams, gate systems, and large containment tanks.

What are Hydrostatic Forces?

Hydrostatic Forces arise from the pressure exerted by a fluid at rest. It occurs when the fluid is stationary relative to the surface it contacts.

Hydrostatic Forces on Plain Surfaces

The pressure in a static fluid increases linearly with depth due to the weight of the fluid column above any given point.

Fluids exert pressure on submerged surfaces, resulting in an upward force acting on them. This Force is due to the net fluid pressure acting on a submerged surface and this force can be written as:

$F = p_{cg}A$

For a uniform liquid at rest, the equation can be rewritten using the liquid’s unit weight:

$F=\gamma \overline{h} A$

where:

F = force on the plate

$\bar{h}$ = depth of the centroid of the surface from the free surface

$\gamma$ = specific weight of the liquid

A = submerged area of the plate

Location of the Center of Pressure

The resulting force position can be defined by the center of pressure (CoP) which denotes the location where the resultant force acts. As a result of the increase in pressure at a greater depth, the center of pressure is always lower than the center of gravity.