## Principles of Hydrostatic Pressures

**Unit Pressure**

Unit pressure or simply called pressure is the amount of force exerted by a fluid distributed uniformly over a unit area.

If the unit pressure is not uniform over the unit area, it can be expressed as the sum of differential pressure.

Since fluid at rest cannot resist shearing stress, pressure is always at right angle to the area where it is acting. It is also worthy to note that the total hydrostatic force *F = pA*, which can be found by cross multiplication.

## Stresses on Thin-walled Pressure Tanks

The circumferential stress, also known as tangential stress, in a tank or pipe can be determined by applying the concept of fluid pressure against curved surfaces. The wall of a tank or pipe carrying fluid under pressure is subjected to tensile forces across its longitudinal and transverse sections.

## Stability of Floating Bodies

Any floating body is subjected by two opposing vertical forces. One is the body's weight W which is downward, and the other is the buoyant force BF which is upward. The weight is acting at the center of gravity G and the buoyant force is acting at the center of buoyancy BO. W and BF are always equal and if these forces are collinear, the body will be in upright position as shown below.

## Analysis of Gravity Dam

Dams are structures whose purpose is to raise the water level on the upstream side of river, stream, or other waterway. The rising water will cause hydrostatic force which will tend the dam to slide horizontally and overturn about its downstream edge or toe. The raised water level on the upstream edge or heel will also cause the water to seep under the dam. The pressure due to this seepage is commonly called hydrostatic uplift and will reduce the stability of the dam against sliding and against overturning.

## Total Hydrostatic Force on Surfaces

**Total Hydrostatic Force on Plane Surfaces**

For horizontal plane surface submerged in liquid, or plane surface inside a gas chamber, or any plane surface under the action of uniform hydrostatic pressure, the total hydrostatic force is given by

where *p* is the uniform pressure and *A* is the area.

In general, the total hydrostatic pressure on any plane surface is equal to the product of the area of the surface and the unit pressure at its center of gravity.

where *p _{cg}* is the pressure at the center of gravity. For homogeneous free liquid at rest, the equation can be expressed in terms of unit weight

*γ*of the liquid.

where $\bar{h}$ is the depth of liquid above the centroid of the submerged area.

## Rotation - Rotating Vessel

When at rest, the surface of mass of liquid is horizontal at PQ as shown in the figure. When this mass of liquid is rotated about a vertical axis at constant angular velocity ω radian per second, it will assume the surface ABC which is parabolic. Every particle is subjected to centripetal force or centrifugal force CF = mω^{2}x which produces centripetal acceleration towards the center of rotation. Other forces that acts are gravity force W = mg and normal force N.