Hydrostatic Pressure

At a point,

Pascal’s law

The hydrostatic pressure at a point is the same from all directions. Applies only for hydrostatic pressure.

Proof

Consider the fluid element shown, containing the point .

From the image:

For equilibrium:

As all approaches : . Therefore

Variation along directions

Proof

Let be the pressure at the point .

By considering equilibrium of this fluid element containing .

In the direction,

Similarly can be proven.

In the direction,

For incompressible fluids

is constant. .

Piezometric pressure

Pressure difference between 2 points

In a homogenous, incompressible fluid in equilibrium:

1. Piezometric pressure is constant throughout the fluid
2. Pressure varies linearly with depth only
3. Isobars (surface of constant pressure) are horizontal.