# Pressure prism

Pressure variation along depth

Hydrostatic pressure is the pressure exerted by a fluid at rest; for example on the sides of a swimming pool, glass of water or the bottom of the ocean. Its value at a given location within the fluid is the product the fluid density (ρ), the depth (d) and the forces applied by gravity (g), plus any background pressures, such as Atmospheric pressure.

Hydrostatic Pressure on surfaces surrounding (or within) fluid volumes can be represented by the Pressure Prism, which is a useful visualization technique.

Hydrostatic pressure increases linearly with depth. Generally it can be expressed by the relationship;

```                        P = ρgd             where,    P is gauge Pressure above atmospheric Pressure
ρ is density of fluid
g is gravitational acceleration
d is depth of the fluid
```

where pressure at top is zero and at bottom is ρgH . Where H is total depth of fluid volume.

Variation of pressure along depth can be seen in figure 1.

Further, the centre of pressure on the wall can be calculated by the formula

```                 HCOP  =  ∫ px x dx / ∫ px  dx    where px  is pressure at x distance from the bottom
```

by which we get the height of COP for a plane surface as H/3 from bottom which is also shown in figure 2.

Pressure Prism

If we have two different kind of fluids in our volume then the slope of our pressure prism will not be constant over the depth and rather be somewhat like shown in figure 3.

Bi-Fluid Pressure Prism

It is because slope of pressure prism is dependent on fluid density which becomes different here at a certain depth.

Above discussed pressure prisms was in case we have straight surfaces as our surrounding surfaces, representation of such prisms for curved surfaces will be more complex.

## References

1. ^ A Brief Introduction To Fluid Mechanics [Paperback] by Donald F. Young, Bruce R. Munson, Theodore H. Okiishi, Wade W. Huebsch