•  Thus, the important conclusion about hydrostatic condition is as follows: “Pressure in a continuously distributed uniform static fluid varies only with vertical distance and is independent of the shape of the container. The pressure is the same at all point on a given horizontal plane in the fluid. The pressure increases/decreases with depth of the fluid. The hydrostatic pressure distribution in oceans and atmospheres is shown in Fig. 1.2.2. Considering the sea-level for the reference , the pressure decreases with altitude (b) where the fluid medium is air . For an ocean, when the depth (h) is increased (vertically downward) the pressure gets increased for water .

Fig. 1.2.2: Hydrostatic pressure distribution in oceans and atmosphere.

•  Liquids are generally incompressible so that the density variations are neglected in hydrostatics. So, Eq. (1.2.7) reduces to the following form;

(1.2.8)

where the term is called as pressure head of the fluid.

•  Gases are compressible with density proportional to pressure. Apply perfect gas law, in Eq. (1.2.6).

(1.2.9)

(1.2.10)

This equation needs the assumption of temperature variation T(z) e.g. in an isothermal atmosphere, where T =T₀,

(1.2.11)