Hydrostatic Law

Hydrostatic Law of Pressure for Static Fluids

According to the hydrostatic law, at any point inside a static fluid the vertical rate of increase of pressure must equal the local specific weight of the fluid.

The law may be applicable for both compressible and incompressible fluids provided their local density ρ is taken into account. The law is also true for viscous and inviscid fluids as these fluids under static conditions don’t introduce any shearing effect.

As shown in the figure, consider a vertical elementary fluid prism having a cross sectional area a and length δz, where it encloses the point O.

In order to assess the above law and understand what hydrostatic pressure is, let’s evaluate the pressure at the point O.

As per the law, for maintaining an equilibrium condition in the z-direction, the sum of all the vertical forces acting at the point O must disappear.

Assume p as the pressure at a depth z below the open surface, the increment in pressure at a vertical depth δz asδp, such that the pressure at a depth δz + z below the open surface is p + δp.

Therefore the net resultant pressure exerted upwards becomes:

(p + δp).a – p.a = δp.a,

Also since the gravity force over this prism acts downwards and equals the weight of the enclosed fluid,

Weight = ρg.(δz.a)

Now, to maintain equilibrium,

δpa = ρg.(δz.a),

Therefore, it implies

dp/dz = ρg,

The above expression explains regarding what hydrostatic pressure is and perfectly complies with the stated definition.