Hydrostatic law

HYDROSTATIC LAW

The pressure at any point in a fluid at rest is obtained by the Hydrostatic law which states that the rate of increase of pressure in a vertically downward direction must be equal to the specific weight of the fluid at that point. This is proved as:

Consider a small fluid element as shown in fig 1.17.

Let

ΔA = cross-sectional area of element

Δh = height of fluid element

P = pressure on face AB

h = distance of fluid element from free surface.

The forces acting on the fluid element are:

1. Pressure force on AB = P × ΔA and acting perpendicular to face AB in the downward direction.

2. Pressure force on acting perpendicular to face CD, vertically upward direction.

3. Weight of fluid element = Density × g × volume = ρ × g × (ΔA × Δh)

4. Pressure forces on surfaces BC and AD are equal and opposite. For equilibrium of fluid element, we have

Where w = weight density of fluid EQ states that rate of increase of pressure in a vertical direction is equal to weight density of the fluid at that point. This is Hrdrostatic law.

By integrating the above eq for liquids

∫ dp = ∫ ρg dh

P = ρ g h

where P is the pressure above atmospheric pressure and h is the height of the point from free surfaces.