What is Pressure Head in Fluid Mechanics?

Pressure head in fluid mechanics is the pressure exerted by a liquid column on the base of the container. It is represented as the height of the liquid column. Pressure head is also called static head or static pressure headwhich is represented by ‘Z’.

The equation to determine the pressure head on a fluid is derived and explained below.

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Pressure Head Formula

The pressure head is given by the formula:

Pressure head Z

Where,

Z = Pressure Head

p = fluid pressure (Pressure at unit area)

g= Acceleration due to gravity

rho

Determination of Pressure Head (Z)

The pressure head in fluid mechanics can be determined by considering the pressure acting at any point on a fluid in rest condition. As per the hydrostatic law, the rate of increase of pressure in the vertically downward direction must be equal to the specific weight of the fluid at that point.

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Consider a fluid element ABCD as shown in figure-1 below.

The cross-sectional area of the fluid element is delta(A) and the height of the fluid element is delta(Z).

Forces Acting on a Fluid Element
Fig.1.Forces Acting on a Fluid Element

The pressure on the face AB is ‘p’. The distance of the fluid element from the free surface is ‘Z’.

From the figure above, the forces acting on the element surfaces are:

1. Force on surface AB:

The force is acting perpendicular to the face AB in the downward direction.

2. On surface DC :

equation

This force is acting perpendicular to the face DC in the upward direction.

3. Weight of the fluid element ABCD:

From the figure, the forces acting on AB are equal and opposite to the forces acting on BC. Hence, for the equilibrium of the fluid element,

equation
equation

Hence the equation-1 states that, the rate of increase of the pressure in the vertical direction is equal to the weight of the fluid. This is hydrostatic law.

By intergrating the Eq.1,

equation
equation

Z is the height of the point from the free surface which forms the pressure head. ‘p’ is the pressure above the atmospheric pressure.

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