The vertical height of the free surface above any point in a liquid at rest is called a pressure head. The Pressure head formula may be expressed as,

H= (p/w)

H is the height of the liquid

and w is the specific weight of the water.

Since the pressure at any point in a liquid depends on the height of the free surface above the point, it is convenient to express fluid pressure in terms of pressure head. The pressure is then expressed in terms of meters ( or centimeters) of a liquid column.

P = (a * r * h) can be used to obtain a relationship between the heights of columns of different liquid which would develop the same pressure at any point. Thus, if h1 and h2  are the heights of the column of liquid of specific weight w1 and w2 require to develop the same pressure p1 at any point, then from p=arh,

P = (w1 * h1) = (w2 * h2)

If S1 and S2 are the specific gravity of the two liquids and W is the specific weight of water then since W1= S1W and W2 = S2W sinB equation written as,

S1 * h1= S2 * h2

Further, if h1 and h2 are the depth of two points below the free surface in a static mass of liquid of specific weight W and P1 and P2 are the respective pressure intensities at these points, the from P=arh the pressure difference between these points is obtained as,

(P1 – P2) = W ( h1 – h2 )

Thus, it may be stated that the difference in pressure at any two points in a static mass of liquid varies directly as the difference in depth ( or elevation ) of the two points.

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The pressure at any point in a compressible fluid:- For a compressible fluid since the density varies with the pressure. The equation can be integrated only if the relation between W and P is known. Moreover, in a compressible fluid there being no free surface, the integration of the equation gives the variation of pressure between any points lying in a static mass of fluid.

Thus, if P1 and P2 are the pressure intensities at two points which are at elevation Z1 and Z2 above an arbitrarily assumed datum, then integration of equation is,

Integration P1 to P2 dp /w = – integration Z1 to Z2 multiply dz =( Z1 – Z2)

The left-hand side of the above expression has been evaluated using different relation between W and P as indicated in the section.