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Pressure-Density-Height Relationship

Let us take an imaginary cylindrical fluid element which is at rest under the action o; forces as shown in Fig 2.3.

Σ F z = 0

 

 

 

 

 

 

 

dp / dz = w

dp / dz =pg [ p = mass density]

 

Equation (2.2) is the mathematical expression of Hydrostatic law which states that rate of change of pressure with respect to vertical depth is equal to weight density of the fluid.

 

or                             p2 – p1 = pg (z2 – z1)

p = p g z

 

where p is the pressure above atmospheric pressure and z is the height of the point from the free liquid surface or pressure head.