Explain compressibility of Fluids.

Compressibility is a measure of change in the volume of fluid under the effect of force/pressure or stress.

When fluid is acted upon by force, volume gets reduced. This effect is also judge by 'Bulk Modulus of elasticity'. The Compressibility coefficient can also be expressed as reciprocal of Bulk Modulus of elasticity.

Thus, - (Change in Volume/Original Volume = Change in Pressure/Bulk Modulus) as given by Equation (1).

The negative (-ve) sign suggests the volume gets decreased when pressure increases. When we consider the unit mass of fluid, Volume is reciprocal of density (as given by Equation (2)). Now by differentiating the and substituting the value of V and dV, final equation is equation (3) which gives relation between change in pressure and chan....Show More

Compressibility is a measure of change in the volume of fluid under the effect of force/pressure or stress.

When fluid is acted upon by force, volume gets reduced. This effect is also judge by 'Bulk Modulus of elasticity'. The Compressibility coefficient can also be expressed as reciprocal of Bulk Modulus of elasticity.

Thus, - (Change in Volume/Original Volume = Change in Pressure/Bulk Modulus) as given by Equation (1).

The negative (-ve) sign suggests the volume gets decreased when pressure increases. When we consider the unit mass of fluid, Volume is reciprocal of density (as given by Equation (2)). Now by differentiating the and substituting the value of V and dV, final equation is equation (3) which gives relation between change in pressure and change in density of fluid and also density also affected by temperature change. Thus during compression, rise in temperature causes the change in density as well as change in pressure.

For a given mass of fluid,

`m=rho*V`

Differentiating throughout, we get,

`dm=rho*dv+V*drho`

Since mass is constant, dm=0,

or, `0=rho*dv+V*drho`

or, `-(dV)/V=(drho)/(rho)`.... (i)

We know that, the bulk modulus of elasticity is,

`K=1/(beta)`

Where, `beta` is the compressibility of Fluids 

or, `K=-(dp)/((dV)/V)`... (ii)

From (i) and (ii),

`K=rho*(dP)/(drho)`