Question

In the derivation of P1 − P2 = rhogz, it was assumed that the liquid is incompressible. Why will this equation not be strictly valid for a compressible liquid?

Answer 1

Answer:

Explanation:

Whenever solving any problem in chapter Fluid Mechanics, we will assume all fluids as Ideal, which means it is in compressible and have zero viscosity.

This is because if the liquid is in-compressible, then its density will not change., This is because, Density = Mas/Volume.

Mass is always constant. And By making the liquid in-compressible, the volume cannot be changed and hence the density is overall constant.

Now, If the fluid is not in-compressible, this means it is compressible, then density will change since volume of it will be changed by applying the pressure.

Therefore, density will be variable.

Thus, this equation cannot be true for such fluid.

But although, the Mathematics plays a vast role, thus by its indirect method, it can find out by the concept of Integration. Although, it will cause a large problem to us, which is beyond our understanding., Also, if we try to find then we will need many variables, and also need to find limits, etc.

Answer 2

Explanation:

• The density of an incompressible liquid is independent. So, it does not vary according to the changes in pressure and constantly remains same whereas the density of a compressible liquid is dependent and proportional to the pressure.

• That is, the density of a compressible liquid varies according to the changes in pressure.  
• Thus the given equation  $P_{1}-P_{2}=\rho g z$ of an incompressible liquid is strictly not valid for a compressible liquid where, $P_{1}$ and $P_{2}$  are pressures and ρ is the density of the liquid.