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