From my understanding,when there is no change in volume due to pressure applied on a fluid,the fluid can be called as incompressible.As there can be still be change in volume due to other properties,can I say that flow may be compressible?
When you use the incompressible fluid and apply pressure to it then the fluid´s density will not Change i.e.,volume of the incompressible fluid does not changes even with the application of external pressure. May be the outer part within which it is stored might undergo volume Change.
When you say "incompressible" that is what it is by definition. Other things can change and the density of the fluid can change but it is still incompressible. Nothing in the real world is completely incompressible. For example 40°F water at atmospheric pressure has a density of 62.4 lb/ft³ while at 500 psig, that goes up to 62.5 lb/ft³. That is not much of a difference so for the purposes of calculation, we assume cold water is incompressible.