Incompressible vs constant density fluid flow

[tomwilliam2]

This may sound like a basic question, but it's just to get it clear:

When describing fluid flows, does the term "incompressible" mean exactly the same thing as "constant density"?

I was under the impression that if a fluid cannot be compressed, then its density must remain constant for any fixed volume of fluid. My textbook intriguingly says "For an incompressible fluid (including the case of constant density), divergence is zero." This wording seems to suggest you can have an incompressible fluid which does not have constant density...
Can anyone elucidate?
Thanks in advance

 

[boneh3ad]

It depends on your definition of "constant". An incompressible fluid flow must have the material derivative of density equal to zero, so in a sense it is "constant density". It does mean that the individual time and spatial derivatives need not be zero, however.

According to the continuity equation, an equivalent statement to the material derivative being zero is that the divergence of the flow field is zero. That is a more easily measurable and computable quantity, so it is often just used as the definition of incompressibility for ease of use and to avoid confusion with various definitions of "constant".

 

[tomwilliam2]

Thanks, that's very useful.

 

[Studiot]

Your textbook is quite right to be more general.

1) Incompressible flow mechanics is usually about liquids, however even with gas dynamics, some treatments regard the gas as incompressible for sufficient accuracy.

2) In chemical engineering for instance a liquid may possesses a solute concentration gradient and be 'incompressible' at all concentrations, but the density will vary with concentration.

go well

 

[pmacias]

I can clarify the difference between incompressible and constant density fluid flow. Both terms refer to the behavior of a fluid under certain conditions, but they are not exactly the same.

Incompressible fluid flow means that the fluid's volume will remain constant regardless of changes in pressure or temperature. This means that the fluid cannot be compressed or squeezed into a smaller volume. Incompressible fluids have a constant density, but the reverse is not necessarily true. A fluid can have a constant density without being incompressible if its density remains the same under different pressure or temperature conditions.

On the other hand, constant density fluid flow means that the density of the fluid remains constant regardless of changes in pressure or temperature. This means that the fluid can be compressed or expanded, but its density will not change. This is different from incompressible fluid flow, where the volume remains constant.

So, in summary, incompressible fluid flow and constant density fluid flow are related concepts, but they are not interchangeable. Incompressible fluids have a constant density, but constant density fluids may or may not be incompressible depending on how their density changes with pressure and temperature. I hope this helps to clarify any confusion.