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From Franz Durst's Fluid Mechanics: An Introduction to the Theory of Fluid Flows:

When a fluid element reacts to pressure changes by adjusting its volume and consequently its density, the fluid is called compressible. When no volume or density changes occur with pressure or temperature, the fluid is regarded as incompressible although, strictly, incompressible fluids do not exist.

So, strictly speaking, although the fluid is always compressible is there a case where gas fluid flow maintains constant density?

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2 Answers 2

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At the steady state, the density of a flow will be constant. That's tautological.

Fluids like water can be treated as incompressible because its response to a pressure change is negligible for most practical calculations.

For more information see here.

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  • $\begingroup$ Be careful what you mean by "steady state". For example, uniform flow through a nozzle is a "steady state" in the sense that the flow at any fixed point does not change over time, but the pressure, density, and flow velocity are not the same at every point! $\endgroup$
    – alephzero
    Dec 22, 2018 at 21:24
  • $\begingroup$ @alephzero that's a good point. Also, is it considered a steady state if there's an oscillation that lasts forever? $\endgroup$
    – psitae
    Dec 22, 2018 at 21:25
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    $\begingroup$ Aerodynamic calculations frequently assume the air is incompressible if the Mach number is smaller than about 0.2. $\endgroup$
    – D. Halsey
    Dec 22, 2018 at 22:08
  • $\begingroup$ Although I agree with you I'm looking at the flow as a whole. One could argue slow steady state gas flow in a straight, horizontal tube of constant cross-section is incompressible. My question is if the flow behaves in an incompressible manner everywhere. If I were to look at the roughness of the wall at a microscopic level, would I not find points of the flow which have different density than the main flow? $\endgroup$
    – FemtoComm
    Dec 22, 2018 at 22:19
  • $\begingroup$ @FemtoComm: At the walls, the no-slip condition makes the assumption of incompressible flow even better. $\endgroup$
    – D. Halsey
    Dec 23, 2018 at 3:42
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For "normal" gas flows, you can only have a constant density if the fluid pressure is not changing (assuming constant temperature). Unfortunately, fluid flow requires a pressure drop, so as a gas is flowing down a pipe, the pressure is decreasing, the gas volume is increasing, the density is decreasing, and the gas is slowly accelerating down the pipe as a result.

There may be a theoretical way to increase the gas temperature at the correct rate as it flows down a pipe, such that the increase in temperature causes an increase in pressure, and a corresponding change in density profile such that density remains constant. However, this would (again) interfere with the pressure drop required to maintain fluid flow, so the answer appears to be "no" for this question.

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  • $\begingroup$ I am slightly confused by your answer. To be clear, we are talking about fluids, not gas specifically, right? That out of the way, the conclusion is that when there is a pressure differential the fluid does not maintain a constant density. I believe this is not the case for Couette flow between two parallel plates where pressure gradient is zero, if I'm not mistaken. Of course, this takes into account the plates are perfectly plane and there is no energy dissipation in the fluid. $\endgroup$
    – FemtoComm
    Feb 10, 2019 at 2:28
  • $\begingroup$ Fluids are liquids AND gases. $\endgroup$ Feb 10, 2019 at 5:06
  • $\begingroup$ You can move gases without changing the pressure $\endgroup$
    – FGSUZ
    Jul 30, 2020 at 23:27
  • $\begingroup$ @FGSUZ, give me an example of moving gases without changing pressure. $\endgroup$ Jul 31, 2020 at 1:31
  • $\begingroup$ You can push gas through a pipe with a extremely negligible change in temperature. You should only consider change in density with varying temperature $\endgroup$
    – FGSUZ
    Jul 31, 2020 at 13:28

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