# I Can inviscid fluids rightly be called Newtonian?

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1. Sep 1, 2016

### Sklarker

I am studying an inviscid fluid. I am trying to characterise the fluid. Does it make sense to call it Newtonian or should I avoid this designation? What I mean is - if there are no viscous stresses then does it make sense to characterise it's response to viscous stresses? (That box that doesn't exist - what colour is it?!!)
Also if the fluid is incompressible does this imply the fluid is homogeneous, i.e. is it better to use one or other of these terms but not both?

2. Sep 1, 2016

### Staff: Mentor

A Newtonian fluid is one that is viscous. So, if it is inviscid (not viscous), then it is not Newtonian. Why would you be motivated to use the word homogeneous in place of the word incompressible?

3. Sep 1, 2016

### Sklarker

Thanks for the feedback. My motivation is to use whatever is the most appropriate terminology! I'm trying to ensure my assumptions are water tight.

4. Sep 1, 2016

### Staff: Mentor

OK. Then incompressible best describes incompressible.

5. Sep 1, 2016

### Sklarker

I'm thinking that homogeneity requires incompressibility but not the other way round. Perhaps use of the word homogeneity avoids needing to say that it is incompressible and isothermal and several other things

6. Sep 1, 2016

### Staff: Mentor

There are much more important things to obsess about than terminology.

7. Sep 1, 2016

### Sklarker

That's a great help...cheers.

8. Sep 1, 2016

Homogeneity means something entirely different. I've heard it used in one or two different senses in the various fields of fluid mechanics, and none of them have to do with incompressibility. Incompressible has a very specific definition.

9. Sep 3, 2016

### olivermsun

Yes.
But homogeneity in the sense of the "constant density" of the fluid does sort imply incompressibility, unless I am not thinking of something here (it's late!).

10. Sep 4, 2016

Homogeneous does not imply constant density, though. Also, you could have a flow that is moving at Mach 2 or something that has constant density but still compressible. Further, you can have flows that are incompressible but do not have constant density.

11. Sep 4, 2016

### olivermsun

Homogeneous is often used to mean that the fluid properties do not vary in space. That could include density, although, granted, one could also say the fluid is homogeneous in the sense that it is "equally compressible" all around (and thereby still admit acoustic waves).

Also I may be missing something in terms of usage, but what does it mean to you for a flow to be "incompressible"? If a constant density is assumed throughout the fluid, doesn't that basically enforce incompressibility?

Last edited: Sep 4, 2016
12. Sep 4, 2016

Homogeneous is not used in that sense in fluid dynamics parlance. Homogeneous is most commonly used in fluid dynamics to describe statistical homogeneity in fluctuating quantities, such as in the study of turbulence. It might also be used to describe homogeneously mixed fluids as well.

And incompressible flow is one whose divergence is everywhere zero, i.e. $\nabla\cdot\vec{u} = 0$. It would be theoretically possible to have a supersonic, compressible flow that still has a constant density due to other compounding effects, such as heat addition/subtraction and/or viscous losses.

Because of this definition, it's also possible to have a flow that is incompressible but which does not have a constant density. These are typically referred to as variable density flows as a distinct set of phenomena from compressible flows. Variable density mixing is a very active research area, for example.

13. Sep 4, 2016

### olivermsun

In atmospheric (and other environmental) flows, "homogeneous fluid" is used in that way. Meanwhile, I think of the statistical homogeneity associated with turbulence as being a feature of the flow rather than the fluid, whereas the OP seemed to be asking about the fluid being homogeneous.

Anyhow my statement was incorrect. I was thinking of constant density along streamlines, but of course as you point out the fluid parcels going along different streamlines of an incompressible flow can have different densities.

You're quite right. Thanks for the correction.

Last edited: Sep 4, 2016