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Newtonian fluid in compressible flow?

  1. Dec 1, 2015 #1
    When compressible effects are accounted for, viscosity should vary with temperature.
    Doesn't this violate the concept of Newtonian fluids, where shear stress is linearly proportional to the strain rate?
  2. jcsd
  3. Dec 1, 2015 #2


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    No. The shear stress is still linearly proportional to the strain rate through the viscosity. It's simply the case that viscosity may not be constant. That said, viscosity varies quite slowly with temperature so the Mach number has to be relatively high to start getting the kind of heating required for the effect to be all that noticeable.
  4. Dec 1, 2015 #3
    Oh, so if the viscosity becomes a function of the strain rate. In that case, it would violate newtonian fluid?
  5. Dec 2, 2015 #4
    Yes. We call such fluids non-Newtonian fluids.

    Incidentally, for liquids, the viscosity varies pretty rapidly with temperature. Typical values are a few percent per degree C.

  6. Dec 2, 2015 #5
    But even if the viscosity varies with temperature, it doesn't necessarily mean it is a non-newtonian fluid right?
    As long as the viscosity does not vary with the strain rate, the shear stress is still a linear function of the strain rate, even if the viscosity is varying with other parameters?
  7. Dec 2, 2015 #6


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    There are all sorts of fluids where the viscosity varies with temperature and these fluids are Newtonian. Many heavy oils are heated to make them easier to pump by reducing their viscosity.

    Remember, the definition states that the shear is linearly proportional to the strain rate. The definition is silent on whether temperature is considered. It's also silent on whether density makes a difference: there are relatively light Newtonian fluids and relatively heavy ones.
  8. Dec 2, 2015 #7
    Right (like SteamKing said).
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