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Applicability of Bernoulli's principle to ideal gases

  1. Aug 22, 2010 #1
    Bernoulli's equation as I understand it is an expression (or possibly a consequence) of conservation of energy in an incompressible fluid flow.

    My question is: how can the "standard" Bernoulli's equation ever apply to an ideal gas?

    Wikipedia gives a different version of Bernoulli's equation for a compressible fluid, which assumes adiabatic compression and has a coefficient with some gammas in front of the pressure term. Shouldn't this version always apply to an ideal gas fluid, and not the standard equation?

    I understand that there are arguments that an ideal fluid basically doesn't significantly compress if it's significantly subsonic, but I don't see how these arguments affect the equation of state of the fluid, which is what tells us how the internal energy of the gas behaves.
  2. jcsd
  3. Aug 22, 2010 #2


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    An ideal fluid can mean that the fluid has zero viscosity as well as being incompressable. The zero viscosity part makes flows indeterminate, since there is no interaction between adjacent flows. Assuming a constant mass flow within a pipe, the entire cross-section of fluid could be moving at some relatively slow speed, or you could have a very small tube of flow moving at some relatively high speed, while surrounding fluid is not moving at all.

    The reference to significantly sub-sonic flows normally applies to real air flow around a typical wing. The amount of compression effect (change in density) of air around a typical wing is 5% or less at mach 0.3, and much lower at slower speeds, so it can be ignored if just trying to get a ball park estimate on flows, and use the simpler form of Bernoulli's equation.
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