Bernoulli's principle is said to be applicable to compressible fluids at low mach numbers, with the pressure substituted by pressure potential, which is linear with temperature (http://www.cns.gatech.edu/~predrag/courses/PHYS-4421-13/Lautrup/compressible.pdf). As a consequence, a change in tube diameter supposedly leads to a change in velocity, temperature, and pressure all together.

So why doesn't this match my real-world experience? Example: When I blow through pursed lips, my mouth doesn't become burning hot from the (significantly) expanding cross section as air enters from my (narrower) throat, and it doesn't then become freezing at my lips due to the again reduced cross section. Or if I blow into a bag with a hole on the opposite site, again, there's huge diameter expansion and then huge contraction, without any perceptible heating or cooling. What am I missing here? There seems to be a change in velocity at all of the diameter changes, but where's the change in temperature?


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