Bernoulli's principle and gases: not matching real-world experience

Question

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?

Answer 1

Air isn't much compressible at velocities you can reach by blowing air (on the order of 50 m/s max, which is quite low compared to the speed of sound), so we don't except much thermal effects.

The lecture notes you're pointing to actually gives numbers. At most, the temperature difference is the stagnation temperature (eq. 17.21). By taking 50 m/s, the maximum temperature difference is about 1.5°C, which is already difficult to feel. So thermal effects are, indeed, quite small at theses velocities.