- #1
Thomas2
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According to the popular interpretation of 'Bernoulli's Principle', moving air should always be associated with a lower static gas pressure than resting air, but clearly this can not be correct:
If one considers a pipe with air resting in it, then the static pressure on the inside of the wall (due to the random motion of molecules) is given through the ideal gas law as p=n*k*T (where n is the volume number density of air, k the Boltzmann constant and T the temperature).
Now consider the air in the pipe not resting but moving uniformly through it, i.e. assume that the amount of air leaving the pipe at one end is exactly replaced by the amount of air entering the pipe at the other end. Because the total amount of air is the same as for the stationary case, the density n is the same as well and hence also to static gas pressure p=n*k*T (assuming that the gas temperature is unchanged).
The walls of the pipe experience therefore the same static pressure whether or not the air is moving in it (in contradiction to the popular view based on Bernoulli's Principle).
If one considers a pipe with air resting in it, then the static pressure on the inside of the wall (due to the random motion of molecules) is given through the ideal gas law as p=n*k*T (where n is the volume number density of air, k the Boltzmann constant and T the temperature).
Now consider the air in the pipe not resting but moving uniformly through it, i.e. assume that the amount of air leaving the pipe at one end is exactly replaced by the amount of air entering the pipe at the other end. Because the total amount of air is the same as for the stationary case, the density n is the same as well and hence also to static gas pressure p=n*k*T (assuming that the gas temperature is unchanged).
The walls of the pipe experience therefore the same static pressure whether or not the air is moving in it (in contradiction to the popular view based on Bernoulli's Principle).