How does one calculate the pressure of air flowing in a tube? My specific application is air traveling in a 1/2-inch tube at a velocity of 14 inches/second. I know that Bernoulli would have the answer, but I cannot find it myself. — NT, Cambridge, MA
Without more information about the air in your tube, it’s not possible to determine its pressure. Bernoulli’s equation is frequently misunderstood to say that high-speed air is low-pressure air and that low speed air is high-pressure air—two observations that aren’t necessarily true. Just because air is moving rapidly doesn’t mean that its pressure is low. For example, the air in an airplane cabin is moving quickly but its pressure is higher than that of the air outside the cabin. Similarly, if you were to throw a tank of compressed air across the room, its pressure would remain high despite its increase in speed.
What Bernoulli’s equation really says is that air has three forms for its energy and that as long as that air flows smoothly and without significant friction through a system of stationary obstacles, the sum of those three energies can’t change. The three energies are kinetic energy (the energy of motion), gravitational potential energy, and an energy associated with pressure that I call pressure potential energy. The obstacles must remain stationary so that they can’t do work on the air and thus change its total energy. Since the sum of those three energies doesn’t change as air flows through a stationary environment, its pressure typically falls whenever its speed rises and vice versa. If the air also changes altitude significantly, then gravitational potential energy must be included in these energy exchanges.
So the reason why I can’t answer your question about air in a pipe is that I don’t know what the air’s total energy was before it flowed through the pipe. While I can calculate the air’s kinetic energy from its speed and we can neglect gravitational potential energy because the air isn’t changing altitudes much in the pipe, I need to know what the air’s total energy is in order to determine its pressure potential energy and thus its pressure.