|MLA Citation:||Bloomfield, Louis A. "Question 937"|
How Everything Works 21 Jan 2018. 21 Jan 2018 <http://howeverythingworks.org/print1.php?QNum=937>.
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.