ABSTRACT
Looking at each term, a is area as defined. Force per unit area is pressure, which we will denote as P. Differential force per unit area is the change in pressure with spatial position, also called pressure gradient. Pressure gradient is important, because that’s what causes flow. Mass per unit area, which we will denote as p (Greek letter rho), is a measure of air density. A gas area density might seem odd, but we will always be able to multiply it by particle flow rate to get mass flow. Air velocity multiplied by area is volume flow, which we denote as U. Pressure and volume flow are time varying (otherwise there’s nothing worth writing all these equations for), so we get:
where K = a / cP, and c is the speed of sound in air. Putting equations C.6 and C.7 together, we get:
d (C.3)
d F (x) m dv a (C.5) a dx a dt
A Pressure [density] [volume flow].
