A rigid tank of volume air at an absolute pressure of P and temperature T. At t = 0, air begins escaping from the tank through a valve with a flow area of A 1 . The air passing through the valve has a...

A rigid tank of volume
air at an absolute pressure of P and temperature T. At t = 0, air begins escaping from the tank through a valve with a flow area of A₁. The air passing through the valve has a speed of V₁
and a density
Determine the instantaneous rate of change of density in the tank at t = 0, assuming it to be uniform within the tank.