Problem 6: Examination of unsteady changes within the control volume
Consider the aerospace device shown below, which has two pumps, P1 and P2, which provide
volumetric flow rates, Q1 and Q2, respectively. Find the density as a function of time, p(t), within
the device assuming that the inflow density is $p_1$, and the outflow density is p(t). The known
quantities are: $p_1$, Q1, Q2, and the volume of the device, V, and the initial condition p(0)=$p_1$.
What is the limit of p(t) as $t \to \infty$ and the time scale for reaching this steady-state?