Consider a steady-state system with constant volume, a single constant inflow, and a single constant outflow, but with spatially varying fluid density within the system. Use the following equation $$ V \frac {\mathrm d\rho_{\text{sys}}}{\mathrm dt} + \rho_{\text{sys}} \frac{\mathrm dV}{\mathrm dt} = \sum_{i=1}^{N}Q_{\text{in},i}\rho_{\text{in},i} - \sum_{j=1}^{M}Q_{\text{out},j}\rho_{\text{out},j} $$ to derive a simple formula for the outflow density if $Q_{\text{in}}$, $Q_{\text{out}}$, and $\rho_{\text{in}}$ are known.
I was able to reason that if the volume of the system is constant, than the derivative of volume with respect to time should be zero, giving the following equation. $$ V \frac {\mathrm d\rho_{\text{sys}}}{\mathrm dt} = Q_{\text{in}}\rho_{\text{in}} - Q_{\text{out}}\rho_{\text{out}} $$ At this point, I'm not exactly sure what to do. I thought that maybe since there was constant volume and steady state conditions that $$ Q_{\text{in}} = Q_{\text{out}} $$ However I'm now pretty sure that that would only be the case in a system with constant density. I'm not exactly sure where to go next.