$\dot{m}_{tot}=\dot{m}_a(1+\omega)$ $\rho_{tot}=\dfrac{m_a+m_v}{V}=\dfrac{1}{T}\left(\dfrac{P_a}{R_a}+\dfrac{P_v}{R_v}\right)$ $\dot{V}_{tot}=\dfrac{\dot{m}_{tot}}{\rho_{tot}}$