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qV_O = \frac{qV_o}{B_o} + R_v \,\frac{qV_g}{B_g}

qV_G = \frac{qV_g}{B_g} + R_s \, \frac{qV_o}{B_o}

qV_W =  \frac{q_w}{B_w}

qV_L =  q V_O + qV_W

qV_o = \frac{BV_o \cdot (qV_O - R_v \, qV_G)}{1- R_v \, R_s}

qV_g = \frac{B_g \cdot (qV_G - R_s \, qV_O)}{1- R_v \, R_s}

qV_w = B_w \cdot qV_W

qV_t = qV_o + qV_g + qV_w

s_o = qV_o/qV_t

s_g = qV_g/qV_t

s_w = qV_w/qV_t

s_o+s_g+s_w = 1

\dot m_O = \rho_O \cdot qV_O

\dot m_G = \rho_G \cdot qV_G

\dot m_W = \rho_W \cdot qV_W

\dot m = \dot m_O + \dot m_G + \dot m_W 

m_o = (\rho_O + \rho_G \cdot R_s) \cdot \frac{qV_o}{B_o} 

m_g = (\rho_G + \rho_O \cdot R_v) \cdot \frac{qV_g}{B_g}

\dot m_w = \rho_W \cdot qV_w/B_w

\dot m = \dot m_o + \dot m_g + \dot m_w 

\rho_o = \frac{\rho_O + \rho_G \cdot R_s}{B_o}

\rho_g = \frac{\rho_G + \rho_O \cdot R_v}{B_g}

\rho_w = \frac{\rho_W}{B_w}

\rho_t = \dot m/qV_t = s_o \, \rho_o + s_g \, \rho_g + s_w \, \rho_w  

c = \rho_t^{-1} \cdot ( s_o \, \rho_o \, c_o + s_g \, \rho_g \, c_g + s_w \, \rho_w \, c_w )