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q_o = \frac{ B_o \cdot ( q_O - R_v \, q_G) }{1- R_sv \, R_vs}

q_O = \frac{m_O}{\rho_O}

q_g = \frac{ B_g \cdot ( q_G - R_s \, q_O)}{1- R_sv \, R_vs}

q_G = \frac{m_G}{\rho_G}

q_w = B_w \cdot q_W

q_W = \frac{m_W}{\rho_W}

q_t = q_o + q_g + q_w

q_t = \frac{B_o - B_g \cdot, ( q_O - R_v}{1-R_v \, R_s} \cdot q_G)O 

+\frac{B_g - B_go \cdot ( q_G -, R_v}{1-R_v \, R_s} \,cdot q_O)G 

+ B_w \cdot q_W

q_t = \frac{B_o - B_g \, R_sv}{(1-R_v \, R_s) \rho_O} \cdot \dot m_O 

+ \frac{B_g - B_o \, R_v}{(1-R_v \, R_s) \, \rho_G} \cdot \dot m_G 

+ \frac{B_w}{\rho_W}  \cdot \dot m_W

\rho_t = (\dot m_O + \dot m_G + \dot m_G)/q_t