\frac{p_{m} S}{ρ_{m} g} = \frac{p S}{(ρ_{v} + ρ_{m} - 2 ρ) g} \Rightarrow \frac{p_{m}}{ρ_{m}} = \frac{p}{ρ_{v} + ρ_{m} - 2 ρ}

${\frac{p_mS}{\rho_mg} = \frac{pS}{(\rho_v +\rho_m - 2\rho)g} \quad\Rightarrow\quad \frac{p_m}{\rho_m} = \frac{p}{\rho_v +\rho_m - 2\rho}\quad}$