So here's how I would do it:
\begin{equation}
P_bottom = P_atm + g * (\rho_1 * h_1 + \rho_2 * h_2)
\end{equation}
Applying Bernoulli's equation just before and just after the orifice
\begin{equation}
\frac{\rho1 * v_efflux^2} = P_bottom - P_atm = g * (\rho_1 * h_1 + \rho_2 * h_2) \\
v_efflux = \frac{2g * (\rho_1 * h_1 + \rho_2 * h_2)}{\rho_1}
\end{equation}