A large tank with a nozzle attached contains three immiscible, inviscid fluid as shown. Assuming that the changes in $h_1, h_2$ and $h_3$ are negligible, the instantaneous discharge velocity is
- $\sqrt{2gh_3 \Big( 1+ \frac{\rho_1}{\rho_3} \: \frac{h_1}{h_3} + \frac{\rho_2}{\rho_3} \: \frac{h_2}{h_3} \Big)} \\$
- $\sqrt{2g(h_1+h_2+h_3)} \\$
- $\sqrt{2g \Big( \frac{\rho_1 h_1 + \rho_2 h_2 + \rho_3 h_3}{ \rho_1 + \rho_2 +\rho_3 } \Big)} \\ $
- $\sqrt{2g \Big( \frac{\rho_1 h_2 h_3 + \rho_2 h_3h_1 + \rho_3 h_1h_2}{ \rho_1 h_1 + \rho_2 h_2 + \rho_3 h_3} \Big) }$