# A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in $h_{l}, h_{2}$ and $h_{3}$ are negligible, the instantaneous discharge velocity is (A) $\sqrt{2 g h_{3}\left(1+\frac{\rho_{1}}{\rho_{3}} \frac{h_{1}}{h_{3}}+\frac{\rho_{2}}{\rho_{3}} \frac{h_{2}}{h_{3}}\right)}$ (B) $\sqrt{2 g\left(h_{1}+h_{2}+h_{3}\right)}$ (C) $\sqrt{2 g\left(\frac{\rho_{1} h_{1}+\rho_{2} h_{2}+\rho_{3} h_{3}}{\rho_{1}+\rho_{2}+\rho_{3}}\right)}$ (D) $\sqrt{2 g\left(\frac{\rho_{1} h_{2} h_{3}+\rho_{2} h_{3} h_{1}+\rho_{3} h_{1} h_{2}}{\rho_{1} h_{1}+\rho_{2} h_{2}+\rho_{3} h_{3}}\right)}$

## Question ID - 157479 | Toppr Answer A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in $h_{l}, h_{2}$ and $h_{3}$ are negligible, the instantaneous discharge velocity is (A) $\sqrt{2 g h_{3}\left(1+\frac{\rho_{1}}{\rho_{3}} \frac{h_{1}}{h_{3}}+\frac{\rho_{2}}{\rho_{3}} \frac{h_{2}}{h_{3}}\right)}$ (B) $\sqrt{2 g\left(h_{1}+h_{2}+h_{3}\right)}$ (C) $\sqrt{2 g\left(\frac{\rho_{1} h_{1}+\rho_{2} h_{2}+\rho_{3} h_{3}}{\rho_{1}+\rho_{2}+\rho_{3}}\right)}$ (D) $\sqrt{2 g\left(\frac{\rho_{1} h_{2} h_{3}+\rho_{2} h_{3} h_{1}+\rho_{3} h_{1} h_{2}}{\rho_{1} h_{1}+\rho_{2} h_{2}+\rho_{3} h_{3}}\right)}$

1 Answer - 5876 Votes

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Answer Key : (A) -

$\sqrt{2 g h_{3}\left(1+\frac{\rho_{1}}{\rho_{3}} \frac{h_{1}}{h_{3}}+\frac{\rho_{2}}{\rho_{3}} \frac{h_{2}}{h_{3}}\right)}$