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

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

3537

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