Multiple choice

A large tank with a nozzle attached contains three immiscible, in viscid fluids as shown. Assuming that the changes in h1, h2 and h3 are negligible, the instantaneous discharge velocity is

  1. $\sqrt{2gh_3 \Big( 1+ \frac{\rho_1h_1}{\rho_3h_3}+\frac{\rho_2h_2}{\rho_3h_3}\Big)}$
  2. $\sqrt{2g(h_1 + h_2 + h_3)}$
  3. $\sqrt{2gh_3 \Big(\frac{\rho_1h_1 + \rho_2h_2 + \rho_3h_3}{\rho_1 + \rho_2 + \rho_3}\Big)}$
  4. $\sqrt{2g \Big(\frac{\rho_1h_2h_3 + \rho_2h_3h_1+\rho_3h_1h_2}{\rho_1h_1 + \rho_2h_2 + \rho_3h_3}\Big)}$
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A Correct answer
Explanation

$= \sqrt{2g \times \Big[\frac{\rho_1 h_1}{\rho_3} + \frac{\rho_2h_2}{\rho_3} + h_3 \Big]}\\ = \sqrt{2gh_3 \times \Big[\frac{\rho_1 h_1}{\rho_3h_3} + \frac{\rho_2h_2}{\rho_3h_3}\Big]}$