Question

A large tank is filled with three liquids of densities ρ₁, ρ₂ and ρ₃ up to heights of h₁, h₂ and h₃ respectively. What will be the expression for the instantaneous velocity of discharge through a small opening at the base of the tank? (assume that the diameter of the opening is negligible compared to the height of the liquid column)

a.

\(\sqrt{2g(h_1 + h_2 + h_3)}\)

b.

\(\sqrt{2g(\frac{ρ_1h_1+2ρ_2h_2+3ρ_3h_3}{ρ_1})}\)

c.

\(\sqrt{2g(\frac{ρ_1h_1+\frac{1}{2}ρ_2h_2+\frac{1}{3}ρ_3h_3}{ρ_2})}\)

d.

\(\sqrt{2g(\frac{ρ_1h_1+ρ_2h_2+ρ_3h_3}{ρ_3})}\)

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Answer: (d).\(\sqrt{2g(\frac{ρ_1h_1+ρ_2h_2+ρ_3h_3}{ρ_3})}\)

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Q. A large tank is filled with three liquids of densities ρ₁, ρ₂ and ρ₃ up to heights of h₁, h₂ and h₃ respectively. What will be the expression for the instantaneous velocity of...

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