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Two open tanks A and B contain different liquids filled to certain heights. A hole is made in each tank's wall at the same depth h below the liquid surface. The hole area in A is twice that in B. If the mass flow rate (mass flux) of liquid out of each hole is equal, find the ratio of the densities of the liquid in A to that in B.
- 2/1
- 3/2
- 2/3
- 1/2
Correct answer: 1/2
Solution
By Torricelli's law the efflux speed v = sqrt(2 g h) depends only on the depth h, which is the same for both holes, so v_A = v_B. Mass flux = rho * a * v. Setting them equal: rho_A * a_A * v = rho_B * a_B * v, so rho_A * a_A = rho_B * a_B. Since a_A = 2 a_B, rho_A = rho_B/2, giving rho_A/rho_B = 1/2.
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