Two tanks contain different liquids with density in the ratio $2: 1$. Holes of cross section with ra

Question

Two tanks contain different liquids with density in the ratio $2: 1$. Holes of cross section with ratio $2: 1$ are made at heights $\mathrm{h}_{1}$ and $\mathrm{h}_{2}$ below liquid in the two tanks which have same heights of liquids from bottom of tanks. If the volume flux or rates of flow are the same, then what should be the ratio $\mathrm{h}_{1}$ to $\mathrm{h}_{2}$\

Professor PC Thomas Classes · Answer

Volume flux is av\ $a_{1} v_{1}=a_{2} v_{2}$\ $a_{1} \sqrt{2 g h_{1}}=a_{2} \sqrt{2 g h_{2}}$\ $\mathrm{a}_{1}^{2} 2 \mathrm{gh}_{1}=\mathrm{a}_{2}^{2} 2 \mathrm{gh}_{2}$\ $\frac{\mathrm{h}_{1}}{\mathrm{~h}_{2}}=\frac{\mathrm{a}_{2}^{2}}{\mathrm{a}_{1}^{2}}$\