A small hole of area of cross-section $2\; \mathrm{mm}^{2}$ is present near the bottom of a fully filled open tank of height $2\; \mathrm{m} .$ Taking $\mathrm{g}=10 \;\mathrm{m} / \mathrm{s}^{2},$ the rate of flow of water through the open hole would be nearly ......... $\times 10^{-6} \;m^{3} /s$
NEET 2019, Medium
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velocity of efflux $v=\sqrt{2 g h}$
volume flow rate $=\mathrm{Av}=\mathrm{A} \sqrt{2 \mathrm{gh}}$
${=\left(2 \times 10^{-6}\right)(2 \times 10 \times 2)^{1 / 2}}$
${=4 \sqrt{10} \times 10^{-6} \mathrm{m}^{3} / \mathrm{s}}$
${\cong 12.6 \times 10^{-6} \mathrm{m}^{3} / \mathrm{s}}$
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