(C) According to Torricelli's law, the velocity of efflux $v$ is given by $v = \sqrt{2gh_{eff}}$, where $h_{eff}$ is the equivalent height of a water

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(C) According to Torricelli's law, the velocity of efflux $v$ is given by $v = \sqrt{2gh_{eff}}$, where $h_{eff}$ is the equivalent height of a water column that exerts the same pressure at the bottom.Pressure at the bottom $P = P_{atm} + \rho_k g h_k + \rho_w g h_w$.Here, $\rho_k = 0.8 \,g/cm^3$, $h_k = 25 \,cm = 0.25 \,m$, $\rho_w = 1.0 \,g/cm^3$, $h_w = 20 \,cm = 0.20 \,m$.Equivalent water height $h_{eff} = \frac{\rho_k h_k + \rho_w h_w}{\rho_w} = \frac{0.8 \times 25 + 1.0 \times 20}{1.0} = 20 + 20 = 40 \,cm = 0.4 \,m$.Now, $v = \sqrt{2 \times 9.8 \times 0.4} = \sqrt{7.84} = 2.8 \,m/s$.

Class 11 Physics Fluid Mechanics and Surface Tension Velocity of Efflux and Torricelli's law

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$A$ large vessel with a small hole at the bottom is filled with water and kerosene, with kerosene floating on water. The length of the water column is $20 \,cm$ and that of the kerosene is $25 \,cm$. The velocity with which water flows out of the hole is (density of kerosene $= 0.8 \,g/cm^3$, density of water $= 1.0 \,g/cm^3$, neglect viscous force). (in $\,m/s$)

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$5.6$
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$0.7$
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$2.8$
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$1.4$

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Class 11

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

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