(C) Let $d_w$ and $d_o$ be the densities of water and oil respectively. The pressure at the bottom of the tank is given by $P = h_w d_w g + h_o d_o g$

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$\sqrt{920 \times 980} \, cm/s$

(C) Let $d_w$ and $d_o$ be the densities of water and oil respectively. The pressure at the bottom of the tank is given by $P = h_w d_w g + h_o d_o g$.We can find the equivalent height $h$ of a water column that exerts the same pressure at the bottom: $h d_w g = h_w d_w g + h_o d_o g$.Substituting the given values: $h = h_w + \frac{h_o d_o}{d_w} = 100 + \frac{400 \times 0.9}{1} = 100 + 360 = 460 \, cm$.According to Torricelli's theorem,the velocity of efflux $v$ is given by $v = \sqrt{2gh}$.Substituting the values: $v = \sqrt{2 \times 980 \times 460} = \sqrt{920 \times 980} \, cm/s$.

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

Difficult

$A$ tank is filled with water of density $1 \, g/cm^3$ and oil of density $0.9 \, g/cm^3$. The height of the water layer is $100 \, cm$ and the height of the oil layer is $400 \, cm$. If $g = 980 \, cm/s^2$,then the velocity of efflux from an opening in the bottom of the tank is

A
$\sqrt{900 \times 980} \, cm/s$
B
$\sqrt{1000 \times 980} \, cm/s$
C
$\sqrt{920 \times 980} \, cm/s$
D
$\sqrt{950 \times 980} \, cm/s$

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

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$A$ tank is filled with water of density $1 \, g/cm^3$ and oil of density $0.9 \, g/cm^3$. The height of the water layer is $100 \, cm$ and the height of the oil layer is $400 \, cm$. If $g = 980 \, cm/s^2$,then the velocity of efflux from an opening in the bottom of the tank is

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There is a hole at the bottom of a water tank. The total pressure at the bottom is $3 \, atm$ $(1 \, atm = 10^{5} \, N/m^{2})$. What is the velocity of the water coming out of the hole?

$A$ cylinder containing water up to a height of $25 \ cm$ has a hole of cross-section $\frac{1}{4} \ cm^2$ in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?

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