(D) The volume flow rate $R_v$ is given by $R_v = A \times v$, where $A$ is the area of the hole and $v$ is the velocity of efflux given by Torricelli

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(D) The volume flow rate $R_v$ is given by $R_v = A \times v$, where $A$ is the area of the hole and $v$ is the velocity of efflux given by Torricelli's law $v = \sqrt{2gh}$.For the square hole: Area $A_1 = x^2$, depth $h_1 = 2 \,m$. Velocity $v_1 = \sqrt{2g(2)} = 2\sqrt{g}$. Flow rate $R_{v1} = x^2 \times 2\sqrt{g}$.For the triangular hole: Area $A_2 = \frac{\sqrt{3}}{4} \times (4)^2 = 4\sqrt{3} \,cm^2$, depth $h_2 = 6 \,m$. Velocity $v_2 = \sqrt{2g(6)} = \sqrt{12g} = 2\sqrt{3g}$. Flow rate $R_{v2} = 4\sqrt{3} \times 2\sqrt{3g} = 24\sqrt{g}$.Equating the flow rates: $x^2 \times 2\sqrt{g} = 24\sqrt{g}$.$x^2 = 12$.$x = \sqrt{12} = 2\sqrt{3} \approx 3.46 \,cm$.

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

Easy

$A$ fully filled open water tank has two holes on either side of its walls. One is a square hole of side $x \,cm$ at a depth of $2 \,m$ from the top, and the other hole is an equilateral triangle of side $4 \,cm$ at a depth of $6 \,m$ from the top. If the rate of flow of water is the same from both the holes, then the value of $x$ is: (in $\,cm$)

AP EAMCET 2017 All AP EAMCET

A
$1.73$
B
$12$
C
$6.92$
D
$3.46$

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

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$A$ cylindrical vessel of cross-sectional area $1000 \ cm^2$ is fitted with a frictionless piston of mass $10 \ kg$ and filled with water completely. $A$ small hole of cross-sectional area $10 \ mm^2$ is opened at a point $50 \ cm$ deep from the lower surface of the piston. The velocity of efflux from the hole will be ........... $m/s$.

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