(C) According to Torricelli's law derived from Bernoulli's equation, the velocity of efflux $v$ is given by $v = \sqrt{2gh}$.Given $g = 10 \,m/s^2$ an

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(C) According to Torricelli's law derived from Bernoulli's equation, the velocity of efflux $v$ is given by $v = \sqrt{2gh}$.Given $g = 10 \,m/s^2$ and $h = 10 \,m$, we have $v = \sqrt{2 \times 10 \times 10} = \sqrt{200} = 14.14 \,m/s$.The diameter of the hole is $d = 4 \,mm = 4 \times 10^{-3} \,m$, so the radius $r = 2 \times 10^{-3} \,m$.The area of the hole is $A = \pi r^2 = 3.14 \times (2 \times 10^{-3})^2 = 3.14 \times 4 \times 10^{-6} = 12.56 \times 10^{-6} \,m^2$.The flow rate $Q$ is given by $Q = A \times v$.$Q = (12.56 \times 10^{-6} \,m^2) \times (14.14 \,m/s) \approx 177.6 \times 10^{-6} \,m^3/s = 1.776 \times 10^{-4} \,m^3/s$.

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

Easy

$A$ large open-top water tank is completely filled with water. $A$ small hole of diameter $4 \,mm$ is made $10 \,m$ below the water level. The flow rate of water through the hole is (Acceleration due to gravity $= 10 \,m/s^2$)

AP EAMCET 2023 All AP EAMCET

A
$14.14 \times 10^{-6} \,m^3/s$
B
$2.1 \times 10^{-6} \,m^3/s$
C
$1.77 \times 10^{-4} \,m^3/s$
D
$0.177 \times 10^{-6} \,m^3/s$

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

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$A$ large open-top water tank is completely filled with water. $A$ small hole of diameter $4 \,mm$ is made $10 \,m$ below the water level. The flow rate of water through the hole is (Acceleration due to gravity $= 10 \,m/s^2$)

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