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(C) The velocity of efflux $(v)$ for an orifice at depth $h$ is given by Torricelli's Law:$v = \sqrt{2gh}$Given $h = 20.0 \ m$ and $g = 10 \ m s^{-2}$

Vedclass · Accepted Answer

$1.4$

Vedclass · Answer

(C) The velocity of efflux $(v)$ for an orifice at depth $h$ is given by Torricelli's Law:$v = \sqrt{2gh}$Given $h = 20.0 \ m$ and $g = 10 \ m s^{-2}$:$v = \sqrt{2 	imes 10 	imes 20} = \sqrt{400} = 20 \ m s^{-1}$The volume flow rate $(Q)$ is the product of the area of the orifice $(A)$ and the velocity of efflux $(v)$:$Q = A 	imes v$$3.08 	imes 10^{-5} = \left( \frac{\pi d^2}{4} ight) 	imes 20$Rearranging for $d^2$:$d^2 = \frac{4 	imes 3.08 	imes 10^{-5}}{20 	imes \pi} = \frac{12.32 	imes 10^{-5}}{62.83} \approx 1.96 	imes 10^{-6} \ m^2$Taking the square root:$d = \sqrt{1.96 	imes 10^{-6}} = 1.4 	imes 10^{-3} \ m = 1.4 \ mm$

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