A large storage tank, open at the top and filled with water, develops a small ho

Question

A large storage tank, open at the top and filled with water, develops a small hole in its side at a point 16.8 m below the water level. The rate of flow from the leak is found to be 3.20 10-3 m3/min. (a) Determine the speed at which the water leaves the hole. I already got this (18.14 m/s) (b) Determine the diameter of the hole. I need help with this. Please provide numerical answer in mm

Explanation / Answer

b)From part a we have v = speed at which the water leaves the hole = 18.14 m/s Let the radius of the hole = r =>Area = A = pi()*r^2 where pi() = 22/7 Then given that the rate of flow from the leak is = Q = 3.2*(10^(-3)) m^3/min =>Q = (3.2*(10^(-3)))*(1/60) m^3/s =>A*v = (3.2*(10^(-3)))*(1/60) m^3/s =>A = ((3.2*(10^(-3)))*(1/60))/v = ((3.2*(10^(-3)))*(1/60))/18.14 =>pi()*r^2 = (((3.2*(10^(-3)))*(1/60))/18.14) =>r = radius = sqrt((((3.2*(10^(-3)))*(1/60))/18.14)/pi()) = 0.0009674 m = 0.9674 mm =>Diameter = 2*radius = 2*0.9674 = 1.935 mm

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