Walter buys a large storage tank, which is open to the atmosphere at the top, an

Question

Walter buys a large storage tank, which is open to the atmosphere at the top, and places it outside his laboratory. One day he fills the tank with water for an experiment he’s working on. However, it turns out the storage tank was not worth the price he paid for it, as it soon develops a small hole in the side, 18 m below the level of the water in the tank. The water flows out of the hole in the tank at a rate of 3.0 x 10-3 m3/min. What is: a. the speed of the water leaving the hole? b. the diameter of the hole?

Explanation / Answer

a)Speed of the water through hole is given by

v = sqrt(2gh)

    = sqrt(2*9.8*18)

   speed = 18.78 m/s

b) Q = vA

( 3*10^-3/60) m^3/s = 18.78 m/s * pi*d^2 /4

     d^2 = [(3*10^-3/60 ) m^3/s ] / [18.78 m/s *pi/4]

          = 3.3899 × 10-6 m2

d = sqrt [3.3899 × 10-6 m2]

diameter = 1.841*10^-3m = 1.841 mm

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