While on a Sunday outing to play disc golf you notice that a 1.0 cm diameter hol
ID: 1562350 • Letter: W
Question
While on a Sunday outing to play disc golf you notice that a 1.0 cm diameter hole has somehow been created in the Tuttle dam. The hole is 17 m below the water surface on the other side of the dam. Quickly springing into action, you cover the hole with your hand to stop the leak. How much force to you need to apply to accomplish this? Upon reflection you realize there is no great urgency to your action by calculating the water speed that would result if you removed your hand. Show that this speed is upsilon = 18.2 m/s. Determine how much water would leak out of Tuttle Creek Lake through this hole in one day.Explanation / Answer
a)
A force due to water pressure at h distance below the surface of the water is given by:
F = pressure times the area of the hole.
The pressure is rho g h
Hence the force F = rho g h A = 1000*9.81*17*pi*0.5^2*10^-4 = 13.098 N
b)
Using Bernoulli equation,
0.5 rho v^2 = rho g h
0.5 v^2 = gh
v = sqrt(2gh) = sqrt(2*9.81*17) = 18.263 m/s
c)
volume flow rate = Area times the velocity = pi*0.5^2*10^-4*18.263 = 0.00143 m^3/s
Hence the amount of water in one day = 24*3600*0.00143*1000 kg = 123552 kilograms
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