A closed and elevated vertical cylindrical tank with diameter 1.70 m contains wa

Question

A closed and elevated vertical cylindrical tank with diameter 1.70 m contains water to a depth of 0.900 m . A worker accidently pokes a circular hole with diameter 0.0170 m in the bottom of the tank. As the water drains from the tank, compressed air above the water in the tank maintains a gauge pressure of 5.00×103Pa at the surface of the water. Ignore any effects of viscosity.

Part A

Just after the hole is made, what is the speed of the water as it emerges from the hole?

5.26

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Correct

Part B

What is the ratio of this speed to the efflux speed if the top of the tank is open to the air?

1.25

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Correct

Part C

How much time does it take for all the water to drain from the tank?

35.6

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Part D

What is the ratio of this time to the time it takes for the tank to drain if the top of the tank is open to the air?

5.26

Explanation / Answer

(a) v2 = 5.26 m/s

(b) Ratio = 1.25

(c) t = 35.6 min

(d) You need to find dV/dt for the slower velocity now: dV/dt=(pi*(0.0170/2)^2)(4.08) = 9.26e-4
V=pi(0.85)^2*0.9= 2.04 m^3
Compare these ratios: 9.26e-4= 2.04/t
t=36.72 min

Ratio = 36.72/35.6 = 1.031

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