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Water steadily enters a tank of diameter D T at a flow rate Q. A small hole in the bottom of the tank (with diameter D 0 ) allows water to escape. We will show in class that the water velocity through the hole is given by√2gH , where H is the depth of water in the tank.
(a) If the tank is initially empty, derive an expression for the maximum height (H max ) that the water will reach in the tank. Check your answer using your intuition: is H max proportional to, inversely proportional to, or independent of D T , D 0 and Q? Does this make sense?
(b) Once this maximum height is reached, the flow coming into the tank (i.e. Q) is turned off. If the hole diameter is one-fifth of the tank diameter, and the maximum height is 50 cm, how quickly will the water surface fall as soon as the incoming flow is turned off?
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