Water flows into a vertical cylindrical tank of cross-sectional area A ft at the rate of Q ft/min. At the same time, the water drains out under the influence of gravity through a hole of area a ft' in the base of the tank. If the water is initially h ft deep, find the instantaneous depth as a function of time. What is the limiting depth of the water as time increases indefinitely?
Water flows into a vertical cylindrical tank of cross-sectional area A ft at the rate of Q ft/min. At the same time, the water drains out under the influence of gravity through a hole of area a ft' in the base of the tank. If the water is initially h ft deep, find the instantaneous depth as a function of time. What is the limiting depth of the water as time increases indefinitely?
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