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Consider a cylindrical water tank of constant cross section A . Water is pumped into the tank at a constant rate k and leaks out through a small hole of area a in the bottom of the tank. From Torricelli's theorem in hydrodynamics it follows that the rate at which water flows through the hole is αa √(2 g h), where h is the current depth of water in the tank, g is the acceleration due to gravity, and αis a contraction coefficient that satisfies 0.5 ≤α≤1.0 . (a) Show that the depth of water in the
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