A pond forms as water collects in a conical depression of
Chapter 2, Problem 18(choose chapter or problem)
A pond forms as water collects in a conical depression of radius a and depth h. Suppose thatwater flows in at a constant rate k and is lost through evaporation at a rate proportionalto the surface area.(a) Show that the volume V(t) of water in the pond at time t satisfies the differentialequationdV/dt = k (3a/h)2/3V2/3,where is the coefficient of evaporation.(b) Find the equilibrium depth of water in the pond. Is the equilibrium asymptoticallystable?(c) Find a condition that must be satisfied if the pond is not to overflow.
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