Consider a spherical tank containing compressed air. It is known from the elementary compressible theory that if a hole is opened on the tank, the compressed air will leave the tank at a mass flow rate of \(\dot{m}=k ho\) where \(k\) is a constant and \(ho\) is the density at any time. Assuming an initial density \(ho_{0}\) and pressure \(P_{0}\), derive an expression for \(P(t)\).

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PD. Po D/2 m = kp