sol7 - Professor Philip S. Marcus O2 Problem Set 7...

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Professor Philip S. Marcus O2 Problem Set 7 – Solutions a) Using Bernoulli, from the top surface of the water in the hot tub to the leak: P air ( z = H ) + 0 + gH = P air ( z = 0) + V 2 0 / 2. Or, V 0 = r 2 gH - (2 aH/ρ ). b) Continuing with Bernoulli and using the streamline from a point on the top surface of the water in the hot tub to an arbitrary point at location ( x, z ) in the jet: P air ( z = H ) + 0 + gH = P air ( z ) + [ V ( x, z )] 2 / 2 + gz . Or, V ( x, z ) = r 2 g ( H - z ) + 2[ P air ( z = H ) - P air ( z )] = r 2( H - z )( g - a/ρ ). Note the value of x does not directly enter. c) Use this control volume shown on the last page. Mass conservation tell us that what goes in at Point 1 goes out at Point 2 . Or, using the formal mass balance equation, where M is the mass in the control volume: ˙ M = 0 = ρA 1 ( V 1 · n 1 ) + ρA 2 ( V 2 · n 2 ). We have constructed the sides of the control volume so that
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sol7 - Professor Philip S. Marcus O2 Problem Set 7...

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