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Physics 1 Problem Solutions 148

Physics 1 Problem Solutions 148 - 144 Chapt 15 Fluids the...

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144 Chapt. 15 Fluids the water coming out of the primary. The volume of water V accumulated in the catchment measures time: V 0 V is the volume of water remaining in the primary. a) Show that the differential bit of water volume sent to the catchment is dV = A h v h dt, where v h is the water velocity at the hole and dt is a time differential. HINT: Actually, this is one of those obviously it’s ... things. b) Using the continuity equation Av = Constant and Bernoulli’s equation P + 1 2 ρv 2 + ρgy = Constant show that A h v h = k radicalbig V 0 V , where k = A h A 0 radicalBigg 2 g 1 ( A h /A 0 ) 2 . c) Solve the differential equation dV dt = A h v h = k radicalbig V 0 V with the initial condition V = 0 at t = 0: i.e., find V explicitly as a function of time. At what time t max does V reach a maximum? What is V max ? At what time t empty is the primary empty? If one drops the 2nd order term in the V ( t ) solution, what would V be at time t empty ?
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