PSet_02_solution

# PSet_02_solution - Spring 2003 10.450 Process Dynamics...

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Spring 2003 10.450 Process Dynamics, Operations, and Control Problem Sets - 2 1. Harvey goes his own way in the world. Harvey’s bathtub is a half-cylinder of radius 30 cm, length 160 cm. When he welded it up from scrap pipe, he neglected to install an overflow drain; hence he must be very careful to avoid overfilling, because his bathroom is directly over the room housing his collection of sugar cube replicas of 16 th century cathedrals. He’s filling it at a rate of 7 kg s -1 with 40ºC water. When the level is 17 cm, he hops into the tub. How long does he have to turn the water off? By the way, Harvey weighs in at 185 lb f . The material balance on the tub is d r V = w dt Integrating, we find w V = t r Thus the volume increases linearly with time. When Harvey makes his entrance, he reduces the capacity of the tub to hold water. Then the time remaining is r t remain = w ( V tub - V at 17 cm - V Harvey ) V tub comes from straightforward geometry; 0.226 m 3 . V Harvey requires a value for human density;

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PSet_02_solution - Spring 2003 10.450 Process Dynamics...

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