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Unformatted text preview: Mth 256 W 2001 0201 Model Problems  Bent Petersen Practice problems. Do not turn in. Here are some mixing problems. These problems are not meant to be realistic. The numbers are completely off the wall. Consider a tank initially containing a volume V of brine (salt dissolved in water) of concentration . Let Q ( t ) be the amount of salt in the tank at time t . Note the initial amount of salt is given by Q = V . Suppose brine of concentration i ows into the tank at the volume rate r i . Then salt is entering the tank at the rate i r i . Suppose some evaporation takes place (pure water), say at the volume rate r e . Suppose in addition to everything else the wellmixed brine solution is pumped out of the tank at the volume rate r o . The concentration of this outow is Q V where V is the current volume of brine in the tank. We assume that r i , r e and r o are constant. Then clearly V = V + ( r i r e r o ) t and dQ dt = i r i Q V r o , Q (0) = Q ....
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 Winter '09

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