256winter2001_modprob_0201 - Mth 256 W 2001 0201 Model...

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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 well-mixed 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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