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Unformatted text preview: Week 3b: 3.6 Cooling/Mixing [see Cooling example, week 3] [3.9 Numerical Solutions [Euler, Maple’s dsolve/numeric]] not collected 4.1 Higher Order DE 4.2 Constant Coef, Homogeneous DE ————— Problem: A 200L tank is half full of a solution containing 100g of a desolved chemical. A solution containing 0.5 g/L of the same chemical is pumped into the tank at a rate of 6 L/min. The well-stirred mixture is pumped out at a rate of 4 L/min. Determine the concentration of the chemical in the tank just before overflow. Solution: V = V ( t ) and A = A ( t ) will be the volumn of the solution in the tank (in L) and amount of chemical in the tank (in g), at time t (in min.). The “rate in” is, r 1 = 6 and “rate out”, r 2 = 4; and the “concentration in” is, c 1 = 0 . 5 , while we solve for the “concentration out”, c 2 = A V . ————— First, the initial volumn V = 100 (one half of the tank’s volumn), so V ( t ) = 100 + ( r 1- r 2 ) t = 100 + 2 t (“rate in” - “rate out”). Next, the tank overflows 2 when V is 200, which occurs when t = 50 , (why?) so we’re looking for c 2 (50) ....
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