Differential Equations for Engineers · Modeling and first-order differential equations
A 400-liter tank initially contains 80 liters of brine with 12 kg of dissolved salt
Problem
A 400-liter tank initially contains 80 liters of brine with 12 kg of dissolved salt. Brine containing 0.15 kg of salt per liter enters at 6 L/min, and the well-stirred mixture leaves at 4 L/min. Let Q(t) be the mass of salt in kilograms at time t minutes. Write the first-order IVP for Q(t) on the interval while the tank is filling, and determine the time T at which the tank first becomes full. Then find Q(T).
Hint
The volume grows linearly because inflow exceeds outflow; salt leaves at the well-stirred concentration times the outflow rate.
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