Application of Differential Equations — Mixing Problems (Part 1)

Lecture slides covering mixing problems as applications of first-order ODEs.

Key Points

  • Models the amount of a substance $A(t)$ in a tank over time.
  • General form: rate of change = rate in − rate out.
  • Rate in: (concentration in) × (flow rate in)
  • Rate out: (concentration out) × (flow rate out)

Examples Covered

  1. 600L container, 150L initial with 30kg flavour: constant volume (in = out = 2 L/min), 5 kg/L concentration in. Find $A(t)$ and amount after 180s.
  2. 120L tank, 40L initial with 2kg juice: in = 3 L/min, out = 2 L/min (variable volume). Find $A(t)$, amount after 10 min, time to overflow.
  3. 120-gal basin, 50 gal initial with 200oz pollutant: in = 4 gal/min, out = 7 gal/min (draining). Find $A(t)$, amount after 0.25 hr, time to empty.

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