Engineering Board Exam Reviewer · Environmental Engineering · hard

Downstream of an outfall, a river has an initial ultimate BOD of 20 mg/L and an initial DO deficit of 1.0 mg/L. With k1 = 0.23/ day and k2 = 0.50/ day, at what time does the critical (minimum) DO occur?

  1. 2.65 days
  2. 2.88 days
  3. 3.70 days
  4. 5.30 days

Answer

A. 2.65 days

Solution

tc = [1/(k2 - k1)] (k2/k1)[1 - D0(k2 - k1)/(k1L0)] = (1/0.27) 2.174[1 - 0.27/4.6] = 2.65 days. (Critical deficit Dc = (k1/k2)L0e-k1tc = 5.00 mg/L.)

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