The initial ultimate BOD after mixing of the James River is 32.5 mg/L. The DO in the river after the wastewater and river have mixed is at saturation. The river temperature is 10oC. At 10oC, the deoxygenation rate constant, k1 is 0.32 d-1 and the reaeration rate constant, k2 is 0.32 d-1. Determine the critical point tc and the critical DO.

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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The initial ultimate BOD after mixing of the James River is 32.5 mg/L. The DO in the river after the wastewater and river have mixed is at saturation. The river temperature is 10oC. At 10oC, the deoxygenation rate constant, k1 is 0.32 d-1 and the reaeration rate constant, k2 is 0.32 d-1. Determine the critical point tc and the critical DO. 

Expert Solution
Step 1

The critical point(t) is determined by the equation:

tc=1Kd(1-D0L)

Where Kd is the deoxygenation rate constant at 10°C=0.32/d

L = ultimate BOD = 32.5 mg/L

D0 = initial dissolved oxygen deficit

Oxygen deficit after time t (Dt) can be determined by the Streeter Phelps equation:

Dt=KD×LKR-KD{10-KD×t-10-KR×t} + {D0×10-KR×t}

Where, 

KD & KR are the deoxygenation and re-oxygenation constant at 20°C.

Lets assume the initial dissolved oxygen is = 9.1 mg/L (at saturation)

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