GATE 2020 CE (CE1) – Question 64
A stream carries 5 m³/s with ultimate BOD 30 mg/L. Wastewater of 0.20 m³/s and BOD5 = 500 mg/L mixes instantly and completely. Stream area remains 40 m², and BOD exertion constant is 0.3/day, base-e. Find remaining BOD 3 km downstream (mg/L), to two decimals.
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Correct answer: 49 to 50
Explanation
Wastewater ultimate BOD is $500/(1-e^{-1.5})=643.608$ mg/L. Mixed ultimate BOD is $[5(30)+0.2(643.608)]/5.2=53.6003$ mg/L. Velocity is $5.2/40=0.13$ m/s and travel time $3000/(0.13\cdot86400)=0.267094$ day. Remaining BOD is $L_0e^{-kt}\approx\mathbf{49.47}$ mg/L.