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GATE 2017 CE (CE1) – Question 64

Water and Waste Water Quality and Treatment · Water quality standards, parameters and water quality index · 2 marks · Numerical answer

Two wastewater streams A and B have identical ultimate BOD and mix to form stream C. Stream A is at 20°C and stream C at 10°C. A has 5-day BOD 50 mg/L measured at 20°C, base-10 BOD rate constant $k_{20}=0.115$ day⁻¹ and temperature coefficient 1.135. Find C’s 5-day BOD at 10°C in mg/L, to one decimal place.

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Correct answer: 20.0 to 22.0

Explanation

The common ultimate BOD is $L_0=50/[1-10^{-0.115(5)}]=68.126$ mg/L; mixing streams with identical ultimate BOD leaves this value unchanged. Temperature correction gives $k_{10}=0.115(1.135)^{10-20}=0.032393$ day⁻¹. Therefore $BOD_5(10)=L_0[1-10^{-5k_{10}}]\simeq21.2$ mg/L. The use of base-10 kinetics is essential; replacing it with a natural exponential without converting the rate constant changes the result.

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