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Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is 20°C and the temperature of the stream C is 10°C. It is given that
• The 5-day BOD of the stream A measured at 20°C=50 mg/l
• BOD rate constant (base 10) at 20°C=0.115 per day
• Temperature coefficient = 1.135
• The 5-day BOD of the stream A measured at 20°C=50 mg/l
• BOD rate constant (base 10) at 20°C=0.115 per day
• Temperature coefficient = 1.135
The 5 –day BOD (in mg/l, up to one decimal place) of the stream C, calculated at 10°C, is______
Correct answer is '21.21'. Can you explain this answer?
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5-Day BOD Calculation at 20°C for Stream A
Given:
- 5-day BOD of Stream A at 20°C = 50 mg/l
- BOD rate constant (base 10) at 20°C = 0.115 per day
- Temperature coefficient = 1.135
To calculate the 5-day BOD of Stream C at 10°C, we need to use the temperature coefficient to adjust the BOD rate constant and then apply the formula for BOD decay.
Adjusting BOD Rate Constant for Temperature
The temperature coefficient is used to adjust the BOD rate constant based on the temperature difference between Stream A and Stream C.
Formula:
Adjusted rate constant = Rate constant at reference temperature * Temperature coefficient^(Temperature difference in °C/10)
In this case, the reference temperature is 20°C and the temperature difference is 20°C - 10°C = 10°C.
Adjusted rate constant = 0.115 per day * (1.135^(10/10)) = 0.115 per day * 1.135^1 = 0.130525 per day
Calculating 5-Day BOD for Stream C at 10°C
Now we can use the adjusted rate constant to calculate the 5-day BOD for Stream C at 10°C.
Formula:
BODC = BODA * (Rate constant A / Rate constant C)
Where:
BODC = 5-day BOD of Stream C at 10°C
BODA = 5-day BOD of Stream A at 20°C
Rate constant A = Rate constant of Stream A at 20°C
Rate constant C = Adjusted rate constant for Stream C at 10°C
Substituting the values:
BODC = 50 mg/l * (0.115 per day / 0.130525 per day) = 50 mg/l * 0.880685 = 44.03425 mg/l
Rounding off to one decimal place, the 5-day BOD of Stream C at 10°C is approximately 44.0 mg/l.
Conclusion:
The given answer of 21.21 mg/l is incorrect based on the calculations. The correct 5-day BOD of Stream C at 10°C is 44.0 mg/l.
Given:
- 5-day BOD of Stream A at 20°C = 50 mg/l
- BOD rate constant (base 10) at 20°C = 0.115 per day
- Temperature coefficient = 1.135
To calculate the 5-day BOD of Stream C at 10°C, we need to use the temperature coefficient to adjust the BOD rate constant and then apply the formula for BOD decay.
Adjusting BOD Rate Constant for Temperature
The temperature coefficient is used to adjust the BOD rate constant based on the temperature difference between Stream A and Stream C.
Formula:
Adjusted rate constant = Rate constant at reference temperature * Temperature coefficient^(Temperature difference in °C/10)
In this case, the reference temperature is 20°C and the temperature difference is 20°C - 10°C = 10°C.
Adjusted rate constant = 0.115 per day * (1.135^(10/10)) = 0.115 per day * 1.135^1 = 0.130525 per day
Calculating 5-Day BOD for Stream C at 10°C
Now we can use the adjusted rate constant to calculate the 5-day BOD for Stream C at 10°C.
Formula:
BODC = BODA * (Rate constant A / Rate constant C)
Where:
BODC = 5-day BOD of Stream C at 10°C
BODA = 5-day BOD of Stream A at 20°C
Rate constant A = Rate constant of Stream A at 20°C
Rate constant C = Adjusted rate constant for Stream C at 10°C
Substituting the values:
BODC = 50 mg/l * (0.115 per day / 0.130525 per day) = 50 mg/l * 0.880685 = 44.03425 mg/l
Rounding off to one decimal place, the 5-day BOD of Stream C at 10°C is approximately 44.0 mg/l.
Conclusion:
The given answer of 21.21 mg/l is incorrect based on the calculations. The correct 5-day BOD of Stream C at 10°C is 44.0 mg/l.
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Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is 20°C and the temperature of the stream C is 10°C. It is given that• The 5-day BOD of the stream A measured at 20°C=50 mg/l• BOD rate constant (base 10) at 20°C=0.115 per day• Temperature coefficient = 1.135The 5 –day BOD (in mg/l, up to one decimal place) of the stream C, calculated at 10°C, is______Correct answer is '21.21'. Can you explain this answer?
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Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is 20°C and the temperature of the stream C is 10°C. It is given that• The 5-day BOD of the stream A measured at 20°C=50 mg/l• BOD rate constant (base 10) at 20°C=0.115 per day• Temperature coefficient = 1.135The 5 –day BOD (in mg/l, up to one decimal place) of the stream C, calculated at 10°C, is______Correct answer is '21.21'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is 20°C and the temperature of the stream C is 10°C. It is given that• The 5-day BOD of the stream A measured at 20°C=50 mg/l• BOD rate constant (base 10) at 20°C=0.115 per day• Temperature coefficient = 1.135The 5 –day BOD (in mg/l, up to one decimal place) of the stream C, calculated at 10°C, is______Correct answer is '21.21'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is 20°C and the temperature of the stream C is 10°C. It is given that• The 5-day BOD of the stream A measured at 20°C=50 mg/l• BOD rate constant (base 10) at 20°C=0.115 per day• Temperature coefficient = 1.135The 5 –day BOD (in mg/l, up to one decimal place) of the stream C, calculated at 10°C, is______Correct answer is '21.21'. Can you explain this answer?.
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