Sludge Age given Volume of Aeration Tank Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sludge Age = (Volume of Tank*MLSS)/(Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)-Volume of Tank*MLSS*Endogenous Respiration Rate Constant)
θc = (V*X)/(Y*Qs*(Qi-Qo)-V*X*Ke)
This formula uses 8 Variables
Variables Used
Sludge Age - (Measured in Second) - Sludge Age is the average time for which the particle of suspended solids remains in aeration.
Volume of Tank - (Measured in Cubic Meter) - Volume of tank is defined as the capacity of flocculation and mixing tank.
MLSS - (Measured in Kilogram per Cubic Meter) - MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics).
Maximum Yield Coefficient - Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.
Sewage Discharge - (Measured in Cubic Meter per Second) - Sewage discharge is the flow rate of sewage when it is being discharged in the river.
Influent BOD - (Measured in Kilogram per Cubic Meter) - Influent BOD is the total amount of BOD which is present in the incoming sewage.
Effluent BOD - (Measured in Kilogram per Cubic Meter) - Effluent BOD is the amount of BOD present in the outing sewage.
Endogenous Respiration Rate Constant - (Measured in 1 Per Second) - Endogenous Respiration Rate Constant is used for designing a complete-mix activated-sludge system.
STEP 1: Convert Input(s) to Base Unit
Volume of Tank: 9 Cubic Meter --> 9 Cubic Meter No Conversion Required
MLSS: 1200 Milligram per Liter --> 1.2 Kilogram per Cubic Meter (Check conversion here)
Maximum Yield Coefficient: 0.5 --> No Conversion Required
Sewage Discharge: 10 Cubic Meter per Second --> 10 Cubic Meter per Second No Conversion Required
Influent BOD: 0.48 Milligram per Liter --> 0.00048 Kilogram per Cubic Meter (Check conversion here)
Effluent BOD: 0.4 Milligram per Liter --> 0.0004 Kilogram per Cubic Meter (Check conversion here)
Endogenous Respiration Rate Constant: 3 1 Per Day --> 3.47222222222222E-05 1 Per Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θc = (V*X)/(Y*Qs*(Qi-Qo)-V*X*Ke) --> (9*1.2)/(0.5*10*(0.00048-0.0004)-9*1.2*3.47222222222222E-05)
Evaluating ... ...
θc = 431999.999999996
STEP 3: Convert Result to Output's Unit
431999.999999996 Second -->4.99999999999995 Day (Check conversion here)
FINAL ANSWER
4.99999999999995 5 Day <-- Sludge Age
(Calculation completed in 00.004 seconds)

Credits

Created by Suraj Kumar
Birsa Institute of Technology (BIT), Sindri
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Meerut Institute of Engineering and Technology (MIET), Meerut
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8 Size and Volume of the Aeration Tank Calculators

Sludge Age given Volume of Aeration Tank
Go Sludge Age = (Volume of Tank*MLSS)/(Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)-Volume of Tank*MLSS*Endogenous Respiration Rate Constant)
Endogenous Respiration Rate Constant given Volume of Aeration Tank
Go Endogenous Respiration Rate Constant = (((Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*MLSS))-1)/Sludge Age
Maximum Yield Coefficient given Volume of Aeration Tank
Go Maximum Yield Coefficient = Volume of Tank/((Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(MLSS*(1+Endogenous Respiration Rate Constant*Sludge Age)))
Sewage Discharge given Volume of Aeration Tank
Go Sewage Discharge = Volume of Tank/((Maximum Yield Coefficient*(Influent BOD-Effluent BOD)*Sludge Age)/(MLSS*(1+Endogenous Respiration Rate Constant*Sludge Age)))
Influent BOD given Volume of Aeration Tank
Go Influent BOD = Effluent BOD+((Volume of Tank*MLSS*(1+Endogenous Respiration Rate Constant*Sludge Age))/(Maximum Yield Coefficient*Sewage Discharge*Sludge Age))
Effluent BOD given Volume of Aeration Tank
Go Effluent BOD = Influent BOD-((Volume of Tank*MLSS*(1+Endogenous Respiration Rate Constant*Sludge Age))/(Maximum Yield Coefficient*Sewage Discharge*Sludge Age))
MLSS given volume of Aeration Tank
Go MLSS = (Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*(1+Endogenous Respiration Rate Constant*Sludge Age))
Volume of Aeration Tank
Go Volume of Tank = (Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(MLSS*(1+Endogenous Respiration Rate Constant*Sludge Age))

Sludge Age given Volume of Aeration Tank Formula

Sludge Age = (Volume of Tank*MLSS)/(Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)-Volume of Tank*MLSS*Endogenous Respiration Rate Constant)
θc = (V*X)/(Y*Qs*(Qi-Qo)-V*X*Ke)

What is Sludge Age ?

The common range for sludge age for a conventional activated sludge plant is between 3 and 15 days. For extended aeration activated sludge plants the range is between about 15 and 30 days. Generally during the winter months, higher sludge ages are required to maintain a sufficient biological mass.

How to Calculate Sludge Age given Volume of Aeration Tank?

Sludge Age given Volume of Aeration Tank calculator uses Sludge Age = (Volume of Tank*MLSS)/(Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)-Volume of Tank*MLSS*Endogenous Respiration Rate Constant) to calculate the Sludge Age, The Sludge Age given Volume of Aeration Tank is defined as the sludge age when we have prior information of other parameters used. Sludge Age is denoted by θc symbol.

How to calculate Sludge Age given Volume of Aeration Tank using this online calculator? To use this online calculator for Sludge Age given Volume of Aeration Tank, enter Volume of Tank (V), MLSS (X), Maximum Yield Coefficient (Y), Sewage Discharge (Qs), Influent BOD (Qi), Effluent BOD (Qo) & Endogenous Respiration Rate Constant (Ke) and hit the calculate button. Here is how the Sludge Age given Volume of Aeration Tank calculation can be explained with given input values -> 2.7E-8 = (9*1.2)/(0.5*10*(0.00048-0.0004)-9*1.2*3.47222222222222E-05).

FAQ

What is Sludge Age given Volume of Aeration Tank?
The Sludge Age given Volume of Aeration Tank is defined as the sludge age when we have prior information of other parameters used and is represented as θc = (V*X)/(Y*Qs*(Qi-Qo)-V*X*Ke) or Sludge Age = (Volume of Tank*MLSS)/(Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)-Volume of Tank*MLSS*Endogenous Respiration Rate Constant). Volume of tank is defined as the capacity of flocculation and mixing tank, MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics), Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed, Sewage discharge is the flow rate of sewage when it is being discharged in the river, Influent BOD is the total amount of BOD which is present in the incoming sewage, Effluent BOD is the amount of BOD present in the outing sewage & Endogenous Respiration Rate Constant is used for designing a complete-mix activated-sludge system.
How to calculate Sludge Age given Volume of Aeration Tank?
The Sludge Age given Volume of Aeration Tank is defined as the sludge age when we have prior information of other parameters used is calculated using Sludge Age = (Volume of Tank*MLSS)/(Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)-Volume of Tank*MLSS*Endogenous Respiration Rate Constant). To calculate Sludge Age given Volume of Aeration Tank, you need Volume of Tank (V), MLSS (X), Maximum Yield Coefficient (Y), Sewage Discharge (Qs), Influent BOD (Qi), Effluent BOD (Qo) & Endogenous Respiration Rate Constant (Ke). With our tool, you need to enter the respective value for Volume of Tank, MLSS, Maximum Yield Coefficient, Sewage Discharge, Influent BOD, Effluent BOD & Endogenous Respiration Rate Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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