Sludge Age given Volume of Aeration Tank Calculator

✖Volume of Tank is defined as the capacity of flocculation and mixing tank.ⓘ Volume of Tank [V]			+10% -10%
✖MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics).ⓘ MLSS [X]			+10% -10%
✖Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.ⓘ Maximum Yield Coefficient [Y]			+10% -10%
✖Sewage discharge is the flow rate of sewage when it is being discharged into the water body.ⓘ Sewage Discharge [Q_s]			+10% -10%
✖Influent BOD is the total amount of BOD which is present in the incoming sewage.ⓘ Influent BOD [Q_i]			+10% -10%
✖Effluent BOD is the amount of dissolved oxygen needed by aerobic biological organisms to break down organic material present in a water sample at a certain temperature over a specific time period.ⓘ Effluent BOD [Q_o]			+10% -10%
✖Endogenous Respiration Rate Constant is used for designing a complete-mix activated-sludge system.ⓘ Endogenous Respiration Rate Constant [K^e]			+10% -10%

✖Sludge Age is the average time for which the particle of suspended solids remains in aeration.ⓘ Sludge Age given Volume of Aeration Tank [θ_c]

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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)
θ_c = (V*X)/(Y*Q_s*(Q_i-Q_o)-V*X*K^e)
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 into the water body.
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 dissolved oxygen needed by aerobic biological organisms to break down organic material present in a water sample at a certain temperature over a specific time period.
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

θ_c = (V*X)/(Y*Q_s*(Q_i-Q_o)-V*X*K^e) --> (9*1.2)/(0.5*10*(0.00048-0.0004)-9*1.2*3.47222222222222E-05)

Evaluating ... ...

θ_c = 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)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< Size and Volume of the Aeration Tank Calculators

Maximum Yield Coefficient given Volume of Aeration Tank

LaTeX 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

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

MLSS given volume of Aeration Tank

LaTeX 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

LaTeX 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

LaTeX Go

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 formula is defined as a measure of the average time that the microorganisms (biomass) remain in the aeration tank of a wastewater treatment plant, considering volume of aeration tank. Sludge Age is denoted by θ_c 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 (Q_s), Influent BOD (Q_i), Effluent BOD (Q_o) & Endogenous Respiration Rate Constant (K^e) and hit the calculate button. Here is how the Sludge Age given Volume of Aeration Tank calculation can be explained with given input values -> 5.8E-5 = (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 formula is defined as a measure of the average time that the microorganisms (biomass) remain in the aeration tank of a wastewater treatment plant, considering volume of aeration tank and is represented as θ_c = (V*X)/(Y*Q_s*(Q_i-Q_o)-V*X*K^e) 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 into the water body, Influent BOD is the total amount of BOD which is present in the incoming sewage, Effluent BOD is the amount of dissolved oxygen needed by aerobic biological organisms to break down organic material present in a water sample at a certain temperature over a specific time period & 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 formula is defined as a measure of the average time that the microorganisms (biomass) remain in the aeration tank of a wastewater treatment plant, considering volume of aeration tank 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 (Q_s), Influent BOD (Q_i), Effluent BOD (Q_o) & Endogenous Respiration Rate Constant (K^e). 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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