Endogenous Respiration Rate Constant given Volume of Aeration Tank Calculator

✖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 in the river.ⓘ 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 BOD present in the outing sewage.ⓘ Effluent BOD [Q_o]			+10% -10%
✖Sludge Age is the average time for which the particle of suspended solids remains in aeration.ⓘ Sludge Age [θ_c]			+10% -10%
✖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%

✖Endogenous Respiration Rate Constant is used for designing a complete-mix activated-sludge system.ⓘ Endogenous Respiration Rate Constant given Volume of Aeration Tank [K^e]

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Formula

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Endogenous Respiration Rate Constant given Volume of Aeration Tank

Formula

`"K"^{"e"} = ((("Y"*"Q"_{"s"}*("Q"_{"i"}-"Q"_{"o"})*"θ"_{"c"})/("V"*"X"))-1)/"θ"_{"c"}`

Example

`"3d⁻¹"=((("0.5"*"10m³/s"*("0.48mg/L"-"0.4mg/L")*"5d")/("9m³"*"1200mg/L"))-1)/"5d"`

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Endogenous Respiration Rate Constant given Volume of Aeration Tank Solution

STEP 0: Pre-Calculation Summary

Formula Used

Endogenous Respiration Rate Constant = (((Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*MLSS))-1)/Sludge Age
K^e = (((Y*Q_s*(Q_i-Q_o)*θ_c)/(V*X))-1)/θ_c
This formula uses 8 Variables

Variables Used

Endogenous Respiration Rate Constant - (Measured in 1 Per Second) - Endogenous Respiration Rate Constant is used for designing a complete-mix activated-sludge system.
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.
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).

STEP 1: Convert Input(s) to Base Unit

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)
Sludge Age: 5 Day --> 432000 Second (Check conversion here)
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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K^e = (((Y*Q_s*(Q_i-Q_o)*θ_c)/(V*X))-1)/θ_c --> (((0.5*10*(0.00048-0.0004)*432000)/(9*1.2))-1)/432000

Evaluating ... ...

K^e = 3.47222222222222E-05

STEP 3: Convert Result to Output's Unit

3.47222222222222E-05 1 Per Second -->3 1 Per Day (Check conversion here)

FINAL ANSWER

3 1 Per Day <-- Endogenous Respiration Rate Constant

(Calculation completed in 00.004 seconds)

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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))

Endogenous Respiration Rate Constant given Volume of Aeration Tank Formula

What is Aeration Tank ?

Aeration tank where air (or oxygen) is injected in the mixed liquor. Settling tank (usually referred to as "final clarifier" or "secondary settling tank") to allow the biological flocs (the sludge blanket) to settle, thus separating the biological sludge from the clear treated water.

How to Calculate Endogenous Respiration Rate Constant given Volume of Aeration Tank?

Endogenous Respiration Rate Constant given Volume of Aeration Tank calculator uses Endogenous Respiration Rate Constant = (((Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*MLSS))-1)/Sludge Age to calculate the Endogenous Respiration Rate Constant, The Endogenous Respiration Rate Constant given Volume of Aeration Tank is defined as the value of rate constant when we have prior information of other parameters used. Endogenous Respiration Rate Constant is denoted by K^e symbol.

How to calculate Endogenous Respiration Rate Constant given Volume of Aeration Tank using this online calculator? To use this online calculator for Endogenous Respiration Rate Constant given Volume of Aeration Tank, enter Maximum Yield Coefficient (Y), Sewage Discharge (Q_s), Influent BOD (Q_i), Effluent BOD (Q_o), Sludge Age (θ_c), Volume of Tank (V) & MLSS (X) and hit the calculate button. Here is how the Endogenous Respiration Rate Constant given Volume of Aeration Tank calculation can be explained with given input values -> 3.7E+7 = (((0.5*10*(0.00048-0.0004)*432000)/(9*1.2))-1)/432000.

FAQ

What is Endogenous Respiration Rate Constant given Volume of Aeration Tank?

The Endogenous Respiration Rate Constant given Volume of Aeration Tank is defined as the value of rate constant when we have prior information of other parameters used and is represented as K^e = (((Y*Q_s*(Q_i-Q_o)*θ_c)/(V*X))-1)/θ_c or 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 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, Sludge Age is the average time for which the particle of suspended solids remains in aeration, 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).

How to calculate Endogenous Respiration Rate Constant given Volume of Aeration Tank?

The Endogenous Respiration Rate Constant given Volume of Aeration Tank is defined as the value of rate constant when we have prior information of other parameters used is calculated using Endogenous Respiration Rate Constant = (((Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*MLSS))-1)/Sludge Age. To calculate Endogenous Respiration Rate Constant given Volume of Aeration Tank, you need Maximum Yield Coefficient (Y), Sewage Discharge (Q_s), Influent BOD (Q_i), Effluent BOD (Q_o), Sludge Age (θ_c), Volume of Tank (V) & MLSS (X). With our tool, you need to enter the respective value for Maximum Yield Coefficient, Sewage Discharge, Influent BOD, Effluent BOD, Sludge Age, Volume of Tank & MLSS 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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