Sludge Age given Endogenous Respiration Rate Constant Calculator

✖Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.ⓘ Maximum Yield Coefficient [Y]			+10% -10%
✖Specific Substrate Utilisation Rate is related to the specific growth rate.ⓘ Specific Substrate Utilisation Rate [U]			+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 Endogenous Respiration Rate Constant [θ_c]

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Formula

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Sludge Age given Endogenous Respiration Rate Constant

Formula

`"θ"_{"c"} = (1/(("Y"*"U")-"K"^{"e"}))`

Example

`"4.6E^-5d"=(1/(("0.5"*"0.5s⁻¹")-"3d⁻¹"))`

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Sludge Age given Endogenous Respiration Rate Constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sludge Age = (1/((Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant))
θ_c = (1/((Y*U)-K^e))
This formula uses 4 Variables

Variables Used

Sludge Age - (Measured in Second) - Sludge Age is the average time for which the particle of suspended solids remains in aeration.
Maximum Yield Coefficient - Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.
Specific Substrate Utilisation Rate - (Measured in 1 Per Second) - Specific Substrate Utilisation Rate is related to the specific growth rate.
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

Maximum Yield Coefficient: 0.5 --> No Conversion Required
Specific Substrate Utilisation Rate: 0.5 1 Per Second --> 0.5 1 Per Second No Conversion Required
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 = (1/((Y*U)-K^e)) --> (1/((0.5*0.5)-3.47222222222222E-05))

Evaluating ... ...

θ_c = 4.00055563272677

STEP 3: Convert Result to Output's Unit

4.00055563272677 Second -->4.63027272306339E-05 Day (Check conversion here)

FINAL ANSWER

4.63027272306339E-05 ≈ 4.6E-5 Day <-- Sludge Age

(Calculation completed in 00.006 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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< 5 Sludge Age Calculators

Sludge Age given Concentration of Solids

Go Sludge Age = (Volume of Tank*MLSS)/((Volume of Wasted Sludge per day*Concentration of solids)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of solids in the effluent)

Sludge Age given MLSS

Go Sludge Age = (Volume of Tank*MLSS)/(Volume of Wasted Sludge per day*Concentration of solids)

Sludge Age given Endogenous Respiration Rate Constant

Go Sludge Age = (1/((Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant))

Sludge Age given Total Solids Removed

Go Sludge Age = (Volume of Tank*Concentration of solids in the effluent)/Mass of solids leaving the system

Sludge Age

Go Sludge Age = Mass of suspended solids/Mass of solids leaving the system

Sludge Age given Endogenous Respiration Rate Constant Formula

Sludge Age = (1/((Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant))
θ_c = (1/((Y*U)-K^e))

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 Endogenous Respiration Rate Constant?

Sludge Age given Endogenous Respiration Rate Constant calculator uses Sludge Age = (1/((Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant)) to calculate the Sludge Age, Sludge Age given Endogenous Respiration Rate Constant calculates sludge age when we have prior information of other parameters used. Sludge Age is denoted by θ_c symbol.

How to calculate Sludge Age given Endogenous Respiration Rate Constant using this online calculator? To use this online calculator for Sludge Age given Endogenous Respiration Rate Constant, enter Maximum Yield Coefficient (Y), Specific Substrate Utilisation Rate (U) & Endogenous Respiration Rate Constant (K^e) and hit the calculate button. Here is how the Sludge Age given Endogenous Respiration Rate Constant calculation can be explained with given input values -> 1.3E-10 = (1/((0.5*0.5)-3.47222222222222E-05)).

FAQ

What is Sludge Age given Endogenous Respiration Rate Constant?

Sludge Age given Endogenous Respiration Rate Constant calculates sludge age when we have prior information of other parameters used and is represented as θ_c = (1/((Y*U)-K^e)) or Sludge Age = (1/((Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant)). Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed, Specific Substrate Utilisation Rate is related to the specific growth rate & Endogenous Respiration Rate Constant is used for designing a complete-mix activated-sludge system.

How to calculate Sludge Age given Endogenous Respiration Rate Constant?

Sludge Age given Endogenous Respiration Rate Constant calculates sludge age when we have prior information of other parameters used is calculated using Sludge Age = (1/((Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant)). To calculate Sludge Age given Endogenous Respiration Rate Constant, you need Maximum Yield Coefficient (Y), Specific Substrate Utilisation Rate (U) & Endogenous Respiration Rate Constant (K^e). With our tool, you need to enter the respective value for Maximum Yield Coefficient, Specific Substrate Utilisation Rate & 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.

How many ways are there to calculate Sludge Age?

In this formula, Sludge Age uses Maximum Yield Coefficient, Specific Substrate Utilisation Rate & Endogenous Respiration Rate Constant. We can use 4 other way(s) to calculate the same, which is/are as follows -

Sludge Age = Mass of suspended solids/Mass of solids leaving the system
Sludge Age = (Volume of Tank*Concentration of solids in the effluent)/Mass of solids leaving the system
Sludge Age = (Volume of Tank*MLSS)/((Volume of Wasted Sludge per day*Concentration of solids)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of solids in the effluent)
Sludge Age = (Volume of Tank*MLSS)/(Volume of Wasted Sludge per day*Concentration of solids)

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