Reciprocal of Sludge Age 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%

✖Reciprocal of sludge age is the time of sludge in terms of days .ⓘ Reciprocal of Sludge Age [θs_reci]

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Formula

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Reciprocal of Sludge Age

Formula

`"θs"_{"reci"} = ("Y"*"U")-"K"^{"e"}`

Example

`"2.9E^-6d"=("0.5"*"0.5s⁻¹")-"3d⁻¹"`

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Reciprocal of Sludge Age Solution

STEP 0: Pre-Calculation Summary

Formula Used

Reciprocal of sludge age = (Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant
θs_reci = (Y*U)-K^e
This formula uses 4 Variables

Variables Used

Reciprocal of sludge age - (Measured in Second) - Reciprocal of sludge age is the time of sludge in terms of days .
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

θs_reci = (Y*U)-K^e --> (0.5*0.5)-3.47222222222222E-05

Evaluating ... ...

θs_reci = 0.249965277777778

STEP 3: Convert Result to Output's Unit

0.249965277777778 Second -->2.8931166409465E-06 Day (Check conversion here)

FINAL ANSWER

2.8931166409465E-06 ≈ 2.9E-6 Day <-- Reciprocal of sludge age

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 3 Sludge Age Calculators

Mass of Wasted Activated Sludge

Go Mass of Solids = (Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD))-(Endogenous Respiration Rate Constant*Volume of Tank*MLSS)

Reciprocal of Sludge Age

Go Reciprocal of sludge age = (Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant

Mass of Substrate Utilised given Maximum Yield Coefficient

Go Mass of substrate utilised = Total Microbial Mass/Maximum Yield Coefficient

Reciprocal of Sludge Age Formula

Reciprocal of sludge age = (Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant
θs_reci = (Y*U)-K^e

What is Sludge age ?

The sludge age is the most fundamental and important parameter in the design, operation and control of biological nutrient removal (BNR) activated sludge (AS) systems.

How to Calculate Reciprocal of Sludge Age?

Reciprocal of Sludge Age calculator uses Reciprocal of sludge age = (Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant to calculate the Reciprocal of sludge age, The Reciprocal of Sludge Age calculates the sludge age when we have other parameters known like maximum yield coefficient , utilisation rate . Reciprocal of sludge age is denoted by θs_reci symbol.

How to calculate Reciprocal of Sludge Age using this online calculator? To use this online calculator for Reciprocal of Sludge Age, 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 Reciprocal of Sludge Age calculation can be explained with given input values -> 1.3E-10 = (0.5*0.5)-3.47222222222222E-05.

FAQ

What is Reciprocal of Sludge Age?

The Reciprocal of Sludge Age calculates the sludge age when we have other parameters known like maximum yield coefficient , utilisation rate and is represented as θs_reci = (Y*U)-K^e or Reciprocal of sludge age = (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 Reciprocal of Sludge Age?

The Reciprocal of Sludge Age calculates the sludge age when we have other parameters known like maximum yield coefficient , utilisation rate is calculated using Reciprocal of sludge age = (Maximum Yield Coefficient*Specific Substrate Utilisation Rate)-Endogenous Respiration Rate Constant. To calculate Reciprocal of Sludge Age, 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.

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