Sludge Age given Concentration of Solids Calculator

✖Volume of Tank is defined as the capacity of flocculation and mixing tank.ⓘ Volume of Tank [V]			+10% -10%
✖MLSS given Sludge Age is the concentration of suspended solids in the mixed liquor of an activated sludge system.ⓘ MLSS given Sludge Age [X_sa]			+10% -10%
✖Volume of Wasted Sludge per day is the amount of sludge that is removed from a wastewater treatment process within a 24-hour period.ⓘ Volume of Wasted Sludge per day [Q_w]			+10% -10%
✖Concentration of Solids in Returned Sludge is the density of solid particles present in the sludge that is returned from the secondary settling tanks to the aeration tank.ⓘ Concentration of Solids in Returned Sludge [X^R]			+10% -10%
✖Peak Sewage Flow refers to the maximum rate at which sewage is discharged from a community or a facility over a short period.ⓘ Peak Sewage Flow [Q_max]			+10% -10%
✖Concentration of Solids in Effluent is the amount of solid particles, both suspended and dissolved, present in a liquid effluent (wastewater or other discharged liquid).ⓘ Concentration of Solids in Effluent [X^E]			+10% -10%

✖Sludge Age given Concentration of Solids is the average length of time that solids (or sludge) remain in the treatment system before being removed.ⓘ Sludge Age given Concentration of Solids [θ_c']

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Sludge Age given Concentration of Solids Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sludge Age given Concentration of Solids = (Volume of Tank*MLSS given Sludge Age)/((Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of Solids in Effluent)
θ_c' = (V*X_sa)/((Q_w*X^R)+(Q_max-Q_w)*X^E)
This formula uses 7 Variables

Variables Used

Sludge Age given Concentration of Solids - (Measured in Second) - Sludge Age given Concentration of Solids is the average length of time that solids (or sludge) remain in the treatment system before being removed.
Volume of Tank - (Measured in Cubic Meter) - Volume of Tank is defined as the capacity of flocculation and mixing tank.
MLSS given Sludge Age - (Measured in Kilogram per Cubic Meter) - MLSS given Sludge Age is the concentration of suspended solids in the mixed liquor of an activated sludge system.
Volume of Wasted Sludge per day - (Measured in Cubic Meter per Second) - Volume of Wasted Sludge per day is the amount of sludge that is removed from a wastewater treatment process within a 24-hour period.
Concentration of Solids in Returned Sludge - (Measured in Kilogram per Cubic Meter) - Concentration of Solids in Returned Sludge is the density of solid particles present in the sludge that is returned from the secondary settling tanks to the aeration tank.
Peak Sewage Flow - (Measured in Cubic Meter per Second) - Peak Sewage Flow refers to the maximum rate at which sewage is discharged from a community or a facility over a short period.
Concentration of Solids in Effluent - (Measured in Kilogram per Cubic Meter) - Concentration of Solids in Effluent is the amount of solid particles, both suspended and dissolved, present in a liquid effluent (wastewater or other discharged liquid).

STEP 1: Convert Input(s) to Base Unit

Volume of Tank: 9 Cubic Meter --> 9 Cubic Meter No Conversion Required
MLSS given Sludge Age: 91200 Milligram per Liter --> 91.2 Kilogram per Cubic Meter (Check conversion here)
Volume of Wasted Sludge per day: 9.5 Cubic Meter per Second --> 9.5 Cubic Meter per Second No Conversion Required
Concentration of Solids in Returned Sludge: 0.526 Milligram per Liter --> 0.000526 Kilogram per Cubic Meter (Check conversion here)
Peak Sewage Flow: 11.17 Cubic Meter per Second --> 11.17 Cubic Meter per Second No Conversion Required
Concentration of Solids in Effluent: 10 Milligram per Liter --> 0.01 Kilogram per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_c' = (V*X_sa)/((Q_w*X^R)+(Q_max-Q_w)*X^E) --> (9*91.2)/((9.5*0.000526)+(11.17-9.5)*0.01)

Evaluating ... ...

θ_c' = 37830.1147624096

STEP 3: Convert Result to Output's Unit

37830.1147624096 Second -->0.437848550490851 Day (Check conversion here)

FINAL ANSWER

0.437848550490851 ≈ 0.437849 Day <-- Sludge Age given Concentration of Solids

(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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< Sludge Age Calculators

Sludge Age given Concentration of Solids

LaTeX Go Sludge Age given Concentration of Solids = (Volume of Tank*MLSS given Sludge Age)/((Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of Solids in Effluent)

Sludge Age given MLSS

LaTeX Go Sludge Age given MLSS = (Volume of Tank*Mixed Liquor Suspended Solids)/(Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)

Sludge Age given Total Solids Removed

LaTeX Go Sludge Age given Total Solids Removed = (Volume of Tank*Concentration of Solids in Effluent)/Mass of Solids Leaving the System

Sludge Age

LaTeX Go Sludge Age = Mass of Suspended Solids/Mass of Solids Leaving the System

< Important Formulas of Sludge Age Calculators

Endogenous Respiration Rate Constant given Mass of Wasted Activated Sludge

LaTeX Go Endogenous Respiration Rate Constant = ((Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD))-Mass of Wasted Activated Sludge)/(Mixed Liquor Suspended Solids*Volume of Tank)

Mass of Wasted Activated Sludge

LaTeX Go Mass of Wasted Activated Sludge = (Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD))-(Endogenous Respiration Rate Constant*Volume of Tank*Mixed Liquor Suspended Solids)

Concentration of Solids in Returned Sludge given MLSS

LaTeX Go Concentration of Solids given MLSS = (Mixed Liquor Suspended Solids*Volume of Tank)/(Volume of Wasted Sludge per day*Sludge Age)

Endogenous Respiration Rate Constant given Maximum Yield Coefficient

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

Sludge Age given Concentration of Solids 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 Concentration of Solids?

Sludge Age given Concentration of Solids calculator uses Sludge Age given Concentration of Solids = (Volume of Tank*MLSS given Sludge Age)/((Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of Solids in Effluent) to calculate the Sludge Age given Concentration of Solids, The Sludge Age given Concentration of Solids formula is defined as the calculation of the sludge age when we have prior information of concentration of solids. Sludge Age given Concentration of Solids is denoted by θ_c' symbol.

How to calculate Sludge Age given Concentration of Solids using this online calculator? To use this online calculator for Sludge Age given Concentration of Solids, enter Volume of Tank (V), MLSS given Sludge Age (X_sa), Volume of Wasted Sludge per day (Q_w), Concentration of Solids in Returned Sludge (X^R), Peak Sewage Flow (Q_max) & Concentration of Solids in Effluent (X^E) and hit the calculate button. Here is how the Sludge Age given Concentration of Solids calculation can be explained with given input values -> 5.1E-6 = (9*91.2)/((9.5*0.000526)+(11.17-9.5)*0.01).

FAQ

What is Sludge Age given Concentration of Solids?

The Sludge Age given Concentration of Solids formula is defined as the calculation of the sludge age when we have prior information of concentration of solids and is represented as θ_c' = (V*X_sa)/((Q_w*X^R)+(Q_max-Q_w)*X^E) or Sludge Age given Concentration of Solids = (Volume of Tank*MLSS given Sludge Age)/((Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of Solids in Effluent). Volume of Tank is defined as the capacity of flocculation and mixing tank, MLSS given Sludge Age is the concentration of suspended solids in the mixed liquor of an activated sludge system, Volume of Wasted Sludge per day is the amount of sludge that is removed from a wastewater treatment process within a 24-hour period, Concentration of Solids in Returned Sludge is the density of solid particles present in the sludge that is returned from the secondary settling tanks to the aeration tank, Peak Sewage Flow refers to the maximum rate at which sewage is discharged from a community or a facility over a short period & Concentration of Solids in Effluent is the amount of solid particles, both suspended and dissolved, present in a liquid effluent (wastewater or other discharged liquid).

How to calculate Sludge Age given Concentration of Solids?

The Sludge Age given Concentration of Solids formula is defined as the calculation of the sludge age when we have prior information of concentration of solids is calculated using Sludge Age given Concentration of Solids = (Volume of Tank*MLSS given Sludge Age)/((Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of Solids in Effluent). To calculate Sludge Age given Concentration of Solids, you need Volume of Tank (V), MLSS given Sludge Age (X_sa), Volume of Wasted Sludge per day (Q_w), Concentration of Solids in Returned Sludge (X^R), Peak Sewage Flow (Q_max) & Concentration of Solids in Effluent (X^E). With our tool, you need to enter the respective value for Volume of Tank, MLSS given Sludge Age, Volume of Wasted Sludge per day, Concentration of Solids in Returned Sludge, Peak Sewage Flow & Concentration of Solids in Effluent 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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