Concentration of Sludge in Return Line given Wasting Rate from Return Line Calculator

✖The Reactor Volume gives us the capacity of the reactor.ⓘ Reactor Volume [V]			+10% -10%
✖MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics).ⓘ MLSS [X]			+10% -10%
✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Mean Cell Residence Time [θ_c]			+10% -10%
✖WAS Pumping Rate from Return Line is the flow rate of waste sludge from the return line.ⓘ WAS Pumping Rate from Return Line [Q_w']			+10% -10%
✖Effluent Flow Rate is the total quantity of the flow of sewage from the secondary clarifier.ⓘ Effluent Flow Rate [Q_e]			+10% -10%
✖Solid Concentration in Effluent is the total amount of solids that are present in the effluent.ⓘ Solid Concentration in Effluent [X_e]			+10% -10%

✖Sludge Concentration in Return Line is the total BOD that is present in the return line.ⓘ Concentration of Sludge in Return Line given Wasting Rate from Return Line [X_r]

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Formula

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Concentration of Sludge in Return Line given Wasting Rate from Return Line

Formula

`"X"_{"r"} = ("V"*"X"/("θ"_{"c"}*("Q"_{"w"}"'")))-("Q"_{"e"}*"X"_{"e"}/("Q"_{"w"}"'"))`

Example

`"353.5714mg/L"=("1000m³"*"1200mg/L"/("7d"*"400m³/d"))-("500m³/d"*"60mg/L"/"400m³/d")`

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Concentration of Sludge in Return Line given Wasting Rate from Return Line Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sludge Concentration in Return Line = (Reactor Volume*MLSS/(Mean Cell Residence Time*WAS Pumping Rate from Return Line))-(Effluent Flow Rate*Solid Concentration in Effluent/WAS Pumping Rate from Return Line)
X_r = (V*X/(θ_c*Q_w'))-(Q_e*X_e/Q_w')
This formula uses 7 Variables

Variables Used

Sludge Concentration in Return Line - (Measured in Kilogram per Cubic Meter) - Sludge Concentration in Return Line is the total BOD that is present in the return line.
Reactor Volume - (Measured in Cubic Meter) - The Reactor Volume gives us the capacity of the reactor.
MLSS - (Measured in Kilogram per Cubic Meter) - MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics).
Mean Cell Residence Time - (Measured in Second) - Mean Cell Residence Time is the average time that the sludge remains in the reactor.
WAS Pumping Rate from Return Line - (Measured in Cubic Meter per Second) - WAS Pumping Rate from Return Line is the flow rate of waste sludge from the return line.
Effluent Flow Rate - (Measured in Cubic Meter per Second) - Effluent Flow Rate is the total quantity of the flow of sewage from the secondary clarifier.
Solid Concentration in Effluent - (Measured in Kilogram per Cubic Meter) - Solid Concentration in Effluent is the total amount of solids that are present in the effluent.

STEP 1: Convert Input(s) to Base Unit

Reactor Volume: 1000 Cubic Meter --> 1000 Cubic Meter No Conversion Required
MLSS: 1200 Milligram per Liter --> 1.2 Kilogram per Cubic Meter (Check conversion here)
Mean Cell Residence Time: 7 Day --> 604800 Second (Check conversion here)
WAS Pumping Rate from Return Line: 400 Cubic Meter per Day --> 0.00462962962962963 Cubic Meter per Second (Check conversion here)
Effluent Flow Rate: 500 Cubic Meter per Day --> 0.00578703703703704 Cubic Meter per Second (Check conversion here)
Solid Concentration in Effluent: 60 Milligram per Liter --> 0.06 Kilogram per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

X_r = (V*X/(θ_c*Q_w'))-(Q_e*X_e/Q_w') --> (1000*1.2/(604800*0.00462962962962963))-(0.00578703703703704*0.06/0.00462962962962963)

Evaluating ... ...

X_r = 0.353571428571428

STEP 3: Convert Result to Output's Unit

0.353571428571428 Kilogram per Cubic Meter -->353.571428571428 Milligram per Liter (Check conversion here)

FINAL ANSWER

353.571428571428 ≈ 353.5714 Milligram per Liter <-- Sludge Concentration in Return Line

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Environmental Engineering » Design of a complete mix activated sludge reactor » Concentration of Solids » Concentration of Sludge in Return Line given Wasting Rate from Return Line

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< 3 Concentration of Solids Calculators

Concentration of Sludge in Return Line given Wasting Rate from Return Line

Go Sludge Concentration in Return Line = (Reactor Volume*MLSS/(Mean Cell Residence Time*WAS Pumping Rate from Return Line))-(Effluent Flow Rate*Solid Concentration in Effluent/WAS Pumping Rate from Return Line)

Concentration of Solids in Effluent given Wasting Rate from Return Line

Go Solid Concentration in Effluent = (Reactor Volume*MLSS/(Mean Cell Residence Time*Effluent Flow Rate))-(WAS Pumping Rate from Return Line*Sludge Concentration in Return Line/Effluent Flow Rate)

Concentration of Sludge in Return Line given RAS Pumping Rate from Aeration Tank

Go Sludge Concentration in Return Line = MLSS*(Average daily influent flow rate+Return Activated Sludge)/(Return Activated Sludge+WAS Pumping Rate from Return Line)

Concentration of Sludge in Return Line given Wasting Rate from Return Line Formula

What is wasting rate?

The Wasting rate from return line is the time required to waste sludge from the return sludge line because return activated sludge is more concentrated and requires smaller waste sludge pumps.

How to Calculate Concentration of Sludge in Return Line given Wasting Rate from Return Line?

Concentration of Sludge in Return Line given Wasting Rate from Return Line calculator uses Sludge Concentration in Return Line = (Reactor Volume*MLSS/(Mean Cell Residence Time*WAS Pumping Rate from Return Line))-(Effluent Flow Rate*Solid Concentration in Effluent/WAS Pumping Rate from Return Line) to calculate the Sludge Concentration in Return Line, Concentration of Sludge in Return Line given Wasting Rate from Return Line is total amount of microorganisms present in return line. when lacking site-specific operational data, value commonly assumed is 8000 mg/L. Sludge Concentration in Return Line is denoted by X_r symbol.

How to calculate Concentration of Sludge in Return Line given Wasting Rate from Return Line using this online calculator? To use this online calculator for Concentration of Sludge in Return Line given Wasting Rate from Return Line, enter Reactor Volume (V), MLSS (X), Mean Cell Residence Time (θ_c), WAS Pumping Rate from Return Line (Q_w'), Effluent Flow Rate (Q_e) & Solid Concentration in Effluent (X_e) and hit the calculate button. Here is how the Concentration of Sludge in Return Line given Wasting Rate from Return Line calculation can be explained with given input values -> 225000 = (1000*1.2/(604800*0.00462962962962963))-(0.00578703703703704*0.06/0.00462962962962963).

FAQ

What is Concentration of Sludge in Return Line given Wasting Rate from Return Line?

Concentration of Sludge in Return Line given Wasting Rate from Return Line is total amount of microorganisms present in return line. when lacking site-specific operational data, value commonly assumed is 8000 mg/L and is represented as X_r = (V*X/(θ_c*Q_w'))-(Q_e*X_e/Q_w') or Sludge Concentration in Return Line = (Reactor Volume*MLSS/(Mean Cell Residence Time*WAS Pumping Rate from Return Line))-(Effluent Flow Rate*Solid Concentration in Effluent/WAS Pumping Rate from Return Line). The Reactor Volume gives us the capacity of the reactor, MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics), Mean Cell Residence Time is the average time that the sludge remains in the reactor, WAS Pumping Rate from Return Line is the flow rate of waste sludge from the return line, Effluent Flow Rate is the total quantity of the flow of sewage from the secondary clarifier & Solid Concentration in Effluent is the total amount of solids that are present in the effluent.

How to calculate Concentration of Sludge in Return Line given Wasting Rate from Return Line?

Concentration of Sludge in Return Line given Wasting Rate from Return Line is total amount of microorganisms present in return line. when lacking site-specific operational data, value commonly assumed is 8000 mg/L is calculated using Sludge Concentration in Return Line = (Reactor Volume*MLSS/(Mean Cell Residence Time*WAS Pumping Rate from Return Line))-(Effluent Flow Rate*Solid Concentration in Effluent/WAS Pumping Rate from Return Line). To calculate Concentration of Sludge in Return Line given Wasting Rate from Return Line, you need Reactor Volume (V), MLSS (X), Mean Cell Residence Time (θ_c), WAS Pumping Rate from Return Line (Q_w'), Effluent Flow Rate (Q_e) & Solid Concentration in Effluent (X_e). With our tool, you need to enter the respective value for Reactor Volume, MLSS, Mean Cell Residence Time, WAS Pumping Rate from Return Line, Effluent Flow Rate & Solid Concentration in Effluent 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 Concentration in Return Line?

In this formula, Sludge Concentration in Return Line uses Reactor Volume, MLSS, Mean Cell Residence Time, WAS Pumping Rate from Return Line, Effluent Flow Rate & Solid Concentration in Effluent. We can use 1 other way(s) to calculate the same, which is/are as follows -

Sludge Concentration in Return Line = MLSS*(Average daily influent flow rate+Return Activated Sludge)/(Return Activated Sludge+WAS Pumping Rate from Return Line)

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