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%
✖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%
✖Sludge Concentration in Return Line is the total BOD that is present in the return line.ⓘ Sludge Concentration in Return Line [X_r]			+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%

✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Wasting Rate from Return Line [θ_c]

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Formula

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Wasting Rate from Return Line

Formula

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

Example

`"10.90909d"=("1000m³"*"1200mg/L")/(("400m³/d"*"200mg/L")+("500m³/d"*"60mg/L"))`

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Wasting Rate from Return Line Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Mean Cell Residence Time - (Measured in Second) - Mean Cell Residence Time is the average time that the sludge remains in the reactor.
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).
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.
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.
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)
WAS Pumping Rate from Return Line: 400 Cubic Meter per Day --> 0.00462962962962963 Cubic Meter per Second (Check conversion here)
Sludge Concentration in Return Line: 200 Milligram per Liter --> 0.2 Kilogram per Cubic Meter (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

θ_c = (V*X)/((Q_w'*X_r)+(Q_e*X_e)) --> (1000*1.2)/((0.00462962962962963*0.2)+(0.00578703703703704*0.06))

Evaluating ... ...

θ_c = 942545.454545454

STEP 3: Convert Result to Output's Unit

942545.454545454 Second -->10.9090909090909 Day (Check conversion here)

FINAL ANSWER

10.9090909090909 ≈ 10.90909 Day <-- Mean Cell Residence Time

(Calculation completed in 00.004 seconds)

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Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 2 Wasting Rate Calculators

Wasting Rate from Return Line

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

Wasting Rate from Return Line when Concentration of Solid in Effluent is Low

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

Wasting Rate from Return Line Formula

What is Solid Return Time?

Solids Retention Time (SRT) in the activated sludge process is critical for ensuring effective wastewater treatment. SRT sets the growth rate of microorganisms in the activated sludge process, thereby selecting the microbial composition of the mixed liquor and its settling and treatment properties.

How to Calculate Wasting Rate from Return Line?

Wasting Rate from Return Line calculator uses Mean Cell Residence Time = (Reactor Volume*MLSS)/((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent)) to calculate the Mean Cell Residence Time, The Wasting rate from return line is defined as the time required to waste sludge from the return sludge line because return activated sludge is more concentrated and requires smaller waste sludge pumps. Mean Cell Residence Time is denoted by θ_c symbol.

How to calculate Wasting Rate from Return Line using this online calculator? To use this online calculator for Wasting Rate from Return Line, enter Reactor Volume (V), MLSS (X), WAS Pumping Rate from Return Line (Q_w'), Sludge Concentration in Return Line (X_r), Effluent Flow Rate (Q_e) & Solid Concentration in Effluent (X_e) and hit the calculate button. Here is how the Wasting Rate from Return Line calculation can be explained with given input values -> 0.000126 = (1000*1.2)/((0.00462962962962963*0.2)+(0.00578703703703704*0.06)).

FAQ

What is Wasting Rate from Return Line?

The Wasting rate from return line is defined as the time required to waste sludge from the return sludge line because return activated sludge is more concentrated and requires smaller waste sludge pumps and is represented as θ_c = (V*X)/((Q_w'*X_r)+(Q_e*X_e)) or Mean Cell Residence Time = (Reactor Volume*MLSS)/((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent)). The Reactor Volume gives us the capacity of the reactor, MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics), WAS Pumping Rate from Return Line is the flow rate of waste sludge from the return line, Sludge Concentration in Return Line is the total BOD that is present in 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 Wasting Rate from Return Line?

The Wasting rate from return line is defined as the time required to waste sludge from the return sludge line because return activated sludge is more concentrated and requires smaller waste sludge pumps is calculated using Mean Cell Residence Time = (Reactor Volume*MLSS)/((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent)). To calculate Wasting Rate from Return Line, you need Reactor Volume (V), MLSS (X), WAS Pumping Rate from Return Line (Q_w'), Sludge Concentration in Return Line (X_r), 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, WAS Pumping Rate from Return Line, Sludge Concentration in 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 Mean Cell Residence Time?

In this formula, Mean Cell Residence Time uses Reactor Volume, MLSS, WAS Pumping Rate from Return Line, Sludge Concentration in 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 -

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

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