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Wasting Rate from Return Line Formula

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

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Mean Cell Residence Time is the average time that the sludge remains in the reactor. Check FAQs

θ c = \frac{V \cdot X}{(Q w' \cdot X r) + (Q e \cdot X e)}

θ_c - Mean Cell Residence Time?V - Reactor Volume?X - MLSS?Q_w' - WAS Pumping Rate from Return Line?X_r - Sludge Concentration in Return Line?Q_e - Effluent Flow Rate?X_e - Solid Concentration in Effluent?

Wasting Rate from Return Line Example

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Here is how the Wasting Rate from Return Line equation looks like with Values.

Here is how the Wasting Rate from Return Line equation looks like with Units.

Here is how the Wasting Rate from Return Line equation looks like.

7 = \frac{1000 \cdot 1200}{(400 \cdot 200) + (1523.81 \cdot 60)}

7d = \frac{1000m³ \cdot 1200mg/L}{(400m³/d \cdot 200mg/L) + (1523.81m³/d \cdot 60mg/L)}

7 = \frac{1000 \cdot 1200}{(400 \cdot 200) + (1523.81 \cdot 60)}

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Wasting Rate from Return Line Solution

Follow our step by step solution on how to calculate Wasting Rate from Return Line?

FIRST Step Consider the formula

θ c = \frac{V \cdot X}{(Q w' \cdot X r) + (Q e \cdot X e)}

Next Step Substitute values of Variables

∴

θ c = \frac{1000m³ \cdot 1200mg/L}{(400m³/d \cdot 200mg/L) + (1523.81m³/d \cdot 60mg/L)}

Next Step Convert Units

∴

θ c = \frac{1000m³ \cdot 1.2kg/m³}{(0.0046m³/s \cdot 0.2kg/m³) + (0.0176m³/s \cdot 0.06kg/m³)}

Next Step Prepare to Evaluate

∴

θ c = \frac{1000 \cdot 1.2}{(0.0046 \cdot 0.2) + (0.0176 \cdot 0.06)}

Next Step Evaluate

∴

θ c = 604799.899200017s

Next Step Convert to Output's Unit

∴

θ c = 6.99999883333353d

LAST Step Rounding Answer

∴

θ c = 7d

Wasting Rate from Return Line Formula Elements

Variables

Mean Cell Residence Time

Mean Cell Residence Time is the average time that the sludge remains in the reactor.

Symbol: θ_c

Measurement: TimeUnit: d

Note: Value should be between 5 to 15.

Formulas to find Mean Cell Residence Time

Reactor Volume

Reactor Volume refers to the physical volume of a reactor used in chemical processes.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Reactor Volume

MLSS

MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics).

Symbol: X

Measurement: DensityUnit: mg/L

Note: Value should be between 1000 to 6500.

Formulas to find MLSS

WAS Pumping Rate from Return Line

WAS Pumping Rate from Return Line is the flow rate of waste sludge from the return line.

Symbol: Q_w'

Measurement: Volumetric Flow RateUnit: m³/d

Note: Value should be greater than 0.

Formulas to find WAS Pumping Rate from Return Line

Sludge Concentration in Return Line

Sludge Concentration in Return Line refers to the concentration of suspended solids in the sludge that is being pumped back from the secondary clarifier to the aeration tank.

Symbol: X_r

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Sludge Concentration in Return Line

Effluent Flow Rate

Effluent Flow Rate is the total quantity of the flow of sewage from the secondary clarifier.

Symbol: Q_e

Measurement: Volumetric Flow RateUnit: m³/d

Note: Value should be greater than 0.

Formulas to find Effluent Flow Rate

Solid Concentration in Effluent

Solid Concentration in Effluent is the total amount of solids that are present in the effluent.

Symbol: X_e

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Solid Concentration in Effluent

Other Formulas to find Mean Cell Residence Time

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

θ c = \frac{V \cdot X}{Q w' \cdot X r}

How to Evaluate Wasting Rate from Return Line?

Wasting Rate from Return Line evaluator 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 evaluate the Mean Cell Residence Time, The Wasting Rate from Return Line formula 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 evaluate Wasting Rate from Return Line using this online evaluator? To use this online evaluator 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.

FAQs on Wasting Rate from Return Line

What is the formula to find Wasting Rate from Return Line?

The formula of Wasting Rate from Return Line is expressed as 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)). Here is an example- 8.1E-5 = (1000*1.2)/((0.00462962962962963*0.2)+(0.0176366898148148*0.06)).

How to calculate Wasting Rate from Return Line?

With 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) we can find Wasting Rate from Return Line using the formula - 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)).

What are the other ways to Calculate Mean Cell Residence Time?

Here are the different ways to Calculate Mean Cell Residence Time-

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

Can the Wasting Rate from Return Line be negative?

No, the Wasting Rate from Return Line, measured in Time cannot be negative.

Which unit is used to measure Wasting Rate from Return Line?

Wasting Rate from Return Line is usually measured using the Day[d] for Time. Second[d], Millisecond[d], Microsecond[d] are the few other units in which Wasting Rate from Return Line can be measured.

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Wasting Rate from Return Line Formula

​GoWasting Rate from Return Line when Concentration of Solid in Effluent is Low Formula

Wasting Rate from Return Line Example

Wasting Rate from Return Line Solution

Wasting Rate from Return Line Formula Elements

Other Formulas to find Mean Cell Residence Time

How to Evaluate Wasting Rate from Return Line?

FAQs on Wasting Rate from Return Line

Variable Name

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