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

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

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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. Check FAQs

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

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

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

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Here is how the Concentration of Sludge in Return Line given Wasting Rate from Return Line equation looks like with Values.

Here is how the Concentration of Sludge in Return Line given Wasting Rate from Return Line equation looks like with Units.

Here is how the Concentration of Sludge in Return Line given Wasting Rate from Return Line equation looks like.

199.9999 = (1000 \cdot \frac{1200}{7 \cdot 400}) - (1523.81 \cdot \frac{60}{400})

199.9999mg/L = (1000m³ \cdot \frac{1200mg/L}{7d \cdot 400m³/d}) - (1523.81m³/d \cdot \frac{60mg/L}{400m³/d})

199.9999 = (1000 \cdot \frac{1200}{7 \cdot 400}) - (1523.81 \cdot \frac{60}{400})

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

Follow our step by step solution on how to calculate Concentration of Sludge in Return Line given Wasting Rate from Return Line?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

X r = (1000m³ \cdot \frac{1200mg/L}{7d \cdot 400m³/d}) - (1523.81m³/d \cdot \frac{60mg/L}{400m³/d})

Next Step Convert Units

∴

X r = (1000m³ \cdot \frac{1.2kg/m³}{604800s \cdot 0.0046m³/s}) - (0.0176m³/s \cdot \frac{0.06kg/m³}{0.0046m³/s})

Next Step Prepare to Evaluate

∴

X r = (1000 \cdot \frac{1.2}{604800 \cdot 0.0046}) - (0.0176 \cdot \frac{0.06}{0.0046})

Next Step Evaluate

∴

X r = 0.199999928571429kg/m³

Next Step Convert to Output's Unit

∴

X r = 199.999928571429mg/L

LAST Step Rounding Answer

∴

X r = 199.9999mg/L

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

Variables

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

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

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

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

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 Sludge Concentration in Return Line

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

X r = X \cdot \frac{Q a + RAS}{RAS + Q w'}

Other formulas in Concentration of Solids category

Go Concentration of Solids in Effluent given Wasting Rate from Return Line

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

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

Concentration of Sludge in Return Line given Wasting Rate from Return Line evaluator 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 evaluate the Sludge Concentration in Return Line, The Concentration of Sludge in Return Line given Wasting Rate from Return Line formula is defined as the 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 evaluate Concentration of Sludge in Return Line given Wasting Rate from Return Line using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Concentration of Sludge in Return Line given Wasting Rate from Return Line?

The formula of Concentration of Sludge in Return Line given Wasting Rate from Return Line is expressed as 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). Here is an example- 199999.9 = (1000*1.2/(604800*0.00462962962962963))-(0.0176366898148148*0.06/0.00462962962962963).

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

With 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) we can find Concentration of Sludge in Return Line given Wasting Rate from Return Line using the formula - 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).

What are the other ways to Calculate Sludge Concentration in Return Line?

Here are the different ways to Calculate Sludge Concentration in Return Line-

Sludge Concentration in Return Line=MLSS*(Average Daily Influent Flow Rate+Return Activated Sludge)/(Return Activated Sludge+WAS Pumping Rate from Return Line)

Can the Concentration of Sludge in Return Line given Wasting Rate from Return Line be negative?

No, the Concentration of Sludge in Return Line given Wasting Rate from Return Line, measured in Density cannot be negative.

Which unit is used to measure 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 usually measured using the Milligram per Liter[mg/L] for Density. Kilogram per Cubic Meter[mg/L], Kilogram per Cubic Centimeter[mg/L], Gram per Cubic Meter[mg/L] are the few other units in which Concentration of Sludge in Return Line given Wasting Rate from Return Line can be measured.

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

​GoConcentration of Sludge in Return Line given RAS Pumping Rate from Aeration Tank Formula

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

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

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

Other Formulas to find Sludge Concentration in Return Line

Other formulas in Concentration of Solids category

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

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

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