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Effluent Substrate Concentration given Volume of Reactor Formula

GoEffluent Substrate Concentration given Net Waste Activated Sludge Formula

GoEffluent Substrate Concentration given Theoretical Oxygen Requirement Formula

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Effluent Substrate Concentration refers to the concentration of organic matter or nutrients present in the treated wastewater (effluent) that is discharged from a wastewater treatment plant. Check FAQs

S = S o - (\frac{V \cdot X a \cdot (1 + (k d \cdot θ c))}{θ c \cdot Q a \cdot Y})

S - Effluent Substrate Concentration?S_o - Influent Substrate Concentration?V - Reactor Volume?X_a - MLVSS?k_d - Endogenous Decay Coefficient?θ_c - Mean Cell Residence Time?Q_a - Average Daily Influent Flow Rate?Y - Maximum Yield Coefficient?

Effluent Substrate Concentration given Volume of Reactor Example

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Here is how the Effluent Substrate Concentration given Volume of Reactor equation looks like with Values.

Here is how the Effluent Substrate Concentration given Volume of Reactor equation looks like with Units.

Here is how the Effluent Substrate Concentration given Volume of Reactor equation looks like.

15.6994 = 25 - (\frac{1000 \cdot 2500 \cdot (1 + (0.05 \cdot 7))}{7 \cdot 1.2 \cdot 0.5})

15.6994mg/L = 25mg/L - (\frac{1000m³ \cdot 2500mg/L \cdot (1 + (0.05d⁻¹ \cdot 7d))}{7d \cdot 1.2m³/d \cdot 0.5})

15.6994 = 25 - (\frac{1000 \cdot 2500 \cdot (1 + (0.05 \cdot 7))}{7 \cdot 1.2 \cdot 0.5})

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Effluent Substrate Concentration given Volume of Reactor Solution

Follow our step by step solution on how to calculate Effluent Substrate Concentration given Volume of Reactor?

FIRST Step Consider the formula

S = S o - (\frac{V \cdot X a \cdot (1 + (k d \cdot θ c))}{θ c \cdot Q a \cdot Y})

Next Step Substitute values of Variables

∴

S = 25mg/L - (\frac{1000m³ \cdot 2500mg/L \cdot (1 + (0.05d⁻¹ \cdot 7d))}{7d \cdot 1.2m³/d \cdot 0.5})

Next Step Convert Units

∴

S = 25mg/L - (\frac{1000m³ \cdot 2500mg/L \cdot (1 + (5.8E-7s⁻¹ \cdot 604800s))}{604800s \cdot 1.2m³/d \cdot 0.5})

Next Step Prepare to Evaluate

∴

S = 25 - (\frac{1000 \cdot 2500 \cdot (1 + (5.8E-7 \cdot 604800))}{604800 \cdot 1.2 \cdot 0.5})

Next Step Evaluate

∴

S = 0.0156994047619048kg/m³

Next Step Convert to Output's Unit

∴

S = 15.6994047619048mg/L

LAST Step Rounding Answer

∴

S = 15.6994mg/L

Effluent Substrate Concentration given Volume of Reactor Formula Elements

Variables

Effluent Substrate Concentration

Effluent Substrate Concentration refers to the concentration of organic matter or nutrients present in the treated wastewater (effluent) that is discharged from a wastewater treatment plant.

Symbol: S

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Effluent Substrate Concentration

Influent Substrate Concentration

Influent Substrate Concentration refers to the concentration of organic matter or nutrients in the raw wastewater entering a treatment plant.

Symbol: S_o

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Influent Substrate Concentration

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

MLVSS

MLVSS refers to the amount of active microbial biomass, which is crucial for the biological degradation of organic pollutants.

Symbol: X_a

Measurement: DensityUnit: mg/L

Note: Value should be between 1000 to 6500.

Formulas to find MLVSS

Endogenous Decay Coefficient

Endogenous Decay Coefficient refers to the rate at which microorganisms in the biomass consume their own cell mass in the absence of an external food source.

Symbol: k_d

Measurement: First Order Reaction Rate ConstantUnit: d⁻¹

Note: Value should be between 0.025 to 0.075.

Formulas to find Endogenous Decay Coefficient

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

Average Daily Influent Flow Rate

Average Daily Influent Flow Rate is the total discharge that comes in the reactor.

Symbol: Q_a

Measurement: Volumetric Flow RateUnit: m³/d

Note: Value should be greater than 0.

Formulas to find Average Daily Influent Flow Rate

Maximum Yield Coefficient

Maximum Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value should be between 0.4 to 0.8.

Formulas to find Maximum Yield Coefficient

Other Formulas to find Effluent Substrate Concentration

Go Effluent Substrate Concentration given Net Waste Activated Sludge

S = S o - (\frac{P x}{Y obs \cdot Q a \cdot 8.34})

Go Effluent Substrate Concentration given Theoretical Oxygen Requirement

S = S o - ((O 2 + (1.42 \cdot P x)) \cdot (\frac{f}{8.34 \cdot Q a}))

Other formulas in Effluent Substrate Concentration category

Go Effluent Flow Rate given Wasting Rate from Return Line

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

How to Evaluate Effluent Substrate Concentration given Volume of Reactor?

Effluent Substrate Concentration given Volume of Reactor evaluator uses Effluent Substrate Concentration = Influent Substrate Concentration-((Reactor Volume*MLVSS*(1+(Endogenous Decay Coefficient*Mean Cell Residence Time)))/(Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient)) to evaluate the Effluent Substrate Concentration, Effluent Substrate Concentration given Volume of Reactor is the total concentration of BOD present in the sludge which came out after treatment. Effluent Substrate Concentration is denoted by S symbol.

How to evaluate Effluent Substrate Concentration given Volume of Reactor using this online evaluator? To use this online evaluator for Effluent Substrate Concentration given Volume of Reactor, enter Influent Substrate Concentration (S_o), Reactor Volume (V), MLVSS (X_a), Endogenous Decay Coefficient (k_d), Mean Cell Residence Time (θ_c), Average Daily Influent Flow Rate (Q_a) & Maximum Yield Coefficient (Y) and hit the calculate button.

FAQs on Effluent Substrate Concentration given Volume of Reactor

What is the formula to find Effluent Substrate Concentration given Volume of Reactor?

The formula of Effluent Substrate Concentration given Volume of Reactor is expressed as Effluent Substrate Concentration = Influent Substrate Concentration-((Reactor Volume*MLVSS*(1+(Endogenous Decay Coefficient*Mean Cell Residence Time)))/(Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient)). Here is an example- 15699.4 = 0.025-((1000*2.5*(1+(5.78703703703704E-07*604800)))/(604800*1.38888888888889E-05*0.5)).

How to calculate Effluent Substrate Concentration given Volume of Reactor?

With Influent Substrate Concentration (S_o), Reactor Volume (V), MLVSS (X_a), Endogenous Decay Coefficient (k_d), Mean Cell Residence Time (θ_c), Average Daily Influent Flow Rate (Q_a) & Maximum Yield Coefficient (Y) we can find Effluent Substrate Concentration given Volume of Reactor using the formula - Effluent Substrate Concentration = Influent Substrate Concentration-((Reactor Volume*MLVSS*(1+(Endogenous Decay Coefficient*Mean Cell Residence Time)))/(Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient)).

What are the other ways to Calculate Effluent Substrate Concentration?

Here are the different ways to Calculate Effluent Substrate Concentration-

Effluent Substrate Concentration=Influent Substrate Concentration-(Net Waste Activated Sludge/(Observed Cell Yield*Average Daily Influent Flow Rate*8.34))
Effluent Substrate Concentration=Influent Substrate Concentration-((Theoretical Oxygen Requirement+(1.42*Net Waste Activated Sludge))*(BOD Conversion Factor/(8.34*Average Daily Influent Flow Rate)))

Can the Effluent Substrate Concentration given Volume of Reactor be negative?

No, the Effluent Substrate Concentration given Volume of Reactor, measured in Density cannot be negative.

Which unit is used to measure Effluent Substrate Concentration given Volume of Reactor?

Effluent Substrate Concentration given Volume of Reactor 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 Effluent Substrate Concentration given Volume of Reactor can be measured.

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Effluent Substrate Concentration given Volume of Reactor Formula

​GoEffluent Substrate Concentration given Net Waste Activated Sludge Formula

​GoEffluent Substrate Concentration given Theoretical Oxygen Requirement Formula

Effluent Substrate Concentration given Volume of Reactor Example

Effluent Substrate Concentration given Volume of Reactor Solution

Effluent Substrate Concentration given Volume of Reactor Formula Elements

Other Formulas to find Effluent Substrate Concentration

Other formulas in Effluent Substrate Concentration category

How to Evaluate Effluent Substrate Concentration given Volume of Reactor?

FAQs on Effluent Substrate Concentration given Volume of Reactor

Variable Name

GoEffluent Substrate Concentration given Net Waste Activated Sludge Formula

GoEffluent Substrate Concentration given Theoretical Oxygen Requirement Formula