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Endogenous Decay Constant given Volume of Reactor Formula

GoEndogenous Decay Coefficient given Observed Cell Yield Formula

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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. Check FAQs

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

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

Endogenous Decay Constant given Volume of Reactor Example

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Here is how the Endogenous Decay Constant given Volume of Reactor equation looks like with Values.

Here is how the Endogenous Decay Constant given Volume of Reactor equation looks like with Units.

Here is how the Endogenous Decay Constant given Volume of Reactor equation looks like.

0.0645 = (\frac{1.2 \cdot 0.5 \cdot (25 - 15)}{1000 \cdot 2500}) - (\frac{1}{7})

0.0645d⁻¹ = (\frac{1.2m³/d \cdot 0.5 \cdot (25mg/L - 15mg/L)}{1000m³ \cdot 2500mg/L}) - (\frac{1}{7d})

0.0645 = (\frac{1.2 \cdot 0.5 \cdot (25 - 15)}{1000 \cdot 2500}) - (\frac{1}{7})

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Endogenous Decay Constant given Volume of Reactor Solution

Follow our step by step solution on how to calculate Endogenous Decay Constant given Volume of Reactor?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

k d = (\frac{1.2m³/d \cdot 0.5 \cdot (25mg/L - 15mg/L)}{1000m³ \cdot 2500mg/L}) - (\frac{1}{7d})

Next Step Convert Units

∴

k d = (\frac{1.2m³/d \cdot 0.5 \cdot (25mg/L - 15mg/L)}{1000m³ \cdot 2500mg/L}) - (\frac{1}{604800s})

Next Step Prepare to Evaluate

∴

k d = (\frac{1.2 \cdot 0.5 \cdot (25 - 15)}{1000 \cdot 2500}) - (\frac{1}{604800})

Next Step Evaluate

∴

k d = 7.46560846560846E-07s⁻¹

Next Step Convert to Output's Unit

∴

k d = 0.0645028571428571d⁻¹

LAST Step Rounding Answer

∴

k d = 0.0645d⁻¹

Endogenous Decay Constant given Volume of Reactor Formula Elements

Variables

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

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

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

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

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

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

Other Formulas to find Endogenous Decay Coefficient

Go Endogenous Decay Coefficient given Observed Cell Yield

k d = \frac{Y obs - Y}{θ c}

How to Evaluate Endogenous Decay Constant given Volume of Reactor?

Endogenous Decay Constant given Volume of Reactor evaluator uses Endogenous Decay Coefficient = ((Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration))/(Reactor Volume*MLVSS))-(1/Mean Cell Residence Time) to evaluate the Endogenous Decay Coefficient, The Endogenous Decay Constant given Volume of Reactor formula is defined as the rate at which biomass decays due to endogenous respiration and other decay processes. Endogenous Decay Coefficient is denoted by k_d symbol.

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

FAQs on Endogenous Decay Constant given Volume of Reactor

What is the formula to find Endogenous Decay Constant given Volume of Reactor?

The formula of Endogenous Decay Constant given Volume of Reactor is expressed as Endogenous Decay Coefficient = ((Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration))/(Reactor Volume*MLVSS))-(1/Mean Cell Residence Time). Here is an example- 5573.047 = ((1.38888888888889E-05*0.5*(0.025-0.015))/(1000*2.5))-(1/604800).

How to calculate Endogenous Decay Constant given Volume of Reactor?

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

What are the other ways to Calculate Endogenous Decay Coefficient?

Here are the different ways to Calculate Endogenous Decay Coefficient-

Endogenous Decay Coefficient=(Observed Cell Yield-Maximum Yield Coefficient)/Mean Cell Residence Time

Can the Endogenous Decay Constant given Volume of Reactor be negative?

No, the Endogenous Decay Constant given Volume of Reactor, measured in First Order Reaction Rate Constant cannot be negative.

Which unit is used to measure Endogenous Decay Constant given Volume of Reactor?

Endogenous Decay Constant given Volume of Reactor is usually measured using the 1 Per Day[d⁻¹] for First Order Reaction Rate Constant. 1 Per Second[d⁻¹], 1 Per Millisecond[d⁻¹], 1 Per Hour[d⁻¹] are the few other units in which Endogenous Decay Constant given Volume of Reactor can be measured.

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Endogenous Decay Constant given Volume of Reactor Formula

​GoEndogenous Decay Coefficient given Observed Cell Yield Formula

Endogenous Decay Constant given Volume of Reactor Example

Endogenous Decay Constant given Volume of Reactor Solution

Endogenous Decay Constant given Volume of Reactor Formula Elements

Other Formulas to find Endogenous Decay Coefficient

How to Evaluate Endogenous Decay Constant given Volume of Reactor?

FAQs on Endogenous Decay Constant given Volume of Reactor

Variable Name

GoEndogenous Decay Coefficient given Observed Cell Yield Formula