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Maximum Yield Coefficient given Volume of Reactor Formula

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Max Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed. Check FAQs

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

Y' - Max Yield Coefficient?V_m - Volume of reactor?X_a - MLVSS?θ_c - Mean Cell Residence Time?k_d - Endogenous Decay Coefficient?Q_a - Average Daily Influent Flow Rate?S_h - Influent Substrate Concentration h?S - Effluent Substrate Concentration?

Maximum Yield Coefficient given Volume of Reactor Example

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Here is how the Maximum Yield Coefficient given Volume of Reactor equation looks like with Values.

Here is how the Maximum Yield Coefficient given Volume of Reactor equation looks like with Units.

Here is how the Maximum Yield Coefficient given Volume of Reactor equation looks like.

1.148 = 0.1 \cdot 2500 \cdot \frac{1 + (7 \cdot 0.05)}{7 \cdot 1.2 \cdot (50 - 15)}

1.148 = 0.1m³ \cdot 2500mg/L \cdot \frac{1 + (7d \cdot 0.05d⁻¹)}{7d \cdot 1.2m³/d \cdot (50mg/L - 15mg/L)}

1.148 = 0.1 \cdot 2500 \cdot \frac{1 + (7 \cdot 0.05)}{7 \cdot 1.2 \cdot (50 - 15)}

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Maximum Yield Coefficient given Volume of Reactor Solution

Follow our step by step solution on how to calculate Maximum Yield Coefficient given Volume of Reactor?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Y' = 0.1m³ \cdot 2500mg/L \cdot \frac{1 + (7d \cdot 0.05d⁻¹)}{7d \cdot 1.2m³/d \cdot (50mg/L - 15mg/L)}

Next Step Convert Units

∴

Y' = 0.1m³ \cdot 2.5kg/m³ \cdot \frac{1 + (604800s \cdot 5.8E-7s⁻¹)}{604800s \cdot 1.4E-5m³/s \cdot (0.05kg/m³ - 0.015kg/m³)}

Next Step Prepare to Evaluate

∴

Y' = 0.1 \cdot 2.5 \cdot \frac{1 + (604800 \cdot 5.8E-7)}{604800 \cdot 1.4E-5 \cdot (0.05 - 0.015)}

Next Step Evaluate

∴

Y' = 1.14795918367347

LAST Step Rounding Answer

∴

Y' = 1.148

Maximum Yield Coefficient given Volume of Reactor Formula Elements

Variables

Max Yield Coefficient

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

Symbol: Y'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.4.

Formulas to find Max Yield Coefficient

Volume of reactor

Volume of reactor refers to the design and operation of wastewater treatment systems.

Symbol: V_m

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Volume of reactor

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

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

Influent Substrate Concentration h

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

Symbol: S_h

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Influent Substrate Concentration h

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

Other formulas in Maximum Yield Coefficient category

Go Maximum Yield Coefficient given Observed Cell Yield

Y = Y obs - (k d \cdot θ c)

How to Evaluate Maximum Yield Coefficient given Volume of Reactor?

Maximum Yield Coefficient given Volume of Reactor evaluator uses Max Yield Coefficient = Volume of reactor*MLVSS*(1+(Mean Cell Residence Time*Endogenous Decay Coefficient))/(Mean Cell Residence Time*Average Daily Influent Flow Rate*(Influent Substrate Concentration h-Effluent Substrate Concentration)) to evaluate the Max Yield Coefficient, The Maximum Yield Coefficient given Volume of Reactor formula is defined as the maximum amount of biomass (microorganisms) produced per unit of substrate (organic matter) consumed in a biological wastewater treatment process. Max Yield Coefficient is denoted by Y' symbol.

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

FAQs on Maximum Yield Coefficient given Volume of Reactor

What is the formula to find Maximum Yield Coefficient given Volume of Reactor?

The formula of Maximum Yield Coefficient given Volume of Reactor is expressed as Max Yield Coefficient = Volume of reactor*MLVSS*(1+(Mean Cell Residence Time*Endogenous Decay Coefficient))/(Mean Cell Residence Time*Average Daily Influent Flow Rate*(Influent Substrate Concentration h-Effluent Substrate Concentration)). Here is an example- 1.147959 = 0.1*2.5*(1+(604800*5.78703703703704E-07))/(604800*1.38888888888889E-05*(0.05-0.015)).

How to calculate Maximum Yield Coefficient given Volume of Reactor?

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

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Maximum Yield Coefficient given Volume of Reactor Formula

Maximum Yield Coefficient given Volume of Reactor Example

Maximum Yield Coefficient given Volume of Reactor Solution

Maximum Yield Coefficient given Volume of Reactor Formula Elements

Other formulas in Maximum Yield Coefficient category

How to Evaluate Maximum Yield Coefficient given Volume of Reactor?

FAQs on Maximum Yield Coefficient given Volume of Reactor

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