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Mixed Liquor Volatile Suspended Solids given Reactor Volume Formula

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Mixed Liquor Volatile Suspended Solids refers to the measure of concentration of the organic matter in the mixed liquor. Check FAQs

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

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

Mixed Liquor Volatile Suspended Solids given Reactor Volume Example

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Here is how the Mixed Liquor Volatile Suspended Solids given Reactor Volume equation looks like with Values.

Here is how the Mixed Liquor Volatile Suspended Solids given Reactor Volume equation looks like with Units.

Here is how the Mixed Liquor Volatile Suspended Solids given Reactor Volume equation looks like.

7.7311 = \frac{7 \cdot 1.2 \cdot 0.5 \cdot (2500 - 15)}{1000 \cdot (1 + (0.05 \cdot 7))}

7.7311mg/L = \frac{7d \cdot 1.2m³/d \cdot 0.5 \cdot (2500mg/L - 15mg/L)}{1000m³ \cdot (1 + (0.05d⁻¹ \cdot 7d))}

7.7311 = \frac{7 \cdot 1.2 \cdot 0.5 \cdot (2500 - 15)}{1000 \cdot (1 + (0.05 \cdot 7))}

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Mixed Liquor Volatile Suspended Solids given Reactor Volume Solution

Follow our step by step solution on how to calculate Mixed Liquor Volatile Suspended Solids given Reactor Volume?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

X a' = \frac{7d \cdot 1.2m³/d \cdot 0.5 \cdot (2500mg/L - 15mg/L)}{1000m³ \cdot (1 + (0.05d⁻¹ \cdot 7d))}

Next Step Convert Units

∴

X a' = \frac{604800s \cdot 1.4E-5m³/s \cdot 0.5 \cdot (2.5kg/m³ - 0.015kg/m³)}{1000m³ \cdot (1 + (5.8E-7s⁻¹ \cdot 604800s))}

Next Step Prepare to Evaluate

∴

X a' = \frac{604800 \cdot 1.4E-5 \cdot 0.5 \cdot (2.5 - 0.015)}{1000 \cdot (1 + (5.8E-7 \cdot 604800))}

Next Step Evaluate

∴

X a' = 0.00773111111111112kg/m³

Next Step Convert to Output's Unit

∴

X a' = 7.73111111111112mg/L

LAST Step Rounding Answer

∴

X a' = 7.7311mg/L

Mixed Liquor Volatile Suspended Solids given Reactor Volume Formula Elements

Variables

Mixed Liquor Volatile Suspended Solids

Mixed Liquor Volatile Suspended Solids refers to the measure of concentration of the organic matter in the mixed liquor.

Symbol: X_a'

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Mixed Liquor Volatile Suspended Solids

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

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

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

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

Other formulas in MLSS and MLVSS category

Go Mixed Liquor Suspended Solids given Wasting Rate from Return Line

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

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

X' = θ c \cdot Q \cdot \frac{X r}{V}

How to Evaluate Mixed Liquor Volatile Suspended Solids given Reactor Volume?

Mixed Liquor Volatile Suspended Solids given Reactor Volume evaluator uses Mixed Liquor Volatile Suspended Solids = (Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient*(MLVSS-Effluent Substrate Concentration))/(Reactor Volume*(1+(Endogenous Decay Coefficient*Mean Cell Residence Time))) to evaluate the Mixed Liquor Volatile Suspended Solids, The Mixed Liquor Volatile Suspended Solids given Reactor Volume formula is defined as the concentration of organic matter (biomass) in the mixed liquor of an aeration tank in a wastewater treatment plant. It represents the portion of the suspended solids in the mixed liquor that can be volatilized at high temperatures, typically at 550°C. Mixed Liquor Volatile Suspended Solids is denoted by X_a' symbol.

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

FAQs on Mixed Liquor Volatile Suspended Solids given Reactor Volume

What is the formula to find Mixed Liquor Volatile Suspended Solids given Reactor Volume?

The formula of Mixed Liquor Volatile Suspended Solids given Reactor Volume is expressed as Mixed Liquor Volatile Suspended Solids = (Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient*(MLVSS-Effluent Substrate Concentration))/(Reactor Volume*(1+(Endogenous Decay Coefficient*Mean Cell Residence Time))). Here is an example- 7731.111 = (604800*1.38888888888889E-05*0.5*(2.5-0.015))/(1000*(1+(5.78703703703704E-07*604800))).

How to calculate Mixed Liquor Volatile Suspended Solids given Reactor Volume?

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

Can the Mixed Liquor Volatile Suspended Solids given Reactor Volume be negative?

No, the Mixed Liquor Volatile Suspended Solids given Reactor Volume, measured in Density cannot be negative.

Which unit is used to measure Mixed Liquor Volatile Suspended Solids given Reactor Volume?

Mixed Liquor Volatile Suspended Solids given Reactor Volume 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 Mixed Liquor Volatile Suspended Solids given Reactor Volume can be measured.

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Mixed Liquor Volatile Suspended Solids given Reactor Volume Formula

Mixed Liquor Volatile Suspended Solids given Reactor Volume Example

Mixed Liquor Volatile Suspended Solids given Reactor Volume Solution

Mixed Liquor Volatile Suspended Solids given Reactor Volume Formula Elements

Other formulas in MLSS and MLVSS category

How to Evaluate Mixed Liquor Volatile Suspended Solids given Reactor Volume?

FAQs on Mixed Liquor Volatile Suspended Solids given Reactor Volume

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