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MLSS given volume of Aeration Tank Formula

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MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics). Check FAQs

X = \frac{Y \cdot Q s \cdot (Q i - Q o) \cdot θ c}{V \cdot (1 + K e \cdot θ c)}

X - MLSS?Y - Maximum Yield Coefficient?Q_s - Sewage Discharge?Q_i - Influent BOD?Q_o - Effluent BOD?θ_c - Sludge Age?V - Volume of Tank?K^e - Endogenous Respiration Rate Constant?

MLSS given volume of Aeration Tank Example

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Here is how the MLSS given volume of Aeration Tank equation looks like with Values.

Here is how the MLSS given volume of Aeration Tank equation looks like with Units.

Here is how the MLSS given volume of Aeration Tank equation looks like.

1200 = \frac{0.5 \cdot 10 \cdot (0.48 - 0.4) \cdot 5}{9 \cdot (1 + 3 \cdot 5)}

1200mg/L = \frac{0.5 \cdot 10m³/s \cdot (0.48mg/L - 0.4mg/L) \cdot 5d}{9m³ \cdot (1 + 3d⁻¹ \cdot 5d)}

1200 = \frac{0.5 \cdot 10 \cdot (0.48 - 0.4) \cdot 5}{9 \cdot (1 + 3 \cdot 5)}

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MLSS given volume of Aeration Tank Solution

Follow our step by step solution on how to calculate MLSS given volume of Aeration Tank?

FIRST Step Consider the formula

X = \frac{Y \cdot Q s \cdot (Q i - Q o) \cdot θ c}{V \cdot (1 + K e \cdot θ c)}

Next Step Substitute values of Variables

∴

X = \frac{0.5 \cdot 10m³/s \cdot (0.48mg/L - 0.4mg/L) \cdot 5d}{9m³ \cdot (1 + 3d⁻¹ \cdot 5d)}

Next Step Convert Units

∴

X = \frac{0.5 \cdot 10m³/s \cdot (0.0005kg/m³ - 0.0004kg/m³) \cdot 432000s}{9m³ \cdot (1 + 3.5E-5s⁻¹ \cdot 432000s)}

Next Step Prepare to Evaluate

∴

X = \frac{0.5 \cdot 10 \cdot (0.0005 - 0.0004) \cdot 432000}{9 \cdot (1 + 3.5E-5 \cdot 432000)}

Next Step Evaluate

∴

X = 1.2kg/m³

LAST Step Convert to Output's Unit

∴

X = 1200mg/L

MLSS given volume of Aeration Tank Formula Elements

Variables

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

Open Variable

Maximum Yield Coefficient

Maximum Yield Coefficient Y represents 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

Open Variable

Sewage Discharge

Sewage discharge is the flow rate of sewage when it is being discharged into the water body.

Symbol: Q_s

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Sewage Discharge

Open Variable

Influent BOD

Influent BOD is the total amount of BOD which is present in the incoming sewage.

Symbol: Q_i

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Influent BOD

Open Variable

Effluent BOD

Effluent BOD is the amount of dissolved oxygen needed by aerobic biological organisms to break down organic material present in a water sample at a certain temperature over a specific time period.

Symbol: Q_o

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Effluent BOD

Open Variable

Sludge Age

Sludge Age is the average time for which the particle of suspended solids remains in aeration.

Symbol: θ_c

Measurement: TimeUnit: d

Note: Value should be greater than 0.

Formulas to find Sludge Age

Open Variable

Volume of Tank

Volume of Tank is defined as the capacity of flocculation and mixing tank.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Tank

Open Variable

Endogenous Respiration Rate Constant

Endogenous Respiration Rate Constant is used for designing a complete-mix activated-sludge system.

Symbol: K^e

Measurement: First Order Reaction Rate ConstantUnit: d⁻¹

Note: Value should be greater than 0.

Formulas to find Endogenous Respiration Rate Constant

Open Variable

Other formulas in Size and Volume of the Aeration Tank category

Go Volume of Aeration Tank

V = \frac{Y \cdot Q s \cdot (Q i - Q o) \cdot θ c}{X \cdot (1 + K e \cdot θ c)}

Go Maximum Yield Coefficient given Volume of Aeration Tank

Y = \frac{V}{\frac{Q s \cdot (Q i - Q o) \cdot θ c}{X \cdot (1 + K e \cdot θ c)}}

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How to Evaluate MLSS given volume of Aeration Tank?

MLSS given volume of Aeration Tank evaluator uses MLSS = (Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*(1+Endogenous Respiration Rate Constant*Sludge Age)) to evaluate the MLSS, The MLSS given volume of Aeration Tank formula is defined as a measure of the concentration of suspended solids in the mixed liquor of an aeration tank in a wastewater treatment plant, considering volume of aeration tank. MLSS is denoted by X symbol.

How to evaluate MLSS given volume of Aeration Tank using this online evaluator? To use this online evaluator for MLSS given volume of Aeration Tank, enter Maximum Yield Coefficient (Y), Sewage Discharge (Q_s), Influent BOD (Q_i), Effluent BOD (Q_o), Sludge Age (θ_c), Volume of Tank (V) & Endogenous Respiration Rate Constant (K^e) and hit the calculate button.

FAQs on MLSS given volume of Aeration Tank

What is the formula to find MLSS given volume of Aeration Tank?

The formula of MLSS given volume of Aeration Tank is expressed as MLSS = (Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*(1+Endogenous Respiration Rate Constant*Sludge Age)). Here is an example- 1.2E+6 = (0.5*10*(0.00048-0.0004)*432000)/(9*(1+3.47222222222222E-05*432000)).

How to calculate MLSS given volume of Aeration Tank?

With Maximum Yield Coefficient (Y), Sewage Discharge (Q_s), Influent BOD (Q_i), Effluent BOD (Q_o), Sludge Age (θ_c), Volume of Tank (V) & Endogenous Respiration Rate Constant (K^e) we can find MLSS given volume of Aeration Tank using the formula - MLSS = (Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*(1+Endogenous Respiration Rate Constant*Sludge Age)).

Can the MLSS given volume of Aeration Tank be negative?

No, the MLSS given volume of Aeration Tank, measured in Density cannot be negative.

Which unit is used to measure MLSS given volume of Aeration Tank?

MLSS given volume of Aeration Tank 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 MLSS given volume of Aeration Tank can be measured.

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