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Sludge Age given Volume of Aeration Tank Formula

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

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

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

Sludge Age given Volume of Aeration Tank Example

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Here is how the Sludge Age given Volume of Aeration Tank equation looks like with Values.

Here is how the Sludge Age given Volume of Aeration Tank equation looks like with Units.

Here is how the Sludge Age given Volume of Aeration Tank equation looks like.

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

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

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

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Sludge Age given Volume of Aeration Tank Solution

Follow our step by step solution on how to calculate Sludge Age given Volume of Aeration Tank?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

θ c = \frac{9m³ \cdot 1.2kg/m³}{0.5 \cdot 10m³/s \cdot (0.0005kg/m³ - 0.0004kg/m³) - 9m³ \cdot 1.2kg/m³ \cdot 3.5E-5s⁻¹}

Next Step Prepare to Evaluate

∴

θ c = \frac{9 \cdot 1.2}{0.5 \cdot 10 \cdot (0.0005 - 0.0004) - 9 \cdot 1.2 \cdot 3.5E-5}

Next Step Evaluate

∴

θ c = 431999.999999996s

Next Step Convert to Output's Unit

∴

θ c = 4.99999999999995d

LAST Step Rounding Answer

∴

θ c = 5d

Sludge Age given Volume of Aeration Tank Formula Elements

Variables

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

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

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

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

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

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

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

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

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 MLSS given volume of Aeration Tank

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

How to Evaluate Sludge Age given Volume of Aeration Tank?

Sludge Age given Volume of Aeration Tank evaluator uses Sludge Age = (Volume of Tank*MLSS)/(Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)-Volume of Tank*MLSS*Endogenous Respiration Rate Constant) to evaluate the Sludge Age, The Sludge Age given Volume of Aeration Tank formula is defined as a measure of the average time that the microorganisms (biomass) remain in the aeration tank of a wastewater treatment plant, considering volume of aeration tank. Sludge Age is denoted by θ_c symbol.

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

FAQs on Sludge Age given Volume of Aeration Tank

What is the formula to find Sludge Age given Volume of Aeration Tank?

The formula of Sludge Age given Volume of Aeration Tank is expressed as Sludge Age = (Volume of Tank*MLSS)/(Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)-Volume of Tank*MLSS*Endogenous Respiration Rate Constant). Here is an example- 5.8E-5 = (9*1.2)/(0.5*10*(0.00048-0.0004)-9*1.2*3.47222222222222E-05).

How to calculate Sludge Age given Volume of Aeration Tank?

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

Can the Sludge Age given Volume of Aeration Tank be negative?

No, the Sludge Age given Volume of Aeration Tank, measured in Time cannot be negative.

Which unit is used to measure Sludge Age given Volume of Aeration Tank?

Sludge Age given Volume of Aeration Tank is usually measured using the Day[d] for Time. Second[d], Millisecond[d], Microsecond[d] are the few other units in which Sludge Age given Volume of Aeration Tank can be measured.

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Sludge Age given Volume of Aeration Tank Formula

Sludge Age given Volume of Aeration Tank Example

Sludge Age given Volume of Aeration Tank Solution

Sludge Age given Volume of Aeration Tank Formula Elements

Other formulas in Size and Volume of the Aeration Tank category

How to Evaluate Sludge Age given Volume of Aeration Tank?

FAQs on Sludge Age given Volume of Aeration Tank

Variable Name