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Endogenous Respiration Rate Constant given Volume of Aeration Tank Formula

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

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

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

Endogenous Respiration Rate Constant given Volume of Aeration Tank Example

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Here is how the Endogenous Respiration Rate Constant given Volume of Aeration Tank equation looks like with Values.

Here is how the Endogenous Respiration Rate Constant given Volume of Aeration Tank equation looks like with Units.

Here is how the Endogenous Respiration Rate Constant given Volume of Aeration Tank equation looks like.

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

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

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

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Endogenous Respiration Rate Constant given Volume of Aeration Tank Solution

Follow our step by step solution on how to calculate Endogenous Respiration Rate Constant given Volume of Aeration Tank?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

K e = \frac{(\frac{0.5 \cdot 10m³/s \cdot (0.0005kg/m³ - 0.0004kg/m³) \cdot 432000s}{9m³ \cdot 1.2kg/m³}) - 1}{432000s}

Next Step Prepare to Evaluate

∴

K e = \frac{(\frac{0.5 \cdot 10 \cdot (0.0005 - 0.0004) \cdot 432000}{9 \cdot 1.2}) - 1}{432000}

Next Step Evaluate

∴

K e = 3.47222222222222E-05s⁻¹

LAST Step Convert to Output's Unit

∴

K e = 3d⁻¹

Endogenous Respiration Rate Constant given Volume of Aeration Tank Formula Elements

Variables

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

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

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

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 Endogenous Respiration Rate Constant given Volume of Aeration Tank?

Endogenous Respiration Rate Constant given Volume of Aeration Tank evaluator uses Endogenous Respiration Rate Constant = (((Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*MLSS))-1)/Sludge Age to evaluate the Endogenous Respiration Rate Constant, The Endogenous Respiration Rate Constant given Volume of Aeration Tank formula is defined as the value of rate constant when we have prior information of volume of aeration tank. Endogenous Respiration Rate Constant is denoted by K^e symbol.

How to evaluate Endogenous Respiration Rate Constant given Volume of Aeration Tank using this online evaluator? To use this online evaluator for Endogenous Respiration Rate Constant 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) & MLSS (X) and hit the calculate button.

FAQs on Endogenous Respiration Rate Constant given Volume of Aeration Tank

What is the formula to find Endogenous Respiration Rate Constant given Volume of Aeration Tank?

The formula of Endogenous Respiration Rate Constant given Volume of Aeration Tank is expressed as Endogenous Respiration Rate Constant = (((Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*MLSS))-1)/Sludge Age. Here is an example- 259200 = (((0.5*10*(0.00048-0.0004)*432000)/(9*1.2))-1)/432000.

How to calculate Endogenous Respiration Rate Constant 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) & MLSS (X) we can find Endogenous Respiration Rate Constant given Volume of Aeration Tank using the formula - Endogenous Respiration Rate Constant = (((Maximum Yield Coefficient*Sewage Discharge*(Influent BOD-Effluent BOD)*Sludge Age)/(Volume of Tank*MLSS))-1)/Sludge Age.

Can the Endogenous Respiration Rate Constant given Volume of Aeration Tank be negative?

No, the Endogenous Respiration Rate Constant given Volume of Aeration Tank, measured in First Order Reaction Rate Constant cannot be negative.

Which unit is used to measure Endogenous Respiration Rate Constant given Volume of Aeration Tank?

Endogenous Respiration Rate Constant given Volume of Aeration Tank 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 Respiration Rate Constant given Volume of Aeration Tank can be measured.

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Endogenous Respiration Rate Constant given Volume of Aeration Tank Formula

Endogenous Respiration Rate Constant given Volume of Aeration Tank Example

Endogenous Respiration Rate Constant given Volume of Aeration Tank Solution

Endogenous Respiration Rate Constant given Volume of Aeration Tank Formula Elements

Other formulas in Size and Volume of the Aeration Tank category

How to Evaluate Endogenous Respiration Rate Constant given Volume of Aeration Tank?

FAQs on Endogenous Respiration Rate Constant given Volume of Aeration Tank

Variable Name