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Sewage Discharge given Volume of Aeration Tank Formula

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

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

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

Sewage Discharge given Volume of Aeration Tank Example

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Here is how the Sewage Discharge given Volume of Aeration Tank equation looks like with Values.

Here is how the Sewage Discharge given Volume of Aeration Tank equation looks like with Units.

Here is how the Sewage Discharge given Volume of Aeration Tank equation looks like.

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

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

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

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Sewage Discharge given Volume of Aeration Tank Solution

Follow our step by step solution on how to calculate Sewage Discharge given Volume of Aeration Tank?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

Q s = \frac{9m³}{\frac{0.5 \cdot (0.0005kg/m³ - 0.0004kg/m³) \cdot 432000s}{1.2kg/m³ \cdot (1 + 3.5E-5s⁻¹ \cdot 432000s)}}

Next Step Prepare to Evaluate

∴

Q s = \frac{9}{\frac{0.5 \cdot (0.0005 - 0.0004) \cdot 432000}{1.2 \cdot (1 + 3.5E-5 \cdot 432000)}}

LAST Step Evaluate

∴

Q s = 10m³/s

Sewage Discharge given Volume of Aeration Tank Formula Elements

Variables

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

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

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

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

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

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 Sewage Discharge given Volume of Aeration Tank?

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

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

FAQs on Sewage Discharge given Volume of Aeration Tank

What is the formula to find Sewage Discharge given Volume of Aeration Tank?

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

How to calculate Sewage Discharge given Volume of Aeration Tank?

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

Can the Sewage Discharge given Volume of Aeration Tank be negative?

No, the Sewage Discharge given Volume of Aeration Tank, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Sewage Discharge given Volume of Aeration Tank?

Sewage Discharge given Volume of Aeration Tank is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Sewage Discharge given Volume of Aeration Tank can be measured.

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Sewage Discharge given Volume of Aeration Tank Formula

Sewage Discharge given Volume of Aeration Tank Example

Sewage Discharge given Volume of Aeration Tank Solution

Sewage Discharge given Volume of Aeration Tank Formula Elements

Other formulas in Size and Volume of the Aeration Tank category

How to Evaluate Sewage Discharge given Volume of Aeration Tank?

FAQs on Sewage Discharge given Volume of Aeration Tank

Variable Name