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Solids Retention Time given Volume of Aerobic Digester Formula

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The Solids Retention Time refers to the average amount of time that solid particles remain in a treatment system, such as a wastewater treatment plant or a bioreactor. Check FAQs

θ = (\frac{Q i \cdot X i}{V ad \cdot X} - (K d \cdot P v))

θ - Solids Retention Time?Q_i - Influent Average Flow Rate?X_i - Influent Suspended Solids?V_ad - Volume of Aerobic Digester?X - Digester Total Suspended Solids?K_d - Reaction Rate Constant?P_v - Volatile Fraction?

Solids Retention Time given Volume of Aerobic Digester Example

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Here is how the Solids Retention Time given Volume of Aerobic Digester equation looks like with Values.

Here is how the Solids Retention Time given Volume of Aerobic Digester equation looks like with Units.

Here is how the Solids Retention Time given Volume of Aerobic Digester equation looks like.

2.0669 = (\frac{5 \cdot 5000.2}{10 \cdot 0.014} - (0.05 \cdot 0.5))

2.0669d = (\frac{5m³/s \cdot 5000.2mg/L}{10m³ \cdot 0.014mg/L} - (0.05d⁻¹ \cdot 0.5))

2.0669 = (\frac{5 \cdot 5000.2}{10 \cdot 0.014} - (0.05 \cdot 0.5))

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Solids Retention Time given Volume of Aerobic Digester Solution

Follow our step by step solution on how to calculate Solids Retention Time given Volume of Aerobic Digester?

FIRST Step Consider the formula

θ = (\frac{Q i \cdot X i}{V ad \cdot X} - (K d \cdot P v))

Next Step Substitute values of Variables

∴

θ = (\frac{5m³/s \cdot 5000.2mg/L}{10m³ \cdot 0.014mg/L} - (0.05d⁻¹ \cdot 0.5))

Next Step Convert Units

∴

θ = (\frac{5m³/s \cdot 5.0002kg/m³}{10m³ \cdot 1.4E-5kg/m³} - (5.8E-7s⁻¹ \cdot 0.5))

Next Step Prepare to Evaluate

∴

θ = (\frac{5 \cdot 5.0002}{10 \cdot 1.4E-5} - (5.8E-7 \cdot 0.5))

Next Step Evaluate

∴

θ = 178578.571428282s

Next Step Convert to Output's Unit

∴

θ = 2.06688161375327d

LAST Step Rounding Answer

∴

θ = 2.0669d

Solids Retention Time given Volume of Aerobic Digester Formula Elements

Variables

Solids Retention Time

The Solids Retention Time refers to the average amount of time that solid particles remain in a treatment system, such as a wastewater treatment plant or a bioreactor.

Symbol: θ

Measurement: TimeUnit: d

Note: Value should be greater than 0.

Formulas to find Solids Retention Time

Influent Average Flow Rate

The Influent Average Flow Rate refers to the average rate at which water or wastewater flows into a treatment system or facility over a specific period of time.

Symbol: Q_i

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Influent Average Flow Rate

Influent Suspended Solids

The Influent Suspended Solids refer to the solid particles present in wastewater or any liquid entering a treatment process.

Symbol: X_i

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Influent Suspended Solids

Volume of Aerobic Digester

The Volume of Aerobic Digester refers to the capacity or size of the digester vessel or tank where the aerobic digestion process takes place.

Symbol: V_ad

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Aerobic Digester

Digester Total Suspended Solids

The Digester Total Suspended Solids refers to the amount of solid particles suspended in the liquid phase of a digester system.

Symbol: X

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Digester Total Suspended Solids

Reaction Rate Constant

The Reaction Rate Constant refers to a parameter used to quantify the rate at which a chemical reaction proceeds.

Symbol: K_d

Measurement: First Order Reaction Rate ConstantUnit: d⁻¹

Note: Value should be greater than 0.

Formulas to find Reaction Rate Constant

Volatile Fraction

The Volatile Fraction refers to the portion of a substance that can vaporize or volatilize under specific conditions, often related to air or water quality assessments.

Symbol: P_v

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Volatile Fraction

Other formulas in Design of an Aerobic Digester category

Go Volume of Digested Sludge

V s = \frac{W s}{ρ water \cdot G s \cdot %s}

Go Weight of Sludge given Volume of Digested Sludge

W s = (ρ water \cdot V s \cdot G s \cdot %s)

How to Evaluate Solids Retention Time given Volume of Aerobic Digester?

Solids Retention Time given Volume of Aerobic Digester evaluator uses Solids Retention Time = ((Influent Average Flow Rate*Influent Suspended Solids)/(Volume of Aerobic Digester*Digester Total Suspended Solids)-(Reaction Rate Constant*Volatile Fraction)) to evaluate the Solids Retention Time, The Solids Retention Time given Volume of Aerobic Digester formula is defined as the average amount of time that solid particles remain in a treatment system, such as a wastewater treatment plant or a bioreactor, when we have prior information of other parameters used. Solids Retention Time is denoted by θ symbol.

How to evaluate Solids Retention Time given Volume of Aerobic Digester using this online evaluator? To use this online evaluator for Solids Retention Time given Volume of Aerobic Digester, enter Influent Average Flow Rate (Q_i), Influent Suspended Solids (X_i), Volume of Aerobic Digester (V_ad), Digester Total Suspended Solids (X), Reaction Rate Constant (K_d) & Volatile Fraction (P_v) and hit the calculate button.

FAQs on Solids Retention Time given Volume of Aerobic Digester

What is the formula to find Solids Retention Time given Volume of Aerobic Digester?

The formula of Solids Retention Time given Volume of Aerobic Digester is expressed as Solids Retention Time = ((Influent Average Flow Rate*Influent Suspended Solids)/(Volume of Aerobic Digester*Digester Total Suspended Solids)-(Reaction Rate Constant*Volatile Fraction)). Here is an example- 6.6E-8 = ((5*5.0002)/(10*1.4E-05)-(5.78703703703704E-07*0.5)).

How to calculate Solids Retention Time given Volume of Aerobic Digester?

With Influent Average Flow Rate (Q_i), Influent Suspended Solids (X_i), Volume of Aerobic Digester (V_ad), Digester Total Suspended Solids (X), Reaction Rate Constant (K_d) & Volatile Fraction (P_v) we can find Solids Retention Time given Volume of Aerobic Digester using the formula - Solids Retention Time = ((Influent Average Flow Rate*Influent Suspended Solids)/(Volume of Aerobic Digester*Digester Total Suspended Solids)-(Reaction Rate Constant*Volatile Fraction)).

Can the Solids Retention Time given Volume of Aerobic Digester be negative?

No, the Solids Retention Time given Volume of Aerobic Digester, measured in Time cannot be negative.

Which unit is used to measure Solids Retention Time given Volume of Aerobic Digester?

Solids Retention Time given Volume of Aerobic Digester is usually measured using the Day[d] for Time. Second[d], Millisecond[d], Microsecond[d] are the few other units in which Solids Retention Time given Volume of Aerobic Digester can be measured.

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Solids Retention Time given Volume of Aerobic Digester Formula

Solids Retention Time given Volume of Aerobic Digester Example

Solids Retention Time given Volume of Aerobic Digester Solution

Solids Retention Time given Volume of Aerobic Digester Formula Elements

Other formulas in Design of an Aerobic Digester category

How to Evaluate Solids Retention Time given Volume of Aerobic Digester?

FAQs on Solids Retention Time given Volume of Aerobic Digester

Variable Name