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Mean Cell Residence Time given Quantity of Volatile Solids Formula

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Mean Cell Residence Time refers to a measure of the extent to which organic matter in sludge has been decomposed or stabilized through treatment processes. Check FAQs

θ c = (\frac{1}{k d}) - (Y \cdot \frac{BOD in - BOD out}{P x \cdot k d})

θ_c - Mean Cell Residence Time?k_d - Endogenous Coefficient?Y - Yield Coefficient?BOD_in - BOD In?BOD_out - BOD Out?P_x - Volatile Solids Produced?

Mean Cell Residence Time given Quantity of Volatile Solids Example

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Here is how the Mean Cell Residence Time given Quantity of Volatile Solids equation looks like with Values.

Here is how the Mean Cell Residence Time given Quantity of Volatile Solids equation looks like with Units.

Here is how the Mean Cell Residence Time given Quantity of Volatile Solids equation looks like.

6.9538 = (\frac{1}{0.05}) - (0.41 \cdot \frac{164 - 4.9}{100 \cdot 0.05})

6.9538d = (\frac{1}{0.05d⁻¹}) - (0.41 \cdot \frac{164kg/d - 4.9kg/d}{100kg/d \cdot 0.05d⁻¹})

6.9538 = (\frac{1}{0.05}) - (0.41 \cdot \frac{164 - 4.9}{100 \cdot 0.05})

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Mean Cell Residence Time given Quantity of Volatile Solids Solution

Follow our step by step solution on how to calculate Mean Cell Residence Time given Quantity of Volatile Solids?

FIRST Step Consider the formula

θ c = (\frac{1}{k d}) - (Y \cdot \frac{BOD in - BOD out}{P x \cdot k d})

Next Step Substitute values of Variables

∴

θ c = (\frac{1}{0.05d⁻¹}) - (0.41 \cdot \frac{164kg/d - 4.9kg/d}{100kg/d \cdot 0.05d⁻¹})

Next Step Convert Units

∴

θ c = (\frac{1}{5.8E-7s⁻¹}) - (0.41 \cdot \frac{0.0019kg/s - 5.7E-5kg/s}{0.0012kg/s \cdot 5.8E-7s⁻¹})

Next Step Prepare to Evaluate

∴

θ c = (\frac{1}{5.8E-7}) - (0.41 \cdot \frac{0.0019 - 5.7E-5}{0.0012 \cdot 5.8E-7})

Next Step Evaluate

∴

θ c = 600808.320000001s

Next Step Convert to Output's Unit

∴

θ c = 6.95380000000001d

LAST Step Rounding Answer

∴

θ c = 6.9538d

Mean Cell Residence Time given Quantity of Volatile Solids Formula Elements

Variables

Mean Cell Residence Time

Mean Cell Residence Time refers to a measure of the extent to which organic matter in sludge has been decomposed or stabilized through treatment processes.

Symbol: θ_c

Measurement: TimeUnit: d

Note: Value should be between 5 to 15.

Formulas to find Mean Cell Residence Time

Open Variable

Endogenous Coefficient

Endogenous Coefficient is referred as modeling the behavior of microorganisms, particularly in wastewater treatment processes.

Symbol: k_d

Measurement: First Order Reaction Rate ConstantUnit: d⁻¹

Note: Value should be greater than 0.

Formulas to find Endogenous Coefficient

Open Variable

Yield Coefficient

Yield Coefficient is referred as the ratio of biomass (microbial cells) produced to the amount of substrate (organic material) consumed during the digestion process.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Yield Coefficient

Open Variable

BOD In

BOD In in anaerobic digester design lies in its role as an indicator of the organic load present in the feedstock. High BOD levels suggest a greater concentration of organic matter.

Symbol: BOD_in

Measurement: Mass Flow RateUnit: kg/d

Note: Value should be greater than 0.

Formulas to find BOD In

Open Variable

BOD Out

BOD Out referred as the amount of dissolved oxygen exits anaerobic digester.

Symbol: BOD_out

Measurement: Mass Flow RateUnit: kg/d

Note: Value should be greater than 0.

Formulas to find BOD Out

Open Variable

Volatile Solids Produced

Volatile Solids Produced refers to the organic fraction of the total solids present in the sludge.

Symbol: P_x

Measurement: Mass Flow RateUnit: kg/d

Note: Value should be greater than 0.

Formulas to find Volatile Solids Produced

Open Variable

Other formulas in Design of an Anaerobic Digester category

Go Volume Required for Anaerobic Digester

V T = (θ \cdot Q s)

Go Hydraulic Retention Time given Volume Required for Anaerobic Digester

θ h = (\frac{V T}{Q s})

Go Influent Sludge Flow Rate given Volume Required for Anaerobic Digester

Q s = (\frac{V T}{θ})

Go Volumetric Loading in Anaerobic Digester

V l = (\frac{BOD day}{V})

See More

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How to Evaluate Mean Cell Residence Time given Quantity of Volatile Solids?

Mean Cell Residence Time given Quantity of Volatile Solids evaluator uses Mean Cell Residence Time = (1/Endogenous Coefficient)-(Yield Coefficient*(BOD In-BOD Out)/(Volatile Solids Produced*Endogenous Coefficient)) to evaluate the Mean Cell Residence Time, The Mean Cell Residence Time given Quantity of Volatile Solids formula is defined as the average time that the microorganisms (biomass) remain in the treatment system. Mean Cell Residence Time is denoted by θ_c symbol.

How to evaluate Mean Cell Residence Time given Quantity of Volatile Solids using this online evaluator? To use this online evaluator for Mean Cell Residence Time given Quantity of Volatile Solids, enter Endogenous Coefficient (k_d), Yield Coefficient (Y), BOD In (BOD_in), BOD Out (BOD_out) & Volatile Solids Produced (P_x) and hit the calculate button.

FAQs on Mean Cell Residence Time given Quantity of Volatile Solids

What is the formula to find Mean Cell Residence Time given Quantity of Volatile Solids?

The formula of Mean Cell Residence Time given Quantity of Volatile Solids is expressed as Mean Cell Residence Time = (1/Endogenous Coefficient)-(Yield Coefficient*(BOD In-BOD Out)/(Volatile Solids Produced*Endogenous Coefficient)). Here is an example- 8.1E-5 = (1/5.78703703703704E-07)-(0.41*(0.00189814814814815-5.6712962962963E-05)/(0.00115740740740741*5.78703703703704E-07)).

How to calculate Mean Cell Residence Time given Quantity of Volatile Solids?

With Endogenous Coefficient (k_d), Yield Coefficient (Y), BOD In (BOD_in), BOD Out (BOD_out) & Volatile Solids Produced (P_x) we can find Mean Cell Residence Time given Quantity of Volatile Solids using the formula - Mean Cell Residence Time = (1/Endogenous Coefficient)-(Yield Coefficient*(BOD In-BOD Out)/(Volatile Solids Produced*Endogenous Coefficient)).

Can the Mean Cell Residence Time given Quantity of Volatile Solids be negative?

No, the Mean Cell Residence Time given Quantity of Volatile Solids, measured in Time cannot be negative.

Which unit is used to measure Mean Cell Residence Time given Quantity of Volatile Solids?

Mean Cell Residence Time given Quantity of Volatile Solids is usually measured using the Day[d] for Time. Second[d], Millisecond[d], Microsecond[d] are the few other units in which Mean Cell Residence Time given Quantity of Volatile Solids can be measured.

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