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Mean Cell Residence Time given Observed Cell Yield Formula

GoMean Cell Residence Time given Reactor Volume Formula

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Mean Cell Residence Time is the average time that the sludge remains in the reactor. Check FAQs

θ c = \frac{Y obs - Y}{k d}

θ_c - Mean Cell Residence Time?Y_obs - Observed Cell Yield?Y - Maximum Yield Coefficient?k_d - Endogenous Decay Coefficient?

Mean Cell Residence Time given Observed Cell Yield Example

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Here is how the Mean Cell Residence Time given Observed Cell Yield equation looks like with Values.

Here is how the Mean Cell Residence Time given Observed Cell Yield equation looks like with Units.

Here is how the Mean Cell Residence Time given Observed Cell Yield equation looks like.

6 = \frac{0.8 - 0.5}{0.05}

6d = \frac{0.8 - 0.5}{0.05d⁻¹}

6 = \frac{0.8 - 0.5}{0.05}

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Mean Cell Residence Time given Observed Cell Yield Solution

Follow our step by step solution on how to calculate Mean Cell Residence Time given Observed Cell Yield?

FIRST Step Consider the formula

θ c = \frac{Y obs - Y}{k d}

Next Step Substitute values of Variables

∴

θ c = \frac{0.8 - 0.5}{0.05d⁻¹}

Next Step Convert Units

∴

θ c = \frac{0.8 - 0.5}{5.8E-7s⁻¹}

Next Step Prepare to Evaluate

∴

θ c = \frac{0.8 - 0.5}{5.8E-7}

Next Step Evaluate

∴

θ c = 518400s

LAST Step Convert to Output's Unit

∴

θ c = 6d

Mean Cell Residence Time given Observed Cell Yield Formula Elements

Variables

Mean Cell Residence Time

Mean Cell Residence Time is the average time that the sludge remains in the reactor.

Symbol: θ_c

Measurement: TimeUnit: d

Note: Value should be between 5 to 15.

Formulas to find Mean Cell Residence Time

Observed Cell Yield

Observed Cell Yield refers to the observed mg of cells produced per mg organic matter removed.

Symbol: Y_obs

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Observed Cell Yield

Maximum Yield Coefficient

Maximum Yield Coefficient refers to 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

Endogenous Decay Coefficient

Endogenous Decay Coefficient refers to the rate at which microorganisms in the biomass consume their own cell mass in the absence of an external food source.

Symbol: k_d

Measurement: First Order Reaction Rate ConstantUnit: d⁻¹

Note: Value should be between 0.025 to 0.075.

Formulas to find Endogenous Decay Coefficient

Other Formulas to find Mean Cell Residence Time

Go Mean Cell Residence Time given Reactor Volume

θ c = \frac{V \cdot X a}{Q a \cdot Y \cdot (S o - S) - (V \cdot X a \cdot k d)}

How to Evaluate Mean Cell Residence Time given Observed Cell Yield?

Mean Cell Residence Time given Observed Cell Yield evaluator uses Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient to evaluate the Mean Cell Residence Time, The Mean Cell Residence Time given Observed Cell Yield formula is defined as the average time that the sludge remains in the reactor (sludge age). For a complete-mix activated sludge process, ranges from 5 to 15 days. Mean Cell Residence Time is denoted by θ_c symbol.

How to evaluate Mean Cell Residence Time given Observed Cell Yield using this online evaluator? To use this online evaluator for Mean Cell Residence Time given Observed Cell Yield, enter Observed Cell Yield (Y_obs), Maximum Yield Coefficient (Y) & Endogenous Decay Coefficient (k_d) and hit the calculate button.

FAQs on Mean Cell Residence Time given Observed Cell Yield

What is the formula to find Mean Cell Residence Time given Observed Cell Yield?

The formula of Mean Cell Residence Time given Observed Cell Yield is expressed as Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient. Here is an example- 6.9E-5 = (0.8-0.5)/5.78703703703704E-07.

How to calculate Mean Cell Residence Time given Observed Cell Yield?

With Observed Cell Yield (Y_obs), Maximum Yield Coefficient (Y) & Endogenous Decay Coefficient (k_d) we can find Mean Cell Residence Time given Observed Cell Yield using the formula - Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient.

What are the other ways to Calculate Mean Cell Residence Time?

Here are the different ways to Calculate Mean Cell Residence Time-

Mean Cell Residence Time=(Reactor Volume*MLVSS)/(Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration)-(Reactor Volume*MLVSS*Endogenous Decay Coefficient))

Can the Mean Cell Residence Time given Observed Cell Yield be negative?

No, the Mean Cell Residence Time given Observed Cell Yield, measured in Time cannot be negative.

Which unit is used to measure Mean Cell Residence Time given Observed Cell Yield?

Mean Cell Residence Time given Observed Cell Yield 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 Observed Cell Yield can be measured.

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