Mean Cell Residence Time given Observed Cell Yield Calculator

✖Observed Cell Yield refers to the observed mg of cells produced per mg organic matter removed.ⓘ Observed Cell Yield [Y_obs]			+10% -10%
✖Maximum Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed.ⓘ Maximum Yield Coefficient [Y]			+10% -10%
✖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.ⓘ Endogenous Decay Coefficient [k_d]			+10% -10%

✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Mean Cell Residence Time given Observed Cell Yield [θ_c]

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Mean Cell Residence Time given Observed Cell Yield Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient
θ_c = (Y_obs-Y)/k_d
This formula uses 4 Variables

Variables Used

Mean Cell Residence Time - (Measured in Second) - Mean Cell Residence Time is the average time that the sludge remains in the reactor.
Observed Cell Yield - Observed Cell Yield refers to the observed mg of cells produced per mg organic matter removed.
Maximum Yield Coefficient - Maximum Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed.
Endogenous Decay Coefficient - (Measured in 1 Per Second) - 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.

STEP 1: Convert Input(s) to Base Unit

Observed Cell Yield: 0.8 --> No Conversion Required
Maximum Yield Coefficient: 0.5 --> No Conversion Required
Endogenous Decay Coefficient: 0.05 1 Per Day --> 5.78703703703704E-07 1 Per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_c = (Y_obs-Y)/k_d --> (0.8-0.5)/5.78703703703704E-07

Evaluating ... ...

θ_c = 518400

STEP 3: Convert Result to Output's Unit

518400 Second -->6 Day (Check conversion here)

FINAL ANSWER

6 Day <-- Mean Cell Residence Time

(Calculation completed in 00.020 seconds)

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Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< Mean Cell Residential Time Calculators

Mean Cell Residence Time given Reactor Volume

LaTeX Go 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))

Mean Cell Residence Time given Observed Cell Yield

LaTeX Go Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient

Mean Cell Residence Time given Observed Cell Yield Formula

LaTeX Go

Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient
θ_c = (Y_obs-Y)/k_d

What is Observed Cell Yield?

Observed Cell Yield represents the observed mg of cells produced per mg organic matter removed. The observed cell yield is always less than the maximum cell yield, (Y).

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

Mean Cell Residence Time given Observed Cell Yield calculator uses Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient to calculate 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 calculate Mean Cell Residence Time given Observed Cell Yield using this online calculator? To use this online calculator 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. Here is how the Mean Cell Residence Time given Observed Cell Yield calculation can be explained with given input values -> 6.9E-5 = (0.8-0.5)/5.78703703703704E-07.

FAQ

What is Mean Cell Residence Time given Observed Cell Yield?

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 and is represented as θ_c = (Y_obs-Y)/k_d or Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient. Observed Cell Yield refers to the observed mg of cells produced per mg organic matter removed, Maximum Yield Coefficient refers to the maximum mg of cells produced per mg organic matter removed & 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.

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

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 is calculated using Mean Cell Residence Time = (Observed Cell Yield-Maximum Yield Coefficient)/Endogenous Decay Coefficient. To calculate Mean Cell Residence Time given Observed Cell Yield, you need Observed Cell Yield (Y_obs), Maximum Yield Coefficient (Y) & Endogenous Decay Coefficient (k_d). With our tool, you need to enter the respective value for Observed Cell Yield, Maximum Yield Coefficient & Endogenous Decay Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mean Cell Residence Time?

In this formula, Mean Cell Residence Time uses Observed Cell Yield, Maximum Yield Coefficient & Endogenous Decay Coefficient. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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