✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Mean Cell Residence Time [θ_c]			+10% -10%
✖Average Daily Influent Flow Rate is the average volume of wastewater entering a treatment facility per day. This is crucial because it helps determine the efficiency of wastewater treatment plants.ⓘ Average Daily Influent Flow Rate [Q^']			+10% -10%
✖Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.ⓘ Maximum Yield Coefficient [Y]			+10% -10%
✖Influent Substrate Concentration is the amount of organic material present in the incoming wastewater that enters a treatment system..ⓘ Influent Substrate Concentration [S_o]			+10% -10%
✖Effluent Substrate Concentration is the amount of organic or inorganic material present in wastewater (effluent) after it has undergone treatment.ⓘ Effluent Substrate Concentration [S]			+10% -10%
✖The Reactor Volume gives us the capacity of the reactor.ⓘ Reactor Volume [V]			+10% -10%
✖Endogenous decay coefficient is a coefficient representing the decrease of cell mass in the MLVSS.ⓘ Endogenous decay coefficient [k_d]			+10% -10%

✖Mixed Liquor Volatile Suspended Solids is a measure of the concentration of organic matter in the mixed liquor, which is the combination of wastewater and activated sludge in treatment process.ⓘ Mixed Liquor Volatile Suspended Solids given Reactor Volume [X_a']

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Formula

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Mixed Liquor Volatile Suspended Solids given Reactor Volume

Formula

`"X"_{"a'"} = ("θ"_{"c"}*"Q"^{"'"}*"Y"*("S"_{"o"}-"S"))/("V"*(1+("k"_{"d"}*"θ"_{"c"})))`

Example

`"98.7mg/L"=("14d"*"10.2m³/d"*"0.5"*("2500mg/L"-"150mg/L"))/("1000m³"*(1+("0.050d⁻¹"*"14d")))`

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Mixed Liquor Volatile Suspended Solids given Reactor Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mixed Liquor Volatile Suspended Solids = (Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration))/(Reactor Volume*(1+(Endogenous decay coefficient*Mean Cell Residence Time)))
X_a' = (θ_c*Q^'*Y*(S_o-S))/(V*(1+(k_d*θ_c)))
This formula uses 8 Variables

Variables Used

Mixed Liquor Volatile Suspended Solids - (Measured in Kilogram per Cubic Meter) - Mixed Liquor Volatile Suspended Solids is a measure of the concentration of organic matter in the mixed liquor, which is the combination of wastewater and activated sludge in treatment process.
Mean Cell Residence Time - (Measured in Second) - Mean Cell Residence Time is the average time that the sludge remains in the reactor.
Average Daily Influent Flow Rate - (Measured in Cubic Meter per Second) - Average Daily Influent Flow Rate is the average volume of wastewater entering a treatment facility per day. This is crucial because it helps determine the efficiency of wastewater treatment plants.
Maximum Yield Coefficient - Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed.
Influent Substrate Concentration - (Measured in Kilogram per Cubic Meter) - Influent Substrate Concentration is the amount of organic material present in the incoming wastewater that enters a treatment system..
Effluent Substrate Concentration - (Measured in Kilogram per Cubic Meter) - Effluent Substrate Concentration is the amount of organic or inorganic material present in wastewater (effluent) after it has undergone treatment.
Reactor Volume - (Measured in Cubic Meter) - The Reactor Volume gives us the capacity of the reactor.
Endogenous decay coefficient - (Measured in 1 Per Second) - Endogenous decay coefficient is a coefficient representing the decrease of cell mass in the MLVSS.

STEP 1: Convert Input(s) to Base Unit

Mean Cell Residence Time: 14 Day --> 1209600 Second (Check conversion here)
Average Daily Influent Flow Rate: 10.2 Cubic Meter per Day --> 0.000118055555555556 Cubic Meter per Second (Check conversion here)
Maximum Yield Coefficient: 0.5 --> No Conversion Required
Influent Substrate Concentration: 2500 Milligram per Liter --> 2.5 Kilogram per Cubic Meter (Check conversion here)
Effluent Substrate Concentration: 150 Milligram per Liter --> 0.15 Kilogram per Cubic Meter (Check conversion here)
Reactor Volume: 1000 Cubic Meter --> 1000 Cubic Meter 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

X_a' = (θ_c*Q^'*Y*(S_o-S))/(V*(1+(k_d*θ_c))) --> (1209600*0.000118055555555556*0.5*(2.5-0.15))/(1000*(1+(5.78703703703704E-07*1209600)))

Evaluating ... ...

X_a' = 0.0987000000000004

STEP 3: Convert Result to Output's Unit

0.0987000000000004 Kilogram per Cubic Meter -->98.7000000000004 Milligram per Liter (Check conversion here)

FINAL ANSWER

98.7000000000004 ≈ 98.7 Milligram per Liter <-- Mixed Liquor Volatile Suspended Solids

(Calculation completed in 00.004 seconds)

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Mixed Liquor Volatile Suspended Solids given Reactor Volume

Go Mixed Liquor Volatile Suspended Solids = (Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration))/(Reactor Volume*(1+(Endogenous decay coefficient*Mean Cell Residence Time)))

Mixed Liquor Suspended Solids given Wasting Rate from Return Line

Go Mixed Liquor Suspended Solids = Mean Cell Residence Time*((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent))/Reactor Volume

MLSS given RAS Pumping Rate from Aeration Tank

Go Mixed Liquor Suspended Solids = Sludge Concentration in Return Line*(Return Activated Sludge+WAS Pumping Rate from Return Line)/(Average Daily Influent Flow Rate+Return Activated Sludge)

MLSS using Wasting rate from Return Line when Concentration of Solid in Effluent is Low

Go Mixed Liquor Suspended Solids = Mean Cell Residence Time*WAS Pumping Rate from Return Line*Sludge Concentration in Return Line/Reactor Volume

Mixed Liquor Volatile Suspended Solids given Reactor Volume Formula

What is Volume of Reactor?

The volume of the reactor is the total capacity of the reactor which is allowed in the reactor. It is calculated in cubic meters.

How do you process sludge?

Step 1 – Sludge Thickening. The first step in the sewage sludge treatment plan is called thickening.
Step 2 – Sludge Digestion. After amassing all the solids from the sewage sludge begins the sludge digestion process
Step 3 – Dewatering
Step 4 – Disposal.

How to Calculate Mixed Liquor Volatile Suspended Solids given Reactor Volume?

Mixed Liquor Volatile Suspended Solids given Reactor Volume calculator uses Mixed Liquor Volatile Suspended Solids = (Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration))/(Reactor Volume*(1+(Endogenous decay coefficient*Mean Cell Residence Time))) to calculate the Mixed Liquor Volatile Suspended Solids, The Mixed Liquor Volatile Suspended Solids given Reactor Volume is defined as the concentration of organic matter (biomass) in the mixed liquor of an aeration tank in a wastewater treatment plant. It represents the portion of the suspended solids in the mixed liquor that can be volatilized at high temperatures, typically at 550°C. Mixed Liquor Volatile Suspended Solids is denoted by X_a' symbol.

How to calculate Mixed Liquor Volatile Suspended Solids given Reactor Volume using this online calculator? To use this online calculator for Mixed Liquor Volatile Suspended Solids given Reactor Volume, enter Mean Cell Residence Time (θ_c), Average Daily Influent Flow Rate (Q^'), Maximum Yield Coefficient (Y), Influent Substrate Concentration (S_o), Effluent Substrate Concentration (S), Reactor Volume (V) & Endogenous decay coefficient (k_d) and hit the calculate button. Here is how the Mixed Liquor Volatile Suspended Solids given Reactor Volume calculation can be explained with given input values -> 98700 = (1209600*0.000118055555555556*0.5*(2.5-0.15))/(1000*(1+(5.78703703703704E-07*1209600))).

FAQ

What is Mixed Liquor Volatile Suspended Solids given Reactor Volume?

The Mixed Liquor Volatile Suspended Solids given Reactor Volume is defined as the concentration of organic matter (biomass) in the mixed liquor of an aeration tank in a wastewater treatment plant. It represents the portion of the suspended solids in the mixed liquor that can be volatilized at high temperatures, typically at 550°C and is represented as X_a' = (θ_c*Q^'*Y*(S_o-S))/(V*(1+(k_d*θ_c))) or Mixed Liquor Volatile Suspended Solids = (Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration))/(Reactor Volume*(1+(Endogenous decay coefficient*Mean Cell Residence Time))). Mean Cell Residence Time is the average time that the sludge remains in the reactor, Average Daily Influent Flow Rate is the average volume of wastewater entering a treatment facility per day. This is crucial because it helps determine the efficiency of wastewater treatment plants, Maximum Yield Coefficient Y represents the maximum mg of cells produced per mg organic matter removed, Influent Substrate Concentration is the amount of organic material present in the incoming wastewater that enters a treatment system, Effluent Substrate Concentration is the amount of organic or inorganic material present in wastewater (effluent) after it has undergone treatment, The Reactor Volume gives us the capacity of the reactor & Endogenous decay coefficient is a coefficient representing the decrease of cell mass in the MLVSS.

How to calculate Mixed Liquor Volatile Suspended Solids given Reactor Volume?

The Mixed Liquor Volatile Suspended Solids given Reactor Volume is defined as the concentration of organic matter (biomass) in the mixed liquor of an aeration tank in a wastewater treatment plant. It represents the portion of the suspended solids in the mixed liquor that can be volatilized at high temperatures, typically at 550°C is calculated using Mixed Liquor Volatile Suspended Solids = (Mean Cell Residence Time*Average Daily Influent Flow Rate*Maximum Yield Coefficient*(Influent Substrate Concentration-Effluent Substrate Concentration))/(Reactor Volume*(1+(Endogenous decay coefficient*Mean Cell Residence Time))). To calculate Mixed Liquor Volatile Suspended Solids given Reactor Volume, you need Mean Cell Residence Time (θ_c), Average Daily Influent Flow Rate (Q^'), Maximum Yield Coefficient (Y), Influent Substrate Concentration (S_o), Effluent Substrate Concentration (S), Reactor Volume (V) & Endogenous decay coefficient (k_d). With our tool, you need to enter the respective value for Mean Cell Residence Time, Average Daily Influent Flow Rate, Maximum Yield Coefficient, Influent Substrate Concentration, Effluent Substrate Concentration, Reactor Volume & Endogenous decay coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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