Volume of Reactor given Wasting Rate from Return Line Calculator

✖Mean Cell Residence Time is the average time that the sludge remains in the reactor.ⓘ Mean Cell Residence Time [θ_c]			+10% -10%
✖WAS Pumping Rate from Return Line is the flow rate of waste sludge from the return line.ⓘ WAS Pumping Rate from Return Line [Q_w']			+10% -10%
✖Sludge Concentration in Return Line is the total BOD that is present in the return line.ⓘ Sludge Concentration in Return Line [X_r]			+10% -10%
✖Effluent Flow Rate is the total quantity of the flow of sewage from the secondary clarifier.ⓘ Effluent Flow Rate [Q_e]			+10% -10%
✖Solid Concentration in Effluent is the total amount of solids that are present in the effluent.ⓘ Solid Concentration in Effluent [X_e]			+10% -10%
✖MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics).ⓘ MLSS [X]			+10% -10%

✖The Reactor Volume gives us the capacity of the reactor.ⓘ Volume of Reactor given Wasting Rate from Return Line [V]

⎘ Copy

👎

Formula

✖

Volume of Reactor given Wasting Rate from Return Line

Formula

`"V" = "θ"_{"c"}*((("Q"_{"w"}"'")*"X"_{"r"})+("Q"_{"e"}*"X"_{"e"}))/"X"`

Example

`"641.6667m³"="7d"*(("400m³/d"*"200mg/L")+("500m³/d"*"60mg/L"))/"1200mg/L"`

Calculator

LaTeX

Reset

👍

Download Environmental Engineering Formula PDF

Volume of Reactor given Wasting Rate from Return Line Solution

STEP 0: Pre-Calculation Summary

Formula Used

Reactor Volume = Mean Cell Residence Time*((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent))/MLSS
V = θ_c*((Q_w'*X_r)+(Q_e*X_e))/X
This formula uses 7 Variables

Variables Used

Reactor Volume - (Measured in Cubic Meter) - The Reactor Volume gives us the capacity of the reactor.
Mean Cell Residence Time - (Measured in Second) - Mean Cell Residence Time is the average time that the sludge remains in the reactor.
WAS Pumping Rate from Return Line - (Measured in Cubic Meter per Second) - WAS Pumping Rate from Return Line is the flow rate of waste sludge from the return line.
Sludge Concentration in Return Line - (Measured in Kilogram per Cubic Meter) - Sludge Concentration in Return Line is the total BOD that is present in the return line.
Effluent Flow Rate - (Measured in Cubic Meter per Second) - Effluent Flow Rate is the total quantity of the flow of sewage from the secondary clarifier.
Solid Concentration in Effluent - (Measured in Kilogram per Cubic Meter) - Solid Concentration in Effluent is the total amount of solids that are present in the effluent.
MLSS - (Measured in Kilogram per Cubic Meter) - MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics).

STEP 1: Convert Input(s) to Base Unit

Mean Cell Residence Time: 7 Day --> 604800 Second (Check conversion here)
WAS Pumping Rate from Return Line: 400 Cubic Meter per Day --> 0.00462962962962963 Cubic Meter per Second (Check conversion here)
Sludge Concentration in Return Line: 200 Milligram per Liter --> 0.2 Kilogram per Cubic Meter (Check conversion here)
Effluent Flow Rate: 500 Cubic Meter per Day --> 0.00578703703703704 Cubic Meter per Second (Check conversion here)
Solid Concentration in Effluent: 60 Milligram per Liter --> 0.06 Kilogram per Cubic Meter (Check conversion here)
MLSS: 1200 Milligram per Liter --> 1.2 Kilogram per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = θ_c*((Q_w'*X_r)+(Q_e*X_e))/X --> 604800*((0.00462962962962963*0.2)+(0.00578703703703704*0.06))/1.2

Evaluating ... ...

V = 641.666666666667

STEP 3: Convert Result to Output's Unit

641.666666666667 Cubic Meter --> No Conversion Required

FINAL ANSWER

641.666666666667 ≈ 641.6667 Cubic Meter <-- Reactor Volume

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Environmental Engineering » Design of a complete mix activated sludge reactor » Volume of Reactor » Volume of Reactor given Wasting Rate from Return Line

Credits

Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has created this Calculator and 500+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Calculator and 1700+ more calculators!

< 5 Volume of Reactor Calculators

Volume of Reactor

Go Reactor Volume = (Mean Cell Residence Time*Maximum Yield Coefficient*Average daily influent flow rate*(Influent Substrate Concentration-Effluent substrate concentration))/(MLVSS*(1+(Mean Cell Residence Time*Endogenous decay coefficient)))

Volume of Reactor given Wasting Rate from Return Line

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

Volume of Reactor using Wasting Rate from Return Line when Concentration of Solid in Effluent is Low

Go Reactor Volume = Mean Cell Residence Time*WAS Pumping Rate from Return Line*Sludge Concentration in Return Line/MLSS

Volume of Reactor given Hydraulic Retention Time

Go Reactor Volume = Hydraulic retention time*Average daily influent flow rate

Volume of Reactor given WAS Pumping Rate from Aeration Tank

Go Reactor Volume = Mean Cell Residence Time*WAS Pumping Rate from Reactor

Volume of Reactor given Wasting Rate from Return Line Formula

What is wasting rate?

The Wasting rate from return line is the time required to waste sludge from the return sludge line because return activated sludge is more concentrated and requires smaller waste sludge pumps.

How to Calculate Volume of Reactor given Wasting Rate from Return Line?

Volume of Reactor given Wasting Rate from Return Line calculator uses Reactor Volume = Mean Cell Residence Time*((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent))/MLSS to calculate the Reactor Volume, The Volume of Reactor given Wasting Rate from Return Line is the total volume of the reactor which can accommodate the incoming sewage. Reactor Volume is denoted by V symbol.

How to calculate Volume of Reactor given Wasting Rate from Return Line using this online calculator? To use this online calculator for Volume of Reactor given Wasting Rate from Return Line, enter Mean Cell Residence Time (θ_c), WAS Pumping Rate from Return Line (Q_w'), Sludge Concentration in Return Line (X_r), Effluent Flow Rate (Q_e), Solid Concentration in Effluent (X_e) & MLSS (X) and hit the calculate button. Here is how the Volume of Reactor given Wasting Rate from Return Line calculation can be explained with given input values -> 916.6667 = 604800*((0.00462962962962963*0.2)+(0.00578703703703704*0.06))/1.2.

FAQ

What is Volume of Reactor given Wasting Rate from Return Line?

The Volume of Reactor given Wasting Rate from Return Line is the total volume of the reactor which can accommodate the incoming sewage and is represented as V = θ_c*((Q_w'*X_r)+(Q_e*X_e))/X or Reactor Volume = Mean Cell Residence Time*((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent))/MLSS. Mean Cell Residence Time is the average time that the sludge remains in the reactor, WAS Pumping Rate from Return Line is the flow rate of waste sludge from the return line, Sludge Concentration in Return Line is the total BOD that is present in the return line, Effluent Flow Rate is the total quantity of the flow of sewage from the secondary clarifier, Solid Concentration in Effluent is the total amount of solids that are present in the effluent & MLSS is the sum of volatile suspended solids (organics) and fixed suspended solids (inorganics).

How to calculate Volume of Reactor given Wasting Rate from Return Line?

The Volume of Reactor given Wasting Rate from Return Line is the total volume of the reactor which can accommodate the incoming sewage is calculated using Reactor Volume = Mean Cell Residence Time*((WAS Pumping Rate from Return Line*Sludge Concentration in Return Line)+(Effluent Flow Rate*Solid Concentration in Effluent))/MLSS. To calculate Volume of Reactor given Wasting Rate from Return Line, you need Mean Cell Residence Time (θ_c), WAS Pumping Rate from Return Line (Q_w'), Sludge Concentration in Return Line (X_r), Effluent Flow Rate (Q_e), Solid Concentration in Effluent (X_e) & MLSS (X). With our tool, you need to enter the respective value for Mean Cell Residence Time, WAS Pumping Rate from Return Line, Sludge Concentration in Return Line, Effluent Flow Rate, Solid Concentration in Effluent & MLSS 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 Reactor Volume?

In this formula, Reactor Volume uses Mean Cell Residence Time, WAS Pumping Rate from Return Line, Sludge Concentration in Return Line, Effluent Flow Rate, Solid Concentration in Effluent & MLSS. We can use 4 other way(s) to calculate the same, which is/are as follows -

Reactor Volume = (Mean Cell Residence Time*Maximum Yield Coefficient*Average daily influent flow rate*(Influent Substrate Concentration-Effluent substrate concentration))/(MLVSS*(1+(Mean Cell Residence Time*Endogenous decay coefficient)))
Reactor Volume = Hydraulic retention time*Average daily influent flow rate
Reactor Volume = Mean Cell Residence Time*WAS Pumping Rate from Return Line*Sludge Concentration in Return Line/MLSS
Reactor Volume = Mean Cell Residence Time*WAS Pumping Rate from Reactor

Home

FREE PDFs

🔍 Search