Solids Retention Time given Volume of Aerobic Digester Calculator

✖Influent average flow rate to the digester is the discharge going to the digester.ⓘ Influent average flow rate [Q_i]			+10% -10%
✖Influent suspended solids refers to small solid particles which remain in suspension in water as a colloid.ⓘ Influent suspended solids [X_i]			+10% -10%
✖The Volume of Aerobic Digester is the capacity of the digester.ⓘ Volume of Aerobic Digester [V_ad]			+10% -10%
✖Digester total suspended solids is the dry-weight of suspended particles, that are not dissolved, in a sample of water.ⓘ Digester total suspended solids [X]			+10% -10%
✖Reaction rate constant quantifies the rate and direction of a chemical reaction.ⓘ Reaction rate constant [K_d]			+10% -10%
✖Volatile fraction of digester suspended solids.ⓘ Volatile fraction [P_v]			+10% -10%

✖Solids retention time is the time the solid fraction of the wastewater spends in a treatment unit.ⓘ Solids Retention Time given Volume of Aerobic Digester [θ]

⎘ Copy

👎

Formula

✖

Solids Retention Time given Volume of Aerobic Digester

Formula

`"θ" = (("Q"_{"i"}*"X"_{"i"})/("V"_{"ad"}*"X")-("K"_{"d"}*"P"_{"v"}))`

Example

`"5.8E^-6d"=(("5m³/s"*"5mg/L")/("10m³"*"5mg/L")-("0.05d⁻¹"*"0.5"))`

Calculator

LaTeX

Reset

👍

Download Environmental Engineering Formula PDF PDF Image

Solids Retention Time given Volume of Aerobic Digester Solution

STEP 0: Pre-Calculation Summary

Formula Used

Solids retention time = ((Influent average flow rate*Influent suspended solids)/(Volume of Aerobic Digester*Digester total suspended solids)-(Reaction rate constant*Volatile fraction))
θ = ((Q_i*X_i)/(V_ad*X)-(K_d*P_v))
This formula uses 7 Variables

Variables Used

Solids retention time - (Measured in Second) - Solids retention time is the time the solid fraction of the wastewater spends in a treatment unit.
Influent average flow rate - (Measured in Cubic Meter per Second) - Influent average flow rate to the digester is the discharge going to the digester.
Influent suspended solids - (Measured in Kilogram per Cubic Meter) - Influent suspended solids refers to small solid particles which remain in suspension in water as a colloid.
Volume of Aerobic Digester - (Measured in Cubic Meter) - The Volume of Aerobic Digester is the capacity of the digester.
Digester total suspended solids - (Measured in Kilogram per Cubic Meter) - Digester total suspended solids is the dry-weight of suspended particles, that are not dissolved, in a sample of water.
Reaction rate constant - (Measured in 1 Per Second) - Reaction rate constant quantifies the rate and direction of a chemical reaction.
Volatile fraction - Volatile fraction of digester suspended solids.

STEP 1: Convert Input(s) to Base Unit

Influent average flow rate: 5 Cubic Meter per Second --> 5 Cubic Meter per Second No Conversion Required
Influent suspended solids: 5 Milligram per Liter --> 0.005 Kilogram per Cubic Meter (Check conversion here)
Volume of Aerobic Digester: 10 Cubic Meter --> 10 Cubic Meter No Conversion Required
Digester total suspended solids: 5 Milligram per Liter --> 0.005 Kilogram per Cubic Meter (Check conversion here)
Reaction rate constant: 0.05 1 Per Day --> 5.78703703703704E-07 1 Per Second (Check conversion here)
Volatile fraction: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = ((Q_i*X_i)/(V_ad*X)-(K_d*P_v)) --> ((5*0.005)/(10*0.005)-(5.78703703703704E-07*0.5))

Evaluating ... ...

θ = 0.499999710648148

STEP 3: Convert Result to Output's Unit

0.499999710648148 Second -->5.78703368805727E-06 Day (Check conversion here)

FINAL ANSWER

5.78703368805727E-06 ≈ 5.8E-6 Day <-- Solids retention time

(Calculation completed in 00.007 seconds)

You are here -

Home » Engineering » Civil » Environmental Engineering » Design of an Aerobic Digester » Solids Retention Time given Volume of Aerobic Digester

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 15 Design of an Aerobic Digester Calculators

Solids Retention Time given Volume of Aerobic Digester

Go Solids retention time = ((Influent average flow rate*Influent suspended solids)/(Volume of Aerobic Digester*Digester total suspended solids)-(Reaction rate constant*Volatile fraction))

Volume of Aerobic Digester

Go Volume of Aerobic Digester = (Influent average flow rate*Influent suspended solids)/(Digester total suspended solids*((Reaction rate constant*Volatile fraction)+Solids retention time))

Digester Total Suspended Solids given Volume of Aerobic Digester

Go Digester total suspended solids = (Influent average flow rate*Influent suspended solids)/(Volume of Aerobic Digester*(Reaction rate constant*Volatile fraction+Solids retention time))

Specific Gravity of Digested Sludge given Volume of Digested Sludge

Go Specific Gravity of Sludge = (Weight of sludge)/(Water Density*Sludge Volume*Percent Solids)

Density of Water given Volume of Digested Sludge

Go Water Density = (Weight of sludge)/(Sludge Volume*Specific Gravity of Sludge*Percent Solids)

Percent Solids given Volume of Digested Sludge

Go Percent Solids = (Weight of sludge)/(Sludge Volume*Water Density*Specific Gravity of Sludge)

Volume of Digested Sludge

Go Sludge Volume = (Weight of sludge)/(Water Density*Specific Gravity of Sludge*Percent Solids)

Weight of Sludge given Volume of Digested Sludge

Go Weight of sludge = (Water Density*Sludge Volume*Specific Gravity of Sludge*Percent Solids)

Initial Weight of Oxygen given Weight of Oxygen Required

Go Weight of initial oxygen = (Weight of oxygen*Volatile suspended solid weight)/(Volume of suspended solid*2.3)

VSS as Mass Flow Rate given Weight of Oxygen Required

Go Volume of suspended solid = (Weight of oxygen*Volatile suspended solid weight)/(2.3*Weight of initial oxygen)

Weight of VSS given Weight of Oxygen Required

Go Volatile suspended solid weight = (Volume of suspended solid*2.3*Weight of initial oxygen)/Weight of oxygen

Weight of Oxygen Required to Destroy VSS

Go Weight of oxygen = (Volume of suspended solid*2.3*Weight of initial oxygen)/Volatile suspended solid weight

Volume of Air Required at Standard Conditions

Go Volume of Air = (Weight of oxygen)/(Density of Air*0.232)

Density of Air given Volume of Air Required

Go Density of Air = (Weight of oxygen)/(Volume of Air*0.232)

Weight of Oxygen given Volume of Air

Go Weight of oxygen = (Volume of Air*Density of Air*0.232)

Solids Retention Time given Volume of Aerobic Digester Formula

What is retention time ?

Retention time (RT) is a measure of the time taken for a solute to pass through a chromatography column. It is calculated as the time from injection to detection. The RT for a compound is not fixed as many factors can influence it even if the same GC and column are used. These include: The gas flow rate.

How to Calculate Solids Retention Time given Volume of Aerobic Digester?

Solids Retention Time given Volume of Aerobic Digester calculator uses Solids retention time = ((Influent average flow rate*Influent suspended solids)/(Volume of Aerobic Digester*Digester total suspended solids)-(Reaction rate constant*Volatile fraction)) to calculate the Solids retention time, The Solids Retention Time given Volume of Aerobic Digester calculates the solids retention time when we have prior information of other parameters used. Solids retention time is denoted by θ symbol.

How to calculate Solids Retention Time given Volume of Aerobic Digester using this online calculator? To use this online calculator for Solids Retention Time given Volume of Aerobic Digester, enter Influent average flow rate (Q_i), Influent suspended solids (X_i), Volume of Aerobic Digester (V_ad), Digester total suspended solids (X), Reaction rate constant (K_d) & Volatile fraction (P_v) and hit the calculate button. Here is how the Solids Retention Time given Volume of Aerobic Digester calculation can be explained with given input values -> 6.7E-11 = ((5*0.005)/(10*0.005)-(5.78703703703704E-07*0.5)).

FAQ

What is Solids Retention Time given Volume of Aerobic Digester?

The Solids Retention Time given Volume of Aerobic Digester calculates the solids retention time when we have prior information of other parameters used and is represented as θ = ((Q_i*X_i)/(V_ad*X)-(K_d*P_v)) or Solids retention time = ((Influent average flow rate*Influent suspended solids)/(Volume of Aerobic Digester*Digester total suspended solids)-(Reaction rate constant*Volatile fraction)). Influent average flow rate to the digester is the discharge going to the digester, Influent suspended solids refers to small solid particles which remain in suspension in water as a colloid, The Volume of Aerobic Digester is the capacity of the digester, Digester total suspended solids is the dry-weight of suspended particles, that are not dissolved, in a sample of water, Reaction rate constant quantifies the rate and direction of a chemical reaction & Volatile fraction of digester suspended solids.

How to calculate Solids Retention Time given Volume of Aerobic Digester?

The Solids Retention Time given Volume of Aerobic Digester calculates the solids retention time when we have prior information of other parameters used is calculated using Solids retention time = ((Influent average flow rate*Influent suspended solids)/(Volume of Aerobic Digester*Digester total suspended solids)-(Reaction rate constant*Volatile fraction)). To calculate Solids Retention Time given Volume of Aerobic Digester, you need Influent average flow rate (Q_i), Influent suspended solids (X_i), Volume of Aerobic Digester (V_ad), Digester total suspended solids (X), Reaction rate constant (K_d) & Volatile fraction (P_v). With our tool, you need to enter the respective value for Influent average flow rate, Influent suspended solids, Volume of Aerobic Digester, Digester total suspended solids, Reaction rate constant & Volatile fraction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search