Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity Calculator

✖Vapor Mass Flowrate is the mass flow rate of vapor component in column.ⓘ Vapor Mass Flowrate [V_W]			+10% -10%
✖Vapor Density in Distillation is defined as the ratio of mass to the volume of vapor at particular temperature in a distillation Column.ⓘ Vapor Density in Distillation [ρ_V]			+10% -10%
✖Maximum Allowable Vapor Velocity is a critical velocity of the vapor component that can be operated in a distillation column.ⓘ Maximum Allowable Vapor Velocity [U_v]			+10% -10%

✖Column Diameter refers to the diameter of the column wherein the mass transfer or any other unit operations takes place.ⓘ Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity [D_c]

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Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity

Formula

`"D"_{"c"} = sqrt((4*"V"_{"W"})/(pi*"ρ"_{"V"}*"U"_{"v"}))`

Example

`"1.655532m"=sqrt((4*"4.157kg/s")/(pi*"1.71kg/m³"*"1.12932479467671m/s"))`

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Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Column Diameter = sqrt((4*Vapor Mass Flowrate)/(pi*Vapor Density in Distillation*Maximum Allowable Vapor Velocity))
D_c = sqrt((4*V_W)/(pi*ρ_V*U_v))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Column Diameter - (Measured in Meter) - Column Diameter refers to the diameter of the column wherein the mass transfer or any other unit operations takes place.
Vapor Mass Flowrate - (Measured in Kilogram per Second) - Vapor Mass Flowrate is the mass flow rate of vapor component in column.
Vapor Density in Distillation - (Measured in Kilogram per Cubic Meter) - Vapor Density in Distillation is defined as the ratio of mass to the volume of vapor at particular temperature in a distillation Column.
Maximum Allowable Vapor Velocity - (Measured in Meter per Second) - Maximum Allowable Vapor Velocity is a critical velocity of the vapor component that can be operated in a distillation column.

STEP 1: Convert Input(s) to Base Unit

Vapor Mass Flowrate: 4.157 Kilogram per Second --> 4.157 Kilogram per Second No Conversion Required
Vapor Density in Distillation: 1.71 Kilogram per Cubic Meter --> 1.71 Kilogram per Cubic Meter No Conversion Required
Maximum Allowable Vapor Velocity: 1.12932479467671 Meter per Second --> 1.12932479467671 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_c = sqrt((4*V_W)/(pi*ρ_V*U_v)) --> sqrt((4*4.157)/(pi*1.71*1.12932479467671))

Evaluating ... ...

D_c = 1.65553201910082

STEP 3: Convert Result to Output's Unit

1.65553201910082 Meter --> No Conversion Required

FINAL ANSWER

1.65553201910082 ≈ 1.655532 Meter <-- Column Diameter

(Calculation completed in 00.004 seconds)

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Malviya National Institute Of Technology (MNIT JAIPUR ), JAIPUR

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< 25 Distillation Tower Design Calculators

Relative Volatility of Two Components Based on Normal Boiling Point and Latent Heat of Vaporization

Go Relative Volatility = exp(0.25164*((1/Normal Boiling Point of Component 1)-(1/Normal Boiling Point of Component 2))*(Latent Heat of Vaporization of Component 1+Latent Heat of Vaporization of Component 2))

Maximum Allowable Vapor Velocity given Plate Spacing and Fluid Densities

Go Maximum Allowable Vapor Velocity = (-0.171*(Plate Spacing)^2+0.27*Plate Spacing-0.047)*((Liquid Density-Vapor Density in Distillation)/Vapor Density in Distillation)^0.5

Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity

Go Column Diameter = sqrt((4*Vapor Mass Flowrate)/(pi*Vapor Density in Distillation*Maximum Allowable Vapor Velocity))

Tower Cross Sectional Area given Gas Volumetric Flow and Flooding Velocity

Go Tower Cross Sectional Area = Volumetric Gas Flow/((Fractional Approach to Flooding Velocity*Flooding Velocity)*(1-Fractional Downcomer Area))

Minimum External Reflux given Compositions

Go External Reflux Ratio = (Distillate Composition-Equilibrium Vapor Composition)/(Equilibrium Vapor Composition-Equilibrium Liquid Composition)

Maximum Allowable Mass Velocity using Bubble Cap Trays

Go Maximum Allowable Mass Velocity = Entrainment Factor*(Vapor Density in Distillation*(Liquid Density-Vapor Density in Distillation)^(1/2))

Minimum Internal Reflux given Compositions

Go Internal Reflux Ratio = (Distillate Composition-Equilibrium Vapor Composition)/(Distillate Composition-Equilibrium Liquid Composition)

Dry Plate Pressure Drop in Distillation Column Design

Go Dry Plate Head Loss = 51*((Vapor Velocity Based on Hole Area/Orifice Coefficient)^2)*(Vapor Density in Distillation/Liquid Density)

Flooding Velocity in Distillation Column Design

Go Flooding Velocity = Capacity Factor*((Liquid Density-Vapor Density in Distillation)/Vapor Density in Distillation)^0.5

Weep Point Velocity in Distillation Column Design

Go Weep Point Vapor Velocity Based on Hole Area = (Weep Point Correlation Constant-0.90*(25.4-Hole Diameter))/((Vapor Density in Distillation)^0.5)

Liquid Vapor Flow Factor in Distillation Column Design

Go Flow Factor = (Liquid Mass Flowrate/Vapor Mass Flowrate)*((Vapor Density in Distillation/Liquid Density)^0.5)

Downcomer Residence Time in Distillation Column

Go Residence Time = (Downcomer Area*Clear Liquid Backup*Liquid Density)/Liquid Mass Flowrate

Internal Reflux Ratio Based on Liquid and Distillate Flowrates

Go Internal Reflux Ratio = Liquid Reflux Flowrate/(Liquid Reflux Flowrate+Distillate Flowrate)

Column Diameter Based on Vapor Flowrate and Mass Velocity of Vapor

Go Column Diameter = ((4*Vapor Mass Flowrate)/(pi*Maximum Allowable Mass Velocity))^(1/2)

Head Loss in Downcomer of Tray Tower

Go Downcomer Headloss = 166*((Liquid Mass Flowrate/(Liquid Density*Downcomer Area)))^2

Height of Liquid Crest over Weir

Go Weir Crest = (750/1000)*((Liquid Mass Flowrate/(Weir Length*Liquid Density))^(2/3))

Active Area given Gas Volumetric Flow and Flow Velocity

Go Active Area = Volumetric Gas Flow/(Fractional Downcomer Area*Flooding Velocity)

Fractional Downcomer Area given Total Cross Sectional Area

Go Fractional Downcomer Area = 2*(Downcomer Area/Tower Cross Sectional Area)

Fractional Active Area given Downcomer Area and Total Column Area

Go Fractional Active Area = 1-2*(Downcomer Area/Tower Cross Sectional Area)

Internal Reflux Ratio Given External Reflux Ratio

Go Internal Reflux Ratio = External Reflux Ratio/(External Reflux Ratio+1)

Tower Cross Sectional Area given Fractional Active Area

Go Tower Cross Sectional Area = Active Area/(1-Fractional Downcomer Area)

Tower Cross Sectional Area given Active Area

Go Tower Cross Sectional Area = Active Area/(1-Fractional Downcomer Area)

Clearance Area under Downcomer given Weir Length and Apron Height

Go Clearance Area Under Downcomer = Apron Height*Weir Length

Fractional Active Area given Fractional Downcomer Area

Go Fractional Active Area = 1-Fractional Downcomer Area

Residual Head Loss in Pressure in Distillation Column

Go Residual Head Loss = (12.5*10^3)/Liquid Density

Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity Formula

Column Diameter = sqrt((4*Vapor Mass Flowrate)/(pi*Vapor Density in Distillation*Maximum Allowable Vapor Velocity))
D_c = sqrt((4*V_W)/(pi*ρ_V*U_v))

What is the Significance of Column Diameter?

The column diameter is a critical parameter that has significant implications for the efficiency and performance of the distillation process. The column diameter plays a crucial role in determining the separation and throughput capabilities of a distillation column.
The column diameter directly affects the separation efficiency of a distillation column. A larger column diameter provides more surface area for vapor-liquid contact, allowing for better separation of components in a mixture.

How to Calculate Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity?

Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity calculator uses Column Diameter = sqrt((4*Vapor Mass Flowrate)/(pi*Vapor Density in Distillation*Maximum Allowable Vapor Velocity)) to calculate the Column Diameter, The Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity formula is defined as the diameter of the column where in the vapor component can have a maximum velocity for safe and optimum operations. Column Diameter is denoted by D_c symbol.

How to calculate Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity using this online calculator? To use this online calculator for Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity, enter Vapor Mass Flowrate (V_W), Vapor Density in Distillation (ρ_V) & Maximum Allowable Vapor Velocity (U_v) and hit the calculate button. Here is how the Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity calculation can be explained with given input values -> 1.657974 = sqrt((4*4.157)/(pi*1.71*1.12932479467671)).

FAQ

What is Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity?

The Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity formula is defined as the diameter of the column where in the vapor component can have a maximum velocity for safe and optimum operations and is represented as D_c = sqrt((4*V_W)/(pi*ρ_V*U_v)) or Column Diameter = sqrt((4*Vapor Mass Flowrate)/(pi*Vapor Density in Distillation*Maximum Allowable Vapor Velocity)). Vapor Mass Flowrate is the mass flow rate of vapor component in column, Vapor Density in Distillation is defined as the ratio of mass to the volume of vapor at particular temperature in a distillation Column & Maximum Allowable Vapor Velocity is a critical velocity of the vapor component that can be operated in a distillation column.

How to calculate Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity?

The Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity formula is defined as the diameter of the column where in the vapor component can have a maximum velocity for safe and optimum operations is calculated using Column Diameter = sqrt((4*Vapor Mass Flowrate)/(pi*Vapor Density in Distillation*Maximum Allowable Vapor Velocity)). To calculate Column Diameter given Maximum Vapor Rate and Maximum Vapor Velocity, you need Vapor Mass Flowrate (V_W), Vapor Density in Distillation (ρ_V) & Maximum Allowable Vapor Velocity (U_v). With our tool, you need to enter the respective value for Vapor Mass Flowrate, Vapor Density in Distillation & Maximum Allowable Vapor Velocity 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 Column Diameter?

In this formula, Column Diameter uses Vapor Mass Flowrate, Vapor Density in Distillation & Maximum Allowable Vapor Velocity. We can use 1 other way(s) to calculate the same, which is/are as follows -

Column Diameter = ((4*Vapor Mass Flowrate)/(pi*Maximum Allowable Mass Velocity))^(1/2)

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