Dispersion using General Axis Expression Calculator

✖Diffusion Coefficient for General Axis Dispersion is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.ⓘ Diffusion Coefficient for General Axis Dispersion [D_{f G}]			+10% -10%
✖Velocity of Pulse for General Axis Expression is the Velocity of the Tracer throughout the Reactor, in General Axis Regime.ⓘ Velocity of Pulse for General Axis Expression [u_G]			+10% -10%
✖Diameter of Tube is the Outer Diameter of the Tube, where the Fluid is subjected to flow through it.ⓘ Diameter of Tube [d_Tube]			+10% -10%

✖Dispersion Coefficient for General Axis Expression is distinguished as Spreading of the Tracer in the reactor, that diffuses across a unit area in 1 s, for General Axis Regime.ⓘ Dispersion using General Axis Expression [D_{p G}]

⎘ Copy

👎

Formula

✖

Dispersion using General Axis Expression

Formula

`"D"_{"p G"} = "D"_{"f G"}+("u"_{"G"}^2*"d"_{"Tube"}^2)/(192*"D"_{"f G"})`

Example

`"0.870226m²/s"="0.87m²/s"+(("0.2m/s")^2*("0.971m")^2)/(192*"0.87m²/s")`

Calculator

LaTeX

Reset

👍

Download Flow Pattern, Contacting and Non Ideal Flow Formula PDF PDF Image

Dispersion using General Axis Expression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dispersion Coefficient for General Axis Expression = Diffusion Coefficient for General Axis Dispersion+(Velocity of Pulse for General Axis Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for General Axis Dispersion)
D_{p G} = D_{f G}+(u_G^2*d_Tube^2)/(192*D_{f G})
This formula uses 4 Variables

Variables Used

Dispersion Coefficient for General Axis Expression - (Measured in Square Meter Per Second) - Dispersion Coefficient for General Axis Expression is distinguished as Spreading of the Tracer in the reactor, that diffuses across a unit area in 1 s, for General Axis Regime.
Diffusion Coefficient for General Axis Dispersion - (Measured in Square Meter Per Second) - Diffusion Coefficient for General Axis Dispersion is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.
Velocity of Pulse for General Axis Expression - (Measured in Meter per Second) - Velocity of Pulse for General Axis Expression is the Velocity of the Tracer throughout the Reactor, in General Axis Regime.
Diameter of Tube - (Measured in Meter) - Diameter of Tube is the Outer Diameter of the Tube, where the Fluid is subjected to flow through it.

STEP 1: Convert Input(s) to Base Unit

Diffusion Coefficient for General Axis Dispersion: 0.87 Square Meter Per Second --> 0.87 Square Meter Per Second No Conversion Required
Velocity of Pulse for General Axis Expression: 0.2 Meter per Second --> 0.2 Meter per Second No Conversion Required
Diameter of Tube: 0.971 Meter --> 0.971 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_{p G} = D_{f G}+(u_G^2*d_Tube^2)/(192*D_{f G}) --> 0.87+(0.2^2*0.971^2)/(192*0.87)

Evaluating ... ...

D_{p G} = 0.870225776101533

STEP 3: Convert Result to Output's Unit

0.870225776101533 Square Meter Per Second --> No Conversion Required

FINAL ANSWER

0.870225776101533 ≈ 0.870226 Square Meter Per Second <-- Dispersion Coefficient for General Axis Expression

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Chemical Engineering » Chemical Reaction Engineering » Flow Pattern, Contacting and Non Ideal Flow » Convection Model for Laminar Flow » Dispersion using General Axis Expression

Credits

Created by Pavan Kumar

Anurag Group of Institutions (AGI), Hyderabad

Pavan Kumar has created this Calculator and 100+ more calculators!

Verified by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

Prerana Bakli has verified this Calculator and 1600+ more calculators!

< 9 Convection Model for Laminar Flow Calculators

Concentration of Reactant for Chemical Conversions for Second Order in Laminar Flow Reactors

Go Reactant Concentration = Initial Reactant Conc.*(1-(Rate Constant for Second Order Reaction*Mean Pulse Curve*Initial Reactant Conc.)*(1-((Rate Constant for Second Order Reaction*Mean Pulse Curve*Initial Reactant Conc.)/2)*ln(1+(2/(Rate Constant for Second Order Reaction*Mean Pulse Curve*Initial Reactant Conc.)))))

Dispersion using General Axis Expression

Go Dispersion Coefficient for General Axis Expression = Diffusion Coefficient for General Axis Dispersion+(Velocity of Pulse for General Axis Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for General Axis Dispersion)

Reactant Concentration for Chemical Conversions for Zero Order in Laminar Flow Reactors

Go Reactant Concentration = Initial Reactant Conc.*(1-((Rate Constant for Zero Order Reaction*Mean Pulse Curve)/(2*Initial Reactant Conc.))^2)

Dispersion using Taylor Expression Formula

Go Dispersion Coefficient for Taylor Expression = (Velocity of Pulse for Taylor Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for Taylor Dispersion)

Bodenstein Number

Go Bodenstien Number = (Fluid Velocity*Diameter of Tube)/Diffusion Coefficient of Flow for Dispersion

Mean Residence Time for Proper RTD

Go Mean Residence Time = sqrt(1/(4*(1-F Curve)))

F Curve for Laminar Flow in Pipes for Proper RTD

Go F Curve = 1-(1/(4*Mean Residence Time^2))

Mean Residence Time for Improper RTD

Go Mean Residence Time = 1/(2*(1-F Curve))

F Curve for Laminar Flow in Pipes for Improper RTD

Go F Curve = 1-1/(2*Mean Residence Time)

Dispersion using General Axis Expression Formula

What is Dispersion Number ?

The dispersion number is a dimensionless parameter used in fluid mechanics to characterize the degree of mixing or dispersion in a fluid flow. It is particularly relevant in situations where there is the dispersion of one fluid into another, such as in chemical reactors or mixing vessels. The dispersion number provides information about the relative importance of convection (fluid flow) and diffusion (molecular mixing) in a system. The larger the dispersion number, the more dominant the convective mixing is compared to molecular diffusion.

What is Bodenstien Number ?

Bodenstien Number is the product of Reynolds Number and Schmidt Number, which is used to Determine the Flow Regime.

How to Calculate Dispersion using General Axis Expression?

Dispersion using General Axis Expression calculator uses Dispersion Coefficient for General Axis Expression = Diffusion Coefficient for General Axis Dispersion+(Velocity of Pulse for General Axis Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for General Axis Dispersion) to calculate the Dispersion Coefficient for General Axis Expression, Dispersion using General Axis Expression formula is defined as Flow Models which are used in the situations, where the Bodenstein Number ranges between 10^-2 to 1 and Length vs Diameter of tube ratio is in range of 10^3-10^6, which considers both convective transport and axial diffusion. Dispersion Coefficient for General Axis Expression is denoted by D_{p G} symbol.

How to calculate Dispersion using General Axis Expression using this online calculator? To use this online calculator for Dispersion using General Axis Expression, enter Diffusion Coefficient for General Axis Dispersion (D_{f G}), Velocity of Pulse for General Axis Expression (u_G) & Diameter of Tube (d_Tube) and hit the calculate button. Here is how the Dispersion using General Axis Expression calculation can be explained with given input values -> 0.876224 = 0.87+(0.2^2*0.971^2)/(192*0.87).

FAQ

What is Dispersion using General Axis Expression?

Dispersion using General Axis Expression formula is defined as Flow Models which are used in the situations, where the Bodenstein Number ranges between 10^-2 to 1 and Length vs Diameter of tube ratio is in range of 10^3-10^6, which considers both convective transport and axial diffusion and is represented as D_{p G} = D_{f G}+(u_G^2*d_Tube^2)/(192*D_{f G}) or Dispersion Coefficient for General Axis Expression = Diffusion Coefficient for General Axis Dispersion+(Velocity of Pulse for General Axis Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for General Axis Dispersion). Diffusion Coefficient for General Axis Dispersion is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow, Velocity of Pulse for General Axis Expression is the Velocity of the Tracer throughout the Reactor, in General Axis Regime & Diameter of Tube is the Outer Diameter of the Tube, where the Fluid is subjected to flow through it.

How to calculate Dispersion using General Axis Expression?

Dispersion using General Axis Expression formula is defined as Flow Models which are used in the situations, where the Bodenstein Number ranges between 10^-2 to 1 and Length vs Diameter of tube ratio is in range of 10^3-10^6, which considers both convective transport and axial diffusion is calculated using Dispersion Coefficient for General Axis Expression = Diffusion Coefficient for General Axis Dispersion+(Velocity of Pulse for General Axis Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for General Axis Dispersion). To calculate Dispersion using General Axis Expression, you need Diffusion Coefficient for General Axis Dispersion (D_{f G}), Velocity of Pulse for General Axis Expression (u_G) & Diameter of Tube (d_Tube). With our tool, you need to enter the respective value for Diffusion Coefficient for General Axis Dispersion, Velocity of Pulse for General Axis Expression & Diameter of Tube 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