Dispersion using Taylor Expression Formula Calculator

✖Velocity of Pulse for Taylor Expression is the Velocity of the Tracer throughout the Reactor in the Taylor Regime.ⓘ Velocity of Pulse for Taylor Expression [u_T]			+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%
✖Diffusion Coefficient for Taylor Dispersion is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.ⓘ Diffusion Coefficient for Taylor Dispersion [D_{f T}]			+10% -10%

✖Dispersion Coefficient for Taylor Expression is distinguished as Spreading of the Tracer in the reactor, that diffuses across a unit area in 1 s under the influence of a gradient of one unit.ⓘ Dispersion using Taylor Expression Formula [D_p]

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Dispersion using Taylor Expression Formula

Formula

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

Example

`"368.8429m²/s"=(("5.2m/s")^2*("0.971m")^2)/(192*"0.00036m²/s")`

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Dispersion using Taylor Expression Formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dispersion Coefficient for Taylor Expression = (Velocity of Pulse for Taylor Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for Taylor Dispersion)
D_p = (u_T^2*d_Tube^2)/(192*D_{f T})
This formula uses 4 Variables

Variables Used

Dispersion Coefficient for Taylor Expression - (Measured in Square Meter Per Second) - Dispersion Coefficient for Taylor Expression is distinguished as Spreading of the Tracer in the reactor, that diffuses across a unit area in 1 s under the influence of a gradient of one unit.
Velocity of Pulse for Taylor Expression - (Measured in Meter per Second) - Velocity of Pulse for Taylor Expression is the Velocity of the Tracer throughout the Reactor in the Taylor 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.
Diffusion Coefficient for Taylor Dispersion - (Measured in Square Meter Per Second) - Diffusion Coefficient for Taylor Dispersion is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.

STEP 1: Convert Input(s) to Base Unit

Velocity of Pulse for Taylor Expression: 5.2 Meter per Second --> 5.2 Meter per Second No Conversion Required
Diameter of Tube: 0.971 Meter --> 0.971 Meter No Conversion Required
Diffusion Coefficient for Taylor Dispersion: 0.00036 Square Meter Per Second --> 0.00036 Square Meter Per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_p = (u_T^2*d_Tube^2)/(192*D_{f T}) --> (5.2^2*0.971^2)/(192*0.00036)

Evaluating ... ...

D_p = 368.842891203704

STEP 3: Convert Result to Output's Unit

368.842891203704 Square Meter Per Second --> No Conversion Required

FINAL ANSWER

368.842891203704 ≈ 368.8429 Square Meter Per Second <-- Dispersion Coefficient for Taylor Expression

(Calculation completed in 00.004 seconds)

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

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< 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 Taylor Expression Formula Formula

Dispersion Coefficient for Taylor Expression = (Velocity of Pulse for Taylor Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for Taylor Dispersion)
D_p = (u_T^2*d_Tube^2)/(192*D_{f T})

What is Dispersion Number ?

Suppose an ideal pulse of tracer is introduced into the fluid entering a vessel. The pulse spreads as it passes through the vessel, and to characterize the spreading according to this model, we assume a diffusion-like process superimposed on plug flow. We call this dispersion or longitudinal dispersion to distinguish it from molecular diffusion. The dispersion coefficient D represents this spreading process.

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 Taylor Expression Formula?

Dispersion using Taylor Expression Formula calculator uses Dispersion Coefficient for Taylor Expression = (Velocity of Pulse for Taylor Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for Taylor Dispersion) to calculate the Dispersion Coefficient for Taylor Expression, Dispersion using Taylor Expression formula is defined as Flow Models which are used in the situations, where the Bodenstein Number is less than 10^8 and Length vs Diameter of tube ratio is in range of 50-10^6. Dispersion Coefficient for Taylor Expression is denoted by D_p symbol.

How to calculate Dispersion using Taylor Expression Formula using this online calculator? To use this online calculator for Dispersion using Taylor Expression Formula, enter Velocity of Pulse for Taylor Expression (u_T), Diameter of Tube (d_Tube) & Diffusion Coefficient for Taylor Dispersion (D_{f T}) and hit the calculate button. Here is how the Dispersion using Taylor Expression Formula calculation can be explained with given input values -> 0.151579 = (5.2^2*0.971^2)/(192*0.00036).

FAQ

What is Dispersion using Taylor Expression Formula?

Dispersion using Taylor Expression formula is defined as Flow Models which are used in the situations, where the Bodenstein Number is less than 10^8 and Length vs Diameter of tube ratio is in range of 50-10^6 and is represented as D_p = (u_T^2*d_Tube^2)/(192*D_{f T}) or Dispersion Coefficient for Taylor Expression = (Velocity of Pulse for Taylor Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for Taylor Dispersion). Velocity of Pulse for Taylor Expression is the Velocity of the Tracer throughout the Reactor in the Taylor Regime, Diameter of Tube is the Outer Diameter of the Tube, where the Fluid is subjected to flow through it & Diffusion Coefficient for Taylor Dispersion is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.

How to calculate Dispersion using Taylor Expression Formula?

Dispersion using Taylor Expression formula is defined as Flow Models which are used in the situations, where the Bodenstein Number is less than 10^8 and Length vs Diameter of tube ratio is in range of 50-10^6 is calculated using Dispersion Coefficient for Taylor Expression = (Velocity of Pulse for Taylor Expression^2*Diameter of Tube^2)/(192*Diffusion Coefficient for Taylor Dispersion). To calculate Dispersion using Taylor Expression Formula, you need Velocity of Pulse for Taylor Expression (u_T), Diameter of Tube (d_Tube) & Diffusion Coefficient for Taylor Dispersion (D_{f T}). With our tool, you need to enter the respective value for Velocity of Pulse for Taylor Expression, Diameter of Tube & Diffusion Coefficient for Taylor Dispersion 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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