Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion Calculator

✖Variance of Spread for Dispersion Number <0.01 related to how much a Distribution or Concentration Profile spreads out from a Central Point.ⓘ Variance of Spread for Dispersion Number <0.01 [σ²]			+10% -10%
✖Velocity of Pulse is the Velocity at which a Pulse of Material or Information travels through a Process or a System.ⓘ Velocity of Pulse [u]			+10% -10%
✖The Length of Spread for Small Extents provides Information about how far and how fast the Spread Propagates.ⓘ Length of Spread for Small Extents [L]			+10% -10%

✖Dispersion Coefficient at Dispersion Number < 0.01 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 Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion [D_p]

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Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion

Formula

`"D"_{"p"} = ("σ"^{"2 "}*"u"_{" "}^3)/(2*("L"^{" "}))`

Example

`"0.008715m²/s"=("2.4E^-7"*("0.981m/s")^3)/(2*("1.3E^-5m"))`

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Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dispersion Coefficient at Dispersion Number < 0.01 = (Variance of Spread for Dispersion Number <0.01*Velocity of Pulse^3)/(2*(Length of Spread for Small Extents))
D_p = (σ²*u^3)/(2*(L))
This formula uses 4 Variables

Variables Used

Dispersion Coefficient at Dispersion Number < 0.01 - (Measured in Square Meter Per Second) - Dispersion Coefficient at Dispersion Number < 0.01 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.
Variance of Spread for Dispersion Number <0.01 - Variance of Spread for Dispersion Number <0.01 related to how much a Distribution or Concentration Profile spreads out from a Central Point.
Velocity of Pulse - (Measured in Meter per Second) - Velocity of Pulse is the Velocity at which a Pulse of Material or Information travels through a Process or a System.
Length of Spread for Small Extents - (Measured in Meter) - The Length of Spread for Small Extents provides Information about how far and how fast the Spread Propagates.

STEP 1: Convert Input(s) to Base Unit

Variance of Spread for Dispersion Number <0.01: 2.4E-07 --> No Conversion Required
Velocity of Pulse: 0.981 Meter per Second --> 0.981 Meter per Second No Conversion Required
Length of Spread for Small Extents: 1.3E-05 Meter --> 1.3E-05 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_p = (σ²*u^3)/(2*(L)) --> (2.4E-07*0.981^3)/(2*(1.3E-05))

Evaluating ... ...

D_p = 0.00871454899384615

STEP 3: Convert Result to Output's Unit

0.00871454899384615 Square Meter Per Second --> No Conversion Required

FINAL ANSWER

0.00871454899384615 ≈ 0.008715 Square Meter Per Second <-- Dispersion Coefficient at Dispersion Number < 0.01

(Calculation completed in 00.020 seconds)

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< 9 Dispersion Model Calculators

Exit Age Distribution based on Dispersion Number

Go Exit Age Distribution = sqrt(Velocity of Pulse Measuring Variance^3/(4*pi*Dispersion Coefficient at Dispersion Number > 100*Length of Spread))*exp(-(Length of Spread-(Velocity of Pulse Measuring Variance*Time Required for Change in Concentration))^2/(4*(Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Velocity of Pulse Measuring Variance))

Mean Residence Time where Dispersion Number is less than 0.01

Go Mean Residence Time = 1+sqrt((ln(Concentration of Solution*2*sqrt(pi*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01))))*4*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01))))

Concentration using Dispersion where Dispersion Number less than 0.01

Go Concentration at Dispersion Number < 0.01 = 1/(2*sqrt(pi*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01))))*exp(-(1-Mean Residence Time)^2/(4*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01))))

Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion

Go Standard Deviation based on θ at Large Deviations = sqrt(2*(Dispersion Coefficient at Dispersion Number > 100/(Length of Spread*Velocity of Pulse))-2*((Dispersion Coefficient at Dispersion Number > 100/(Velocity of Pulse*Length of Spread))^2)*(1-exp(-(Velocity of Pulse*Length of Spread)/Dispersion Coefficient at Dispersion Number > 100)))

Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion

Go Standard Deviation based on θ at Small Extents = sqrt(2*(Dispersion Coefficient at Dispersion Number < 0.01/(Length of Spread for Dispersion Number <0.01*Velocity of Pulse for Dispersion Number <0.01)))

Variance of Spread of Tracer for Small Extents of Dispersion

Go Variance of Spread for Dispersion Number <0.01 = 2*(Dispersion Coefficient at Dispersion Number < 0.01*Length of Spread for Dispersion Number <0.01/Velocity of Pulse for Dispersion Number <0.01^3)

Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion

Go Dispersion Coefficient at Dispersion Number < 0.01 = (Variance of Spread for Dispersion Number <0.01*Velocity of Pulse^3)/(2*(Length of Spread for Small Extents))

Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion

Go Length of Spread for Small Extents = (Variance of Spread for Dispersion Number <0.01*(Velocity of Pulse^3))/(2*Dispersion Coefficient at Dispersion Number < 0.01)

Velocity of Pulse based on Variance of Spread of Tracer

Go Velocity of Pulse Measuring Variance = (2*((Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Variance of Spread))^(1/3)

Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion Formula

Dispersion Coefficient at Dispersion Number < 0.01 = (Variance of Spread for Dispersion Number <0.01*Velocity of Pulse^3)/(2*(Length of Spread for Small Extents))
D_p = (σ²*u^3)/(2*(L))

What is σ2 ?

σ2 is the variance or the measure of the spread of the curve, which are directly linked to Dispersion Number.

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.

How to Calculate Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion?

Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion calculator uses Dispersion Coefficient at Dispersion Number < 0.01 = (Variance of Spread for Dispersion Number <0.01*Velocity of Pulse^3)/(2*(Length of Spread for Small Extents)) to calculate the Dispersion Coefficient at Dispersion Number < 0.01, The Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion formula is defined as Dispersion of Spread of Tracer in the Reactor, if D/uL is less than 0.01. Dispersion Coefficient at Dispersion Number < 0.01 is denoted by D_p symbol.

How to calculate Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion using this online calculator? To use this online calculator for Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion, enter Variance of Spread for Dispersion Number <0.01 (σ²), Velocity of Pulse (u) & Length of Spread for Small Extents (L) and hit the calculate button. Here is how the Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion calculation can be explained with given input values -> 0.008715 = (2.4E-07*0.981^3)/(2*(1.3E-05)).

FAQ

What is Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion?

The Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion formula is defined as Dispersion of Spread of Tracer in the Reactor, if D/uL is less than 0.01 and is represented as D_p = (σ²*u^3)/(2*(L)) or Dispersion Coefficient at Dispersion Number < 0.01 = (Variance of Spread for Dispersion Number <0.01*Velocity of Pulse^3)/(2*(Length of Spread for Small Extents)). Variance of Spread for Dispersion Number <0.01 related to how much a Distribution or Concentration Profile spreads out from a Central Point, Velocity of Pulse is the Velocity at which a Pulse of Material or Information travels through a Process or a System & The Length of Spread for Small Extents provides Information about how far and how fast the Spread Propagates.

How to calculate Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion?

The Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion formula is defined as Dispersion of Spread of Tracer in the Reactor, if D/uL is less than 0.01 is calculated using Dispersion Coefficient at Dispersion Number < 0.01 = (Variance of Spread for Dispersion Number <0.01*Velocity of Pulse^3)/(2*(Length of Spread for Small Extents)). To calculate Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion, you need Variance of Spread for Dispersion Number <0.01 (σ²), Velocity of Pulse (u) & Length of Spread for Small Extents (L). With our tool, you need to enter the respective value for Variance of Spread for Dispersion Number <0.01, Velocity of Pulse & Length of Spread for Small Extents 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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