Length of Spread based on Variance of Spread of Tracer for 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%
✖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 at Dispersion Number < 0.01 [D_p]			+10% -10%

✖The Length of Spread for Small Extents provides Information about how far and how fast the Spread Propagates.ⓘ Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion [L]

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

Formula

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

Example

`"1.3E^-5m"=("2.4E^-7"*(("0.981m/s")^3))/(2*"0.0085m²/s")`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
L = (σ²*(u^3))/(2*D_p)
This formula uses 4 Variables

Variables Used

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.
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.
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.

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
Dispersion Coefficient at Dispersion Number < 0.01: 0.0085 Square Meter Per Second --> 0.0085 Square Meter Per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (σ²*(u^3))/(2*D_p) --> (2.4E-07*(0.981^3))/(2*0.0085)

Evaluating ... ...

L = 1.33281337552941E-05

STEP 3: Convert Result to Output's Unit

1.33281337552941E-05 Meter --> No Conversion Required

FINAL ANSWER

1.33281337552941E-05 ≈ 1.3E-5 Meter <-- Length of Spread for Small Extents

(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)

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

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)
L = (σ²*(u^3))/(2*D_p)

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

Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion calculator uses 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) to calculate the Length of Spread for Small Extents, The Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion formula is defined as Length of Spread of Tracer in the Reactor, if D/uL < 0.01. Length of Spread for Small Extents is denoted by L symbol.

How to calculate Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion using this online calculator? To use this online calculator for Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion, enter Variance of Spread for Dispersion Number <0.01 (σ²), Velocity of Pulse (u) & Dispersion Coefficient at Dispersion Number < 0.01 (D_p) and hit the calculate button. Here is how the Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion calculation can be explained with given input values -> 1.3E-5 = (2.4E-07*(0.981^3))/(2*0.0085).

FAQ

What is Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion?

The Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion formula is defined as Length of Spread of Tracer in the Reactor, if D/uL < 0.01 and is represented as L = (σ²*(u^3))/(2*D_p) or 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). 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 & 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.

How to calculate Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion?

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

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

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

Credits

< 9 Dispersion Model Calculators

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

What is σ2 ?

What is Dispersion Number ?

How to Calculate Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion?

FAQ

What is σ² ?