Variance of Spread of Tracer for Small Extents of Dispersion Calculator

✖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 Dispersion Number <0.01 of a Pulse provides Information about how far and how fast the Spread Propagates.ⓘ Length of Spread for Dispersion Number <0.01 [L']			+10% -10%
✖Velocity of Pulse for Dispersion Number <0.01 is the Velocity at which a Pulse of Material or Information travels through a Process or a System.ⓘ Velocity of Pulse for Dispersion Number <0.01 [u']			+10% -10%

✖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 of Tracer for Small Extents of Dispersion [σ²]

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Variance of Spread of Tracer for Small Extents of Dispersion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
Length of Spread for Dispersion Number <0.01 - (Measured in Meter) - The Length of Spread for Dispersion Number <0.01 of a Pulse provides Information about how far and how fast the Spread Propagates.
Velocity of Pulse for Dispersion Number <0.01 - (Measured in Meter per Second) - Velocity of Pulse for Dispersion Number <0.01 is the Velocity at which a Pulse of Material or Information travels through a Process or a System.

STEP 1: Convert Input(s) to Base Unit

Dispersion Coefficient at Dispersion Number < 0.01: 0.0085 Square Meter Per Second --> 0.0085 Square Meter Per Second No Conversion Required
Length of Spread for Dispersion Number <0.01: 0.92 Meter --> 0.92 Meter No Conversion Required
Velocity of Pulse for Dispersion Number <0.01: 40 Meter per Second --> 40 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ² = 2*(D_p*L'/u'^3) --> 2*(0.0085*0.92/40^3)

Evaluating ... ...

σ² = 2.44375E-07

STEP 3: Convert Result to Output's Unit

2.44375E-07 --> No Conversion Required

FINAL ANSWER

2.44375E-07 ≈ 2.4E-7 <-- Variance of Spread for Dispersion Number <0.01

(Calculation completed in 00.004 seconds)

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< Dispersion Model Calculators

Exit Age Distribution based on Dispersion Number

LaTeX 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))

Concentration using Dispersion where Dispersion Number less than 0.01

LaTeX 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

LaTeX 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)))

Variance of Spread of Tracer for Small Extents of Dispersion

LaTeX 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)

Variance of Spread of Tracer for Small Extents of Dispersion Formula

LaTeX Go

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 Variance of Spread of Tracer for Small Extents of Dispersion?

Variance of Spread of Tracer for Small Extents of Dispersion calculator uses 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) to calculate the Variance of Spread for Dispersion Number <0.01, Variance of Spread of Tracer for Small Extents of Dispersion formula is defined as Measure of Spread of Tracer in the Reactor. Variance of Spread for Dispersion Number <0.01 is denoted by σ² symbol.

How to calculate Variance of Spread of Tracer for Small Extents of Dispersion using this online calculator? To use this online calculator for Variance of Spread of Tracer for Small Extents of Dispersion, enter Dispersion Coefficient at Dispersion Number < 0.01 (D_p), Length of Spread for Dispersion Number <0.01 (L') & Velocity of Pulse for Dispersion Number <0.01 (u') and hit the calculate button. Here is how the Variance of Spread of Tracer for Small Extents of Dispersion calculation can be explained with given input values -> 2.4E-7 = 2*(0.0085*0.92/40^3).

FAQ

What is Variance of Spread of Tracer for Small Extents of Dispersion?

Variance of Spread of Tracer for Small Extents of Dispersion formula is defined as Measure of Spread of Tracer in the Reactor and is represented as σ² = 2*(D_p*L'/u'^3) or 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 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, The Length of Spread for Dispersion Number <0.01 of a Pulse provides Information about how far and how fast the Spread Propagates & Velocity of Pulse for Dispersion Number <0.01 is the Velocity at which a Pulse of Material or Information travels through a Process or a System.

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

Variance of Spread of Tracer for Small Extents of Dispersion formula is defined as Measure of Spread of Tracer in the Reactor is calculated using 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). To calculate Variance of Spread of Tracer for Small Extents of Dispersion, you need Dispersion Coefficient at Dispersion Number < 0.01 (D_p), Length of Spread for Dispersion Number <0.01 (L') & Velocity of Pulse for Dispersion Number <0.01 (u'). With our tool, you need to enter the respective value for Dispersion Coefficient at Dispersion Number < 0.01, Length of Spread for Dispersion Number <0.01 & Velocity of Pulse for 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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