Velocity of Pulse based on Variance of Spread of Tracer Calculator

✖Dispersion Coefficient at Dispersion Number > 100 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 > 100 [D_p']			+10% -10%
✖The Length of Spread of a Pulse provides Information about how far and how fast the Spread Propagates.ⓘ Length of Spread [l]			+10% -10%
✖Variance of Spread related to how much a Distribution or Concentration Profile spreads out from a Central Point.ⓘ Variance of Spread [σ²]			+10% -10%

✖Velocity of Pulse Measuring Variance is the Velocity at which a Pulse of Material or Information travels through a Process or a System.ⓘ Velocity of Pulse based on Variance of Spread of Tracer [u'']

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Formula

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Velocity of Pulse based on Variance of Spread of Tracer

Formula

`"u''" = (2*(("D"_{"p'"}*"l")/"σ"^{"2"}))^(1/3)`

Example

`"7.795034m/s"=(2*(("410m²/s"*"6.4m")/"11.08"))^(1/3)`

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Velocity of Pulse based on Variance of Spread of Tracer Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity of Pulse Measuring Variance = (2*((Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Variance of Spread))^(1/3)
u'' = (2*((D_p'*l)/σ²))^(1/3)
This formula uses 4 Variables

Variables Used

Velocity of Pulse Measuring Variance - (Measured in Meter per Second) - Velocity of Pulse Measuring Variance is the Velocity at which a Pulse of Material or Information travels through a Process or a System.
Dispersion Coefficient at Dispersion Number > 100 - (Measured in Square Meter Per Second) - Dispersion Coefficient at Dispersion Number > 100 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 - (Measured in Meter) - The Length of Spread of a Pulse provides Information about how far and how fast the Spread Propagates.
Variance of Spread - Variance of Spread related to how much a Distribution or Concentration Profile spreads out from a Central Point.

STEP 1: Convert Input(s) to Base Unit

Dispersion Coefficient at Dispersion Number > 100: 410 Square Meter Per Second --> 410 Square Meter Per Second No Conversion Required
Length of Spread: 6.4 Meter --> 6.4 Meter No Conversion Required
Variance of Spread: 11.08 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

u'' = (2*((D_p'*l)/σ²))^(1/3) --> (2*((410*6.4)/11.08))^(1/3)

Evaluating ... ...

u'' = 7.79503414678831

STEP 3: Convert Result to Output's Unit

7.79503414678831 Meter per Second --> No Conversion Required

FINAL ANSWER

7.79503414678831 ≈ 7.795034 Meter per Second <-- Velocity of Pulse Measuring Variance

(Calculation completed in 00.004 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)

Velocity of Pulse based on Variance of Spread of Tracer Formula

Velocity of Pulse Measuring Variance = (2*((Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Variance of Spread))^(1/3)
u'' = (2*((D_p'*l)/σ²))^(1/3)

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 Velocity of Pulse based on Variance of Spread of Tracer?

Velocity of Pulse based on Variance of Spread of Tracer calculator uses Velocity of Pulse Measuring Variance = (2*((Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Variance of Spread))^(1/3) to calculate the Velocity of Pulse Measuring Variance, The Velocity of Pulse based on Variance of Spread of Tracer formula is defined as Velocity of Tracer for Small Extents of Dispersion. Velocity of Pulse Measuring Variance is denoted by u'' symbol.

How to calculate Velocity of Pulse based on Variance of Spread of Tracer using this online calculator? To use this online calculator for Velocity of Pulse based on Variance of Spread of Tracer, enter Dispersion Coefficient at Dispersion Number > 100 (D_p'), Length of Spread (l) & Variance of Spread (σ²) and hit the calculate button. Here is how the Velocity of Pulse based on Variance of Spread of Tracer calculation can be explained with given input values -> 2796.367 = (2*((410*6.4)/11.08))^(1/3).

FAQ

What is Velocity of Pulse based on Variance of Spread of Tracer?

The Velocity of Pulse based on Variance of Spread of Tracer formula is defined as Velocity of Tracer for Small Extents of Dispersion and is represented as u'' = (2*((D_p'*l)/σ²))^(1/3) or Velocity of Pulse Measuring Variance = (2*((Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Variance of Spread))^(1/3). Dispersion Coefficient at Dispersion Number > 100 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 of a Pulse provides Information about how far and how fast the Spread Propagates & Variance of Spread related to how much a Distribution or Concentration Profile spreads out from a Central Point.

How to calculate Velocity of Pulse based on Variance of Spread of Tracer?

The Velocity of Pulse based on Variance of Spread of Tracer formula is defined as Velocity of Tracer for Small Extents of Dispersion is calculated using Velocity of Pulse Measuring Variance = (2*((Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Variance of Spread))^(1/3). To calculate Velocity of Pulse based on Variance of Spread of Tracer, you need Dispersion Coefficient at Dispersion Number > 100 (D_p'), Length of Spread (l) & Variance of Spread (σ²). With our tool, you need to enter the respective value for Dispersion Coefficient at Dispersion Number > 100, Length of Spread & Variance of Spread 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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