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Variance of Spread of Tracer for Small Extents of Dispersion Formula

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Variance of Spread for Dispersion Number <0.01 related to how much a Distribution or Concentration Profile spreads out from a Central Point. Check FAQs

σ 2 = 2 \cdot (D p \cdot \frac{L'}{{u'}^{3}})

σ² - Variance of Spread for Dispersion Number <0.01?D_p - Dispersion Coefficient at Dispersion Number < 0.01?L' - Length of Spread for Dispersion Number <0.01?u' - Velocity of Pulse for Dispersion Number <0.01?

Variance of Spread of Tracer for Small Extents of Dispersion Example

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Here is how the Variance of Spread of Tracer for Small Extents of Dispersion equation looks like with Values.

Here is how the Variance of Spread of Tracer for Small Extents of Dispersion equation looks like with Units.

Here is how the Variance of Spread of Tracer for Small Extents of Dispersion equation looks like.

2.4E-7 = 2 \cdot (0.0085 \cdot \frac{0.92}{40^{3}})

2.4E-7 = 2 \cdot (0.0085m²/s \cdot \frac{0.92m}{{40m/s}^{3}})

2.4E-7 = 2 \cdot (0.0085 \cdot \frac{0.92}{40^{3}})

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Variance of Spread of Tracer for Small Extents of Dispersion Solution

Follow our step by step solution on how to calculate Variance of Spread of Tracer for Small Extents of Dispersion?

FIRST Step Consider the formula

σ 2 = 2 \cdot (D p \cdot \frac{L'}{{u'}^{3}})

Next Step Substitute values of Variables

∴

σ 2 = 2 \cdot (0.0085m²/s \cdot \frac{0.92m}{{40m/s}^{3}})

Next Step Prepare to Evaluate

∴

σ 2 = 2 \cdot (0.0085 \cdot \frac{0.92}{40^{3}})

Next Step Evaluate

∴

σ 2 = 2.44375E-07

LAST Step Rounding Answer

∴

σ 2 = 2.4E-7

Variance of Spread of Tracer for Small Extents of Dispersion Formula Elements

Variables

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.

Symbol: σ²

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Variance of Spread for Dispersion Number <0.01

Dispersion Coefficient at Dispersion Number < 0.01

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.

Symbol: D_p

Measurement: DiffusivityUnit: m²/s

Note: Value should be greater than 0.

Formulas to find Dispersion Coefficient at Dispersion Number < 0.01

Length of Spread for Dispersion Number <0.01

The Length of Spread for Dispersion Number <0.01 of a Pulse provides Information about how far and how fast the Spread Propagates.

Symbol: L'

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Spread for Dispersion Number <0.01

Velocity of Pulse for Dispersion Number <0.01

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.

Symbol: u'

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity of Pulse for Dispersion Number <0.01

Other formulas in Dispersion Model category

Go Concentration using Dispersion where Dispersion Number less than 0.01

C = \frac{1}{2 \cdot \sqrt{π \cdot (\frac{D p}{u' \cdot L'})}} \cdot \exp (- \frac{{(1 - θ)}^{2}}{4 \cdot (\frac{D p}{u' \cdot L'})})

Go Exit Age Distribution based on Dispersion Number

E = \sqrt{\frac{{u''}^{3}}{4 \cdot π \cdot D p' \cdot l}} \cdot \exp (- \frac{{(l - (u'' \cdot Δt))}^{2}}{4 \cdot \frac{D p' \cdot l}{u''}})

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

S.D L.D = \sqrt{2 \cdot (\frac{D p'}{l \cdot u}) - 2 \cdot ({(\frac{D p'}{u \cdot l})}^{2}) \cdot (1 - \exp (- \frac{u \cdot l}{D p'}))}

Go Mean Residence Time where Dispersion Number is less than 0.01

θ = 1 + \sqrt{(\ln (c \cdot 2 \cdot \sqrt{π \cdot (\frac{D p}{u' \cdot L'})}) \cdot 4 \cdot (\frac{D p}{u' \cdot L'}))}

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

Variance of Spread of Tracer for Small Extents of Dispersion evaluator 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 evaluate 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 evaluate Variance of Spread of Tracer for Small Extents of Dispersion using this online evaluator? To use this online evaluator 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.

FAQs on Variance of Spread of Tracer for Small Extents of Dispersion

What is the formula to find Variance of Spread of Tracer for Small Extents of Dispersion?

The formula of Variance of Spread of Tracer for Small Extents of Dispersion is expressed as 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). Here is an example- 2.4E-7 = 2*(0.0085*0.92/40^3).

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

With 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') we can find Variance of Spread of Tracer for Small Extents of Dispersion using the formula - 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).

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Variance of Spread of Tracer for Small Extents of Dispersion Formula

Variance of Spread of Tracer for Small Extents of Dispersion Example

Variance of Spread of Tracer for Small Extents of Dispersion Solution

Variance of Spread of Tracer for Small Extents of Dispersion Formula Elements

Other formulas in Dispersion Model category

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

FAQs on Variance of Spread of Tracer for Small Extents of Dispersion

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