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

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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. Check FAQs

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

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

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

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Here is how the Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion equation looks like with Values.

Here is how the Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion equation looks like with Units.

Here is how the Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion equation looks like.

0.0087 = \frac{2.4E-7 \cdot {0.981}^{3}}{2 \cdot (1.3E-5)}

0.0087m²/s = \frac{2.4E-7 \cdot {0.981m/s}^{3}}{2 \cdot (1.3E-5m)}

0.0087 = \frac{2.4E-7 \cdot {0.981}^{3}}{2 \cdot (1.3E-5)}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

D p = \frac{2.4E-7 \cdot {0.981m/s}^{3}}{2 \cdot (1.3E-5m)}

Next Step Prepare to Evaluate

∴

D p = \frac{2.4E-7 \cdot {0.981}^{3}}{2 \cdot (1.3E-5)}

Next Step Evaluate

∴

D p = 0.00871454899384615m²/s

LAST Step Rounding Answer

∴

D p = 0.0087m²/s

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

Variables

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

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

Velocity of Pulse

Velocity of Pulse 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

Length of Spread for Small Extents

The Length of Spread for Small Extents 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 Small Extents

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 Variance of Spread of Tracer for Small Extents of Dispersion

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

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'}))}

How to Evaluate 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 evaluator 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 evaluate 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 evaluate Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion?

The formula of Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion is expressed as 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)). Here is an example- 0.008715 = (2.4E-07*0.981^3)/(2*(1.3E-05)).

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

With Variance of Spread for Dispersion Number <0.01 (σ²), Velocity of Pulse (u) & Length of Spread for Small Extents (L) we can find Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion using the 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)).

Can the Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion be negative?

No, the Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion, measured in Diffusivity cannot be negative.

Which unit is used to measure 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 is usually measured using the Square Meter Per Second[m²/s] for Diffusivity. Square Centimeter Per Second[m²/s], Square Millimeter per Second[m²/s] are the few other units in which Dispersion Coefficient based on Variance of Spread of Tracer at Small Extents of Dispersion can be measured.

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

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

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

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

Other formulas in Dispersion Model category

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

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

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