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

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The Length of Spread for Small Extents provides Information about how far and how fast the Spread Propagates. Check FAQs

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

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

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

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

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

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

1.3E-5 = \frac{2.4E-7 \cdot ({0.981}^{3})}{2 \cdot 0.0085}

1.3E-5m = \frac{2.4E-7 \cdot ({0.981m/s}^{3})}{2 \cdot 0.0085m²/s}

1.3E-5 = \frac{2.4E-7 \cdot ({0.981}^{3})}{2 \cdot 0.0085}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = \frac{2.4E-7 \cdot ({0.981m/s}^{3})}{2 \cdot 0.0085m²/s}

Next Step Prepare to Evaluate

∴

L = \frac{2.4E-7 \cdot ({0.981}^{3})}{2 \cdot 0.0085}

Next Step Evaluate

∴

L = 1.33281337552941E-05m

LAST Step Rounding Answer

∴

L = 1.3E-5m

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

Variables

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

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

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

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

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

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

The formula of Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion is expressed as 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). Here is an example- 1.3E-5 = (2.4E-07*(0.981^3))/(2*0.0085).

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

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

Can the Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion be negative?

No, the Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion, measured in Length cannot be negative.

Which unit is used to measure 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 is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length of Spread based on Variance of Spread of Tracer for Small Extents of Dispersion can be measured.

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

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

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

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

Other formulas in Dispersion Model category

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

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

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