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Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion Formula

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Standard Deviation based on θ at Small Extents is Calculated using Mean of Pulse Curve and Dispersion Number, which is measure of Spread of Tracer. Check FAQs

S.D S.E = \sqrt{2 \cdot (\frac{D p}{L' \cdot u'})}

S.D_S.E - Standard Deviation based on θ at Small Extents?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?

Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion Example

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Here is how the Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion equation looks like with Values.

Here is how the Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion equation looks like with Units.

Here is how the Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion equation looks like.

0.0215 = \sqrt{2 \cdot (\frac{0.0085}{0.92 \cdot 40})}

0.0215 = \sqrt{2 \cdot (\frac{0.0085m²/s}{0.92m \cdot 40m/s})}

0.0215 = \sqrt{2 \cdot (\frac{0.0085}{0.92 \cdot 40})}

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Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion Solution

Follow our step by step solution on how to calculate Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion?

FIRST Step Consider the formula

S.D S.E = \sqrt{2 \cdot (\frac{D p}{L' \cdot u'})}

Next Step Substitute values of Variables

∴

S.D S.E = \sqrt{2 \cdot (\frac{0.0085m²/s}{0.92m \cdot 40m/s})}

Next Step Prepare to Evaluate

∴

S.D S.E = \sqrt{2 \cdot (\frac{0.0085}{0.92 \cdot 40})}

Next Step Evaluate

∴

S.D S.E = 0.0214931738405274

LAST Step Rounding Answer

∴

S.D S.E = 0.0215

Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion Formula Elements

Variables

Functions

Standard Deviation based on θ at Small Extents

Standard Deviation based on θ at Small Extents is Calculated using Mean of Pulse Curve and Dispersion Number, which is measure of Spread of Tracer.

Symbol: S.D_S.E

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation based on θ at Small Extents

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion?

Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion evaluator uses 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))) to evaluate the Standard Deviation based on θ at Small Extents, Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion formula is defined as Square Root of Measure of Spread of Tracer in the Reactor, based on Mean Residence Time. Standard Deviation based on θ at Small Extents is denoted by S.D_S.E symbol.

How to evaluate Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion using this online evaluator? To use this online evaluator for Standard Deviation of Spread based on Mean Residence Time 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 Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion

What is the formula to find Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion?

The formula of Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion is expressed as 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))). Here is an example- 0.021493 = sqrt(2*(0.0085/(0.92*40))).

How to calculate Standard Deviation of Spread based on Mean Residence Time 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 Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion using the formula - 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))). This formula also uses Square Root (sqrt) function(s).

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Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion Formula

Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion Example

Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion Solution

Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion Formula Elements

Other formulas in Dispersion Model category

How to Evaluate Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion?

FAQs on Standard Deviation of Spread based on Mean Residence Time for Small Extents of Dispersion

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