FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

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

Fx Copy

LaTeX Copy

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

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'}))}

S.D_L.D - Standard Deviation based on θ at Large Deviations?D_p' - Dispersion Coefficient at Dispersion Number > 100?l - Length of Spread?u - Velocity of Pulse?

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

With values

With units

Only example

Here is how the Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion equation looks like with Values.

Here is how the Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion equation looks like with Units.

Here is how the Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion equation looks like.

0.9975 = \sqrt{2 \cdot (\frac{410}{6.4 \cdot 0.981}) - 2 \cdot ({(\frac{410}{0.981 \cdot 6.4})}^{2}) \cdot (1 - \exp (- \frac{0.981 \cdot 6.4}{410}))}

0.9975 = \sqrt{2 \cdot (\frac{410m²/s}{6.4m \cdot 0.981m/s}) - 2 \cdot ({(\frac{410m²/s}{0.981m/s \cdot 6.4m})}^{2}) \cdot (1 - \exp (- \frac{0.981m/s \cdot 6.4m}{410m²/s}))}

0.9975 = \sqrt{2 \cdot (\frac{410}{6.4 \cdot 0.981}) - 2 \cdot ({(\frac{410}{0.981 \cdot 6.4})}^{2}) \cdot (1 - \exp (- \frac{0.981 \cdot 6.4}{410}))}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Chemical Engineering » Category

Chemical Reaction Engineering » fx Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion

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

Follow our step by step solution on how to calculate Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion?

FIRST Step Consider the formula

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'}))}

Next Step Substitute values of Variables

∴

S.D L.D = \sqrt{2 \cdot (\frac{410m²/s}{6.4m \cdot 0.981m/s}) - 2 \cdot ({(\frac{410m²/s}{0.981m/s \cdot 6.4m})}^{2}) \cdot (1 - \exp (- \frac{0.981m/s \cdot 6.4m}{410m²/s}))}

Next Step Prepare to Evaluate

∴

S.D L.D = \sqrt{2 \cdot (\frac{410}{6.4 \cdot 0.981}) - 2 \cdot ({(\frac{410}{0.981 \cdot 6.4})}^{2}) \cdot (1 - \exp (- \frac{0.981 \cdot 6.4}{410}))}

Next Step Evaluate

∴

S.D L.D = 0.997454305299735

LAST Step Rounding Answer

∴

S.D L.D = 0.9975

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

Variables

Functions

Standard Deviation based on θ at Large Deviations

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

Symbol: S.D_L.D

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation based on θ at Large Deviations

Dispersion Coefficient at Dispersion Number > 100

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.

Symbol: D_p'

Measurement: DiffusivityUnit: m²/s

Note: Value should be greater than 0.

Formulas to find Dispersion Coefficient at Dispersion Number > 100

Length of Spread

The Length of Spread 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

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

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

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

Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion evaluator uses 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))) to evaluate the Standard Deviation based on θ at Large Deviations, Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion formula is defined as Measure of how much the concentration profile of the tracer widens or spreads out over time and space. It's often characterized by a Dispersion Coefficient, which can be considered analogous to the Variance in Statistics. Standard Deviation based on θ at Large Deviations is denoted by S.D_L.D symbol.

How to evaluate Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion using this online evaluator? To use this online evaluator for Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion, enter Dispersion Coefficient at Dispersion Number > 100 (D_p'), Length of Spread (l) & Velocity of Pulse (u) and hit the calculate button.

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

What is the formula to find Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion?

The formula of Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion is expressed as 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))). Here is an example- 0.905919 = sqrt(2*(410/(6.4*0.981))-2*((410/(0.981*6.4))^2)*(1-exp(-(0.981*6.4)/410))).

How to calculate Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion?

With Dispersion Coefficient at Dispersion Number > 100 (D_p'), Length of Spread (l) & Velocity of Pulse (u) we can find Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion using the formula - 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))). This formula also uses Exponential Growth (exp), Square Root (sqrt) function(s).

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

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

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

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

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

Other formulas in Dispersion Model category

How to Evaluate Standard Deviation of Tracer based on Mean Residence Time for Large Deviations of Dispersion?

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

Variable Name