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Concentration using Dispersion where Dispersion Number less than 0.01 Formula

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The Concentration at Dispersion Number < 0.01 is the quantity of a solute that is contained in a particular quantity of solvent or solution, at Dispersion Model. Check FAQs

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'})})

C - Concentration at Dispersion Number < 0.01?D_p - Dispersion Coefficient at Dispersion Number < 0.01?u' - Velocity of Pulse for Dispersion Number <0.01?L' - Length of Spread for Dispersion Number <0.01?θ - Mean Residence Time?π - Archimedes' constant?

Concentration using Dispersion where Dispersion Number less than 0.01 Example

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Here is how the Concentration using Dispersion where Dispersion Number less than 0.01 equation looks like with Values.

Here is how the Concentration using Dispersion where Dispersion Number less than 0.01 equation looks like with Units.

Here is how the Concentration using Dispersion where Dispersion Number less than 0.01 equation looks like.

12.0389 = \frac{1}{2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085}{40 \cdot 0.92})}} \cdot \exp (- \frac{{(1 - 0.98)}^{2}}{4 \cdot (\frac{0.0085}{40 \cdot 0.92})})

12.0389mol/m³ = \frac{1}{2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})}} \cdot \exp (- \frac{{(1 - 0.98s)}^{2}}{4 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})})

12.0389 = \frac{1}{2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085}{40 \cdot 0.92})}} \cdot \exp (- \frac{{(1 - 0.98)}^{2}}{4 \cdot (\frac{0.0085}{40 \cdot 0.92})})

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Concentration using Dispersion where Dispersion Number less than 0.01 Solution

Follow our step by step solution on how to calculate Concentration using Dispersion where Dispersion Number less than 0.01?

FIRST Step Consider the formula

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'})})

Next Step Substitute values of Variables

∴

C = \frac{1}{2 \cdot \sqrt{π \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})}} \cdot \exp (- \frac{{(1 - 0.98s)}^{2}}{4 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})})

Next Step Substitute values of Constants

∴

C = \frac{1}{2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})}} \cdot \exp (- \frac{{(1 - 0.98s)}^{2}}{4 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})})

Next Step Prepare to Evaluate

∴

C = \frac{1}{2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085}{40 \cdot 0.92})}} \cdot \exp (- \frac{{(1 - 0.98)}^{2}}{4 \cdot (\frac{0.0085}{40 \cdot 0.92})})

Next Step Evaluate

∴

C = 12.0388651690385mol/m³

LAST Step Rounding Answer

∴

C = 12.0389mol/m³

Concentration using Dispersion where Dispersion Number less than 0.01 Formula Elements

Variables

Constants

Functions

Concentration at Dispersion Number < 0.01

The Concentration at Dispersion Number < 0.01 is the quantity of a solute that is contained in a particular quantity of solvent or solution, at Dispersion Model.

Symbol: C

Measurement: Molar ConcentrationUnit: mol/m³

Note: Value should be greater than 0.

Formulas to find Concentration at 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

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

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

Mean Residence Time

Mean Residence Time is the ratio of Time and Mean Pulse Curve.

Symbol: θ

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Mean Residence Time

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 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'}))}

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 Concentration using Dispersion where Dispersion Number less than 0.01?

Concentration using Dispersion where Dispersion Number less than 0.01 evaluator uses Concentration at Dispersion Number < 0.01 = 1/(2*sqrt(pi*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01))))*exp(-(1-Mean Residence Time)^2/(4*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01)))) to evaluate the Concentration at Dispersion Number < 0.01, Concentration using Dispersion where Dispersion number less than 0.01 formula is defined as Relationship between the Dispersion Number and the dimensionless number E curve for small extent of Dispersion. Concentration at Dispersion Number < 0.01 is denoted by C symbol.

How to evaluate Concentration using Dispersion where Dispersion Number less than 0.01 using this online evaluator? To use this online evaluator for Concentration using Dispersion where Dispersion Number less than 0.01, enter Dispersion Coefficient at Dispersion Number < 0.01 (D_p), Velocity of Pulse for Dispersion Number <0.01 (u'), Length of Spread for Dispersion Number <0.01 (L') & Mean Residence Time (θ) and hit the calculate button.

FAQs on Concentration using Dispersion where Dispersion Number less than 0.01

What is the formula to find Concentration using Dispersion where Dispersion Number less than 0.01?

The formula of Concentration using Dispersion where Dispersion Number less than 0.01 is expressed as Concentration at Dispersion Number < 0.01 = 1/(2*sqrt(pi*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01))))*exp(-(1-Mean Residence Time)^2/(4*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01)))). Here is an example- 12.03887 = 1/(2*sqrt(pi*(0.0085/(40*0.92))))*exp(-(1-0.98)^2/(4*(0.0085/(40*0.92)))).

How to calculate Concentration using Dispersion where Dispersion Number less than 0.01?

With Dispersion Coefficient at Dispersion Number < 0.01 (D_p), Velocity of Pulse for Dispersion Number <0.01 (u'), Length of Spread for Dispersion Number <0.01 (L') & Mean Residence Time (θ) we can find Concentration using Dispersion where Dispersion Number less than 0.01 using the formula - Concentration at Dispersion Number < 0.01 = 1/(2*sqrt(pi*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01))))*exp(-(1-Mean Residence Time)^2/(4*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01)))). This formula also uses Archimedes' constant and , Exponential Growth (exp), Square Root (sqrt) function(s).

Can the Concentration using Dispersion where Dispersion Number less than 0.01 be negative?

No, the Concentration using Dispersion where Dispersion Number less than 0.01, measured in Molar Concentration cannot be negative.

Which unit is used to measure Concentration using Dispersion where Dispersion Number less than 0.01?

Concentration using Dispersion where Dispersion Number less than 0.01 is usually measured using the Mole per Cubic Meter[mol/m³] for Molar Concentration. Mole per Liter[mol/m³], Mole per Cubic Millimeter[mol/m³], Kilomole per Cubic Meter[mol/m³] are the few other units in which Concentration using Dispersion where Dispersion Number less than 0.01 can be measured.

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Concentration using Dispersion where Dispersion Number less than 0.01 Formula

Concentration using Dispersion where Dispersion Number less than 0.01 Example

Concentration using Dispersion where Dispersion Number less than 0.01 Solution

Concentration using Dispersion where Dispersion Number less than 0.01 Formula Elements

Other formulas in Dispersion Model category

How to Evaluate Concentration using Dispersion where Dispersion Number less than 0.01?

FAQs on Concentration using Dispersion where Dispersion Number less than 0.01

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