Concentration using Dispersion where Dispersion Number less than 0.01 Calculator

✖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.ⓘ Dispersion Coefficient at Dispersion Number < 0.01 [D_p]			+10% -10%
✖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.ⓘ Velocity of Pulse for Dispersion Number <0.01 [u']			+10% -10%
✖The Length of Spread for Dispersion Number <0.01 of a Pulse provides Information about how far and how fast the Spread Propagates.ⓘ Length of Spread for Dispersion Number <0.01 [L']			+10% -10%
✖Mean Residence Time is the ratio of Time and Mean Pulse Curve.ⓘ Mean Residence Time [θ]			+10% -10%

✖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.ⓘ Concentration using Dispersion where Dispersion Number less than 0.01 [C]

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Concentration using Dispersion where Dispersion Number less than 0.01

Formula

`"C" = 1/(2*sqrt(pi*("D"_{"p"}/("u'"*"L'"))))*exp(-(1-"θ")^2/(4*("D"_{"p"}/("u'"*"L'"))))`

Example

`"12.03887mol/m³"=1/(2*sqrt(pi*("0.0085m²/s"/("40m/s"*"0.92m"))))*exp(-(1-"0.98s")^2/(4*("0.0085m²/s"/("40m/s"*"0.92m"))))`

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Concentration using Dispersion where Dispersion Number less than 0.01 Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
C = 1/(2*sqrt(pi*(D_p/(u'*L'))))*exp(-(1-θ)^2/(4*(D_p/(u'*L'))))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., 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., sqrt(Number)

Variables Used

Concentration at Dispersion Number < 0.01 - (Measured in Mole per Cubic Meter) - 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.
Dispersion Coefficient at Dispersion Number < 0.01 - (Measured in Square Meter Per Second) - 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.
Velocity of Pulse for Dispersion Number <0.01 - (Measured in Meter per Second) - 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.
Length of Spread for Dispersion Number <0.01 - (Measured in Meter) - The Length of Spread for Dispersion Number <0.01 of a Pulse provides Information about how far and how fast the Spread Propagates.
Mean Residence Time - (Measured in Second) - Mean Residence Time is the ratio of Time and Mean Pulse Curve.

STEP 1: Convert Input(s) to Base Unit

Dispersion Coefficient at Dispersion Number < 0.01: 0.0085 Square Meter Per Second --> 0.0085 Square Meter Per Second No Conversion Required
Velocity of Pulse for Dispersion Number <0.01: 40 Meter per Second --> 40 Meter per Second No Conversion Required
Length of Spread for Dispersion Number <0.01: 0.92 Meter --> 0.92 Meter No Conversion Required
Mean Residence Time: 0.98 Second --> 0.98 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = 1/(2*sqrt(pi*(D_p/(u'*L'))))*exp(-(1-θ)^2/(4*(D_p/(u'*L')))) --> 1/(2*sqrt(pi*(0.0085/(40*0.92))))*exp(-(1-0.98)^2/(4*(0.0085/(40*0.92))))

Evaluating ... ...

C = 12.0388651690385

STEP 3: Convert Result to Output's Unit

12.0388651690385 Mole per Cubic Meter --> No Conversion Required

FINAL ANSWER

12.0388651690385 ≈ 12.03887 Mole per Cubic Meter <-- Concentration at Dispersion Number < 0.01

(Calculation completed in 00.004 seconds)

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< 9 Dispersion Model Calculators

Exit Age Distribution based on Dispersion Number

Go Exit Age Distribution = sqrt(Velocity of Pulse Measuring Variance^3/(4*pi*Dispersion Coefficient at Dispersion Number > 100*Length of Spread))*exp(-(Length of Spread-(Velocity of Pulse Measuring Variance*Time Required for Change in Concentration))^2/(4*(Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Velocity of Pulse Measuring Variance))

Mean Residence Time where Dispersion Number is less than 0.01

Go Mean Residence Time = 1+sqrt((ln(Concentration of Solution*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))))*4*(Dispersion Coefficient at Dispersion Number < 0.01/(Velocity of Pulse for Dispersion Number <0.01*Length of Spread for Dispersion Number <0.01))))

Concentration using Dispersion where Dispersion Number less than 0.01

Go 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))))

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

Go 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)))

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

Go 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)))

Variance of Spread of Tracer for Small Extents of Dispersion

Go Variance of Spread for Dispersion Number <0.01 = 2*(Dispersion Coefficient at Dispersion Number < 0.01*Length of Spread for Dispersion Number <0.01/Velocity of Pulse for Dispersion Number <0.01^3)

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

Go 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))

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

Go 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)

Velocity of Pulse based on Variance of Spread of Tracer

Go Velocity of Pulse Measuring Variance = (2*((Dispersion Coefficient at Dispersion Number > 100*Length of Spread)/Variance of Spread))^(1/3)

Concentration using Dispersion where Dispersion Number less than 0.01 Formula

What is Dispersion Number ?

Suppose an ideal pulse of tracer is introduced into the fluid entering a vessel. The pulse spreads as it passes through the vessel, and to characterize the spreading according to this model, we assume a diffusion-like process superimposed on plug flow. We call this dispersion or longitudinal dispersion to distinguish it from molecular diffusion. The dispersion coefficient D represents this spreading process.

What is θ ?

θ, Mean Residence Time, is the ratio between time and the mean of C_pulse curve.

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

Concentration using Dispersion where Dispersion Number less than 0.01 calculator 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 calculate 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 calculate Concentration using Dispersion where Dispersion Number less than 0.01 using this online calculator? To use this online calculator 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. Here is how the Concentration using Dispersion where Dispersion Number less than 0.01 calculation can be explained with given input values -> 12.03887 = 1/(2*sqrt(pi*(0.0085/(40*0.92))))*exp(-(1-0.98)^2/(4*(0.0085/(40*0.92)))).

FAQ

What is Concentration using Dispersion where Dispersion Number less than 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 and is represented as C = 1/(2*sqrt(pi*(D_p/(u'*L'))))*exp(-(1-θ)^2/(4*(D_p/(u'*L')))) or 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)))). 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, 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, The Length of Spread for Dispersion Number <0.01 of a Pulse provides Information about how far and how fast the Spread Propagates & Mean Residence Time is the ratio of Time and Mean Pulse Curve.

How to calculate Concentration using Dispersion where Dispersion Number less than 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 is calculated using 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 calculate Concentration using Dispersion where Dispersion Number less than 0.01, you need 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). With our tool, you need to enter the respective value for Dispersion Coefficient at Dispersion Number < 0.01, Velocity of Pulse for Dispersion Number <0.01, Length of Spread for Dispersion Number <0.01 & Mean Residence Time and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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