Exit Age Distribution based on Dispersion Number Calculator

✖Velocity of Pulse Measuring Variance is the Velocity at which a Pulse of Material or Information travels through a Process or a System.ⓘ Velocity of Pulse Measuring Variance [u'']			+10% -10%
✖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.ⓘ Dispersion Coefficient at Dispersion Number > 100 [D_p']			+10% -10%
✖The Length of Spread of a Pulse provides Information about how far and how fast the Spread Propagates.ⓘ Length of Spread [l]			+10% -10%
✖Time Required for Change in Concentration is the Time Spent by the Tracer in the Reactor.ⓘ Time Required for Change in Concentration [Δt]			+10% -10%

✖Exit Age Distribution is the Measure of the Stream of the Fluid Leaving Vessel.ⓘ Exit Age Distribution based on Dispersion Number [E]

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Formula

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Exit Age Distribution based on Dispersion Number

Formula

`"E" = sqrt("u''"^3/(4*pi*"D"_{"p'"}*"l"))*exp(-("l"-("u''"*"Δt"))^2/(4*("D"_{"p'"}*"l")/"u''"))`

Example

`"0.119409/s"=sqrt(("7.8m/s")^3/(4*pi*"410m²/s"*"6.4m"))*exp(-("6.4m"-("7.8m/s"*"0.5s"))^2/(4*("410m²/s"*"6.4m")/"7.8m/s"))`

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Exit Age Distribution based on Dispersion Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
E = sqrt(u''^3/(4*pi*D_p'*l))*exp(-(l-(u''*Δt))^2/(4*(D_p'*l)/u''))
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

Exit Age Distribution - (Measured in 1 Per Second) - Exit Age Distribution is the Measure of the Stream of the Fluid Leaving Vessel.
Velocity of Pulse Measuring Variance - (Measured in Meter per Second) - Velocity of Pulse Measuring Variance is the Velocity at which a Pulse of Material or Information travels through a Process or a System.
Dispersion Coefficient at Dispersion Number > 100 - (Measured in Square Meter Per Second) - 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.
Length of Spread - (Measured in Meter) - The Length of Spread of a Pulse provides Information about how far and how fast the Spread Propagates.
Time Required for Change in Concentration - (Measured in Second) - Time Required for Change in Concentration is the Time Spent by the Tracer in the Reactor.

STEP 1: Convert Input(s) to Base Unit

Velocity of Pulse Measuring Variance: 7.8 Meter per Second --> 7.8 Meter per Second No Conversion Required
Dispersion Coefficient at Dispersion Number > 100: 410 Square Meter Per Second --> 410 Square Meter Per Second No Conversion Required
Length of Spread: 6.4 Meter --> 6.4 Meter No Conversion Required
Time Required for Change in Concentration: 0.5 Second --> 0.5 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = sqrt(u''^3/(4*pi*D_p'*l))*exp(-(l-(u''*Δt))^2/(4*(D_p'*l)/u'')) --> sqrt(7.8^3/(4*pi*410*6.4))*exp(-(6.4-(7.8*0.5))^2/(4*(410*6.4)/7.8))

Evaluating ... ...

E = 0.119409236368224

STEP 3: Convert Result to Output's Unit

0.119409236368224 1 Per Second --> No Conversion Required

FINAL ANSWER

0.119409236368224 ≈ 0.119409 1 Per Second <-- Exit Age Distribution

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Chemical Reaction Engineering » Flow Pattern, Contacting and Non Ideal Flow » Dispersion Model » Exit Age Distribution based on Dispersion Number

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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)

Exit Age Distribution based on Dispersion Number Formula

What is Exit Age Distribution ?

The Exit Age Distribution, also known asresidence-time distribution (RTD) of a reactor is a characteristic of the mixing that occurs in the chemical reactor.

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.

How to Calculate Exit Age Distribution based on Dispersion Number?

Exit Age Distribution based on Dispersion Number calculator uses 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)) to calculate the Exit Age Distribution, The Exit Age Distribution based on Dispersion Number formula is defined as product of Mean of C pulse and Exit Age Distribution. Exit Age Distribution is denoted by E symbol.

How to calculate Exit Age Distribution based on Dispersion Number using this online calculator? To use this online calculator for Exit Age Distribution based on Dispersion Number, enter Velocity of Pulse Measuring Variance (u''), Dispersion Coefficient at Dispersion Number > 100 (D_p'), Length of Spread (l) & Time Required for Change in Concentration (Δt) and hit the calculate button. Here is how the Exit Age Distribution based on Dispersion Number calculation can be explained with given input values -> 0.119409 = sqrt(7.8^3/(4*pi*410*6.4))*exp(-(6.4-(7.8*0.5))^2/(4*(410*6.4)/7.8)).

FAQ

What is Exit Age Distribution based on Dispersion Number?

The Exit Age Distribution based on Dispersion Number formula is defined as product of Mean of C pulse and Exit Age Distribution and is represented as E = sqrt(u''^3/(4*pi*D_p'*l))*exp(-(l-(u''*Δt))^2/(4*(D_p'*l)/u'')) or 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)). Velocity of Pulse Measuring Variance is the Velocity at which a Pulse of Material or Information travels through a Process or a System, 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, The Length of Spread of a Pulse provides Information about how far and how fast the Spread Propagates & Time Required for Change in Concentration is the Time Spent by the Tracer in the Reactor.

How to calculate Exit Age Distribution based on Dispersion Number?

The Exit Age Distribution based on Dispersion Number formula is defined as product of Mean of C pulse and Exit Age Distribution is calculated using 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)). To calculate Exit Age Distribution based on Dispersion Number, you need Velocity of Pulse Measuring Variance (u''), Dispersion Coefficient at Dispersion Number > 100 (D_p'), Length of Spread (l) & Time Required for Change in Concentration (Δt). With our tool, you need to enter the respective value for Velocity of Pulse Measuring Variance, Dispersion Coefficient at Dispersion Number > 100, Length of Spread & Time Required for Change in Concentration 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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