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Exit Age Distribution based on Dispersion Number Formula

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Exit Age Distribution is the Measure of the Stream of the Fluid Leaving Vessel. Check FAQs

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''}})

E - Exit Age Distribution?u'' - Velocity of Pulse Measuring Variance?D_p' - Dispersion Coefficient at Dispersion Number > 100?l - Length of Spread?Δt - Time Required for Change in Concentration?π - Archimedes' constant?

Exit Age Distribution based on Dispersion Number Example

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Here is how the Exit Age Distribution based on Dispersion Number equation looks like with Values.

Here is how the Exit Age Distribution based on Dispersion Number equation looks like with Units.

Here is how the Exit Age Distribution based on Dispersion Number equation looks like.

0.1194 = \sqrt{\frac{{7.8}^{3}}{4 \cdot 3.1416 \cdot 410 \cdot 6.4}} \cdot \exp (- \frac{{(6.4 - (7.8 \cdot 0.5))}^{2}}{4 \cdot \frac{410 \cdot 6.4}{7.8}})

0.11941/s = \sqrt{\frac{{7.8m/s}^{3}}{4 \cdot 3.1416 \cdot 410m²/s \cdot 6.4m}} \cdot \exp (- \frac{{(6.4m - (7.8m/s \cdot 0.5s))}^{2}}{4 \cdot \frac{410m²/s \cdot 6.4m}{7.8m/s}})

0.1194 = \sqrt{\frac{{7.8}^{3}}{4 \cdot 3.1416 \cdot 410 \cdot 6.4}} \cdot \exp (- \frac{{(6.4 - (7.8 \cdot 0.5))}^{2}}{4 \cdot \frac{410 \cdot 6.4}{7.8}})

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Exit Age Distribution based on Dispersion Number Solution

Follow our step by step solution on how to calculate Exit Age Distribution based on Dispersion Number?

FIRST Step Consider the formula

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''}})

Next Step Substitute values of Variables

∴

E = \sqrt{\frac{{7.8m/s}^{3}}{4 \cdot π \cdot 410m²/s \cdot 6.4m}} \cdot \exp (- \frac{{(6.4m - (7.8m/s \cdot 0.5s))}^{2}}{4 \cdot \frac{410m²/s \cdot 6.4m}{7.8m/s}})

Next Step Substitute values of Constants

∴

E = \sqrt{\frac{{7.8m/s}^{3}}{4 \cdot 3.1416 \cdot 410m²/s \cdot 6.4m}} \cdot \exp (- \frac{{(6.4m - (7.8m/s \cdot 0.5s))}^{2}}{4 \cdot \frac{410m²/s \cdot 6.4m}{7.8m/s}})

Next Step Prepare to Evaluate

∴

E = \sqrt{\frac{{7.8}^{3}}{4 \cdot 3.1416 \cdot 410 \cdot 6.4}} \cdot \exp (- \frac{{(6.4 - (7.8 \cdot 0.5))}^{2}}{4 \cdot \frac{410 \cdot 6.4}{7.8}})

Next Step Evaluate

∴

E = 0.1194092363682241/s

LAST Step Rounding Answer

∴

E = 0.11941/s

Exit Age Distribution based on Dispersion Number Formula Elements

Variables

Constants

Functions

Exit Age Distribution

Exit Age Distribution is the Measure of the Stream of the Fluid Leaving Vessel.

Symbol: E

Measurement: Time InverseUnit: 1/s

Note: Value should be greater than 0.

Formulas to find Exit Age Distribution

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.

Symbol: u''

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity of Pulse Measuring Variance

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

Time Required for Change in Concentration

Time Required for Change in Concentration is the Time Spent by the Tracer in the Reactor.

Symbol: Δt

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Required for Change in Concentration

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 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 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 Exit Age Distribution based on Dispersion Number?

Exit Age Distribution based on Dispersion Number evaluator 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 evaluate 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 evaluate Exit Age Distribution based on Dispersion Number using this online evaluator? To use this online evaluator 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.

FAQs on Exit Age Distribution based on Dispersion Number

What is the formula to find Exit Age Distribution based on Dispersion Number?

The formula of Exit Age Distribution based on Dispersion Number is expressed as 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)). Here is an example- 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)).

How to calculate Exit Age Distribution based on Dispersion Number?

With 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) we can find Exit Age Distribution based on Dispersion Number using the formula - 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)). This formula also uses Archimedes' constant and , Exponential Growth (exp), Square Root (sqrt) function(s).

Can the Exit Age Distribution based on Dispersion Number be negative?

No, the Exit Age Distribution based on Dispersion Number, measured in Time Inverse cannot be negative.

Which unit is used to measure Exit Age Distribution based on Dispersion Number?

Exit Age Distribution based on Dispersion Number is usually measured using the 1 Per Second[1/s] for Time Inverse. 1 Per Minute[1/s], 1 Per Hour[1/s], 1 Per Day[1/s] are the few other units in which Exit Age Distribution based on Dispersion Number can be measured.

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Exit Age Distribution based on Dispersion Number Formula

Exit Age Distribution based on Dispersion Number Example

Exit Age Distribution based on Dispersion Number Solution

Exit Age Distribution based on Dispersion Number Formula Elements

Other formulas in Dispersion Model category

How to Evaluate Exit Age Distribution based on Dispersion Number?

FAQs on Exit Age Distribution based on Dispersion Number

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