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Mean Residence Time where Dispersion Number is less than 0.01 Formula

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

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'}))}

θ - Mean Residence Time?c - Concentration of Solution?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?π - Archimedes' constant?

Mean Residence Time where Dispersion Number is less than 0.01 Example

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Here is how the Mean Residence Time where Dispersion Number is less than 0.01 equation looks like with Values.

Here is how the Mean Residence Time where Dispersion Number is less than 0.01 equation looks like with Units.

Here is how the Mean Residence Time where Dispersion Number is less than 0.01 equation looks like.

1.0282 = 1 + \sqrt{(\ln (44 \cdot 2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085}{40 \cdot 0.92})}) \cdot 4 \cdot (\frac{0.0085}{40 \cdot 0.92}))}

1.0282s = 1 + \sqrt{(\ln (44mol/m³ \cdot 2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})}) \cdot 4 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m}))}

1.0282 = 1 + \sqrt{(\ln (44 \cdot 2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085}{40 \cdot 0.92})}) \cdot 4 \cdot (\frac{0.0085}{40 \cdot 0.92}))}

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Mean Residence Time where Dispersion Number is less than 0.01 Solution

Follow our step by step solution on how to calculate Mean Residence Time where Dispersion Number is less than 0.01?

FIRST Step Consider the formula

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'}))}

Next Step Substitute values of Variables

∴

θ = 1 + \sqrt{(\ln (44mol/m³ \cdot 2 \cdot \sqrt{π \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})}) \cdot 4 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m}))}

Next Step Substitute values of Constants

∴

θ = 1 + \sqrt{(\ln (44mol/m³ \cdot 2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m})}) \cdot 4 \cdot (\frac{0.0085m²/s}{40m/s \cdot 0.92m}))}

Next Step Prepare to Evaluate

∴

θ = 1 + \sqrt{(\ln (44 \cdot 2 \cdot \sqrt{3.1416 \cdot (\frac{0.0085}{40 \cdot 0.92})}) \cdot 4 \cdot (\frac{0.0085}{40 \cdot 0.92}))}

Next Step Evaluate

∴

θ = 1.02823892694706s

LAST Step Rounding Answer

∴

θ = 1.0282s

Mean Residence Time where Dispersion Number is less than 0.01 Formula Elements

Variables

Constants

Functions

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

Concentration of Solution

The Concentration of Solution is the quantity of a solute that is contained in a particular quantity of solvent or solution.

Symbol: c

Measurement: Molar ConcentrationUnit: mol/m³

Note: Value should be greater than 0.

Formulas to find Concentration of Solution

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

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

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(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 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'}))}

How to Evaluate Mean Residence Time where Dispersion Number is less than 0.01?

Mean Residence Time where Dispersion Number is less than 0.01 evaluator uses 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)))) to evaluate the Mean Residence Time, The Mean Residence Time where Dispersion Number is less than 0.01 formula is defined as Relationship between the Dispersion Number and the Concentration for small extent of Dispersion. Mean Residence Time is denoted by θ symbol.

How to evaluate Mean Residence Time where Dispersion Number is less than 0.01 using this online evaluator? To use this online evaluator for Mean Residence Time where Dispersion Number is less than 0.01, enter Concentration of Solution (c), 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') and hit the calculate button.

FAQs on Mean Residence Time where Dispersion Number is less than 0.01

What is the formula to find Mean Residence Time where Dispersion Number is less than 0.01?

The formula of Mean Residence Time where Dispersion Number is less than 0.01 is expressed as 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)))). Here is an example- 1.028239 = 1+sqrt((ln(44*2*sqrt(pi*(0.0085/(40*0.92))))*4*(0.0085/(40*0.92)))).

How to calculate Mean Residence Time where Dispersion Number is less than 0.01?

With Concentration of Solution (c), 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') we can find Mean Residence Time where Dispersion Number is less than 0.01 using the formula - 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)))). This formula also uses Archimedes' constant and , Natural Logarithm Function, Square Root Function function(s).

Can the Mean Residence Time where Dispersion Number is less than 0.01 be negative?

No, the Mean Residence Time where Dispersion Number is less than 0.01, measured in Time cannot be negative.

Which unit is used to measure Mean Residence Time where Dispersion Number is less than 0.01?

Mean Residence Time where Dispersion Number is less than 0.01 is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Mean Residence Time where Dispersion Number is less than 0.01 can be measured.

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Mean Residence Time where Dispersion Number is less than 0.01 Formula

Mean Residence Time where Dispersion Number is less than 0.01 Example

Mean Residence Time where Dispersion Number is less than 0.01 Solution

Mean Residence Time where Dispersion Number is less than 0.01 Formula Elements

Other formulas in Dispersion Model category

How to Evaluate Mean Residence Time where Dispersion Number is less than 0.01?

FAQs on Mean Residence Time where Dispersion Number is less than 0.01

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