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Mass Diffusing Rate through Hollow Cylinder with Solid Boundary Formula

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GoMass Diffusing Rate through Solid Boundary Plate Formula

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GoMass Diffusing Rate through Solid Boundary Sphere Formula

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Mass Diffusing Rate is the proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species. Check FAQs

m r = \frac{2 \cdot π \cdot D ab \cdot l \cdot (ρ a1 - ρ a2)}{\ln (\frac{r 2}{r 1})}

m_r - Mass Diffusing Rate?D_ab - Diffusion Coefficient When A Diffuse with B?l - Length of Cylinder?ρ_a1 - Mass Concentration of Component A in Mixture 1?ρ_a2 - Mass Concentration of Component A in Mixture 2?r₂ - Outer Radius of Cylinder?r₁ - Inner Radius of Cylinder?π - Archimedes' constant?

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary Example

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Here is how the Mass Diffusing Rate through Hollow Cylinder with Solid Boundary equation looks like with Values.

Here is how the Mass Diffusing Rate through Hollow Cylinder with Solid Boundary equation looks like with Units.

Here is how the Mass Diffusing Rate through Hollow Cylinder with Solid Boundary equation looks like.

9333.7372 = \frac{2 \cdot 3.1416 \cdot 0.8 \cdot 102 \cdot (40 - 20)}{\ln (\frac{7.5}{2.5})}

9333.7372kg/s = \frac{2 \cdot 3.1416 \cdot 0.8m²/s \cdot 102m \cdot (40kg/m³ - 20kg/m³)}{\ln (\frac{7.5m}{2.5m})}

9333.7372 = \frac{2 \cdot 3.1416 \cdot 0.8 \cdot 102 \cdot (40 - 20)}{\ln (\frac{7.5}{2.5})}

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Home » Physics » Mechanical » Heat and Mass Transfer » Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary Solution

Follow our step by step solution on how to calculate Mass Diffusing Rate through Hollow Cylinder with Solid Boundary?

FIRST Step Consider the formula

m r = \frac{2 \cdot π \cdot D ab \cdot l \cdot (ρ a1 - ρ a2)}{\ln (\frac{r 2}{r 1})}

Next Step Substitute values of Variables

∴

m r = \frac{2 \cdot π \cdot 0.8m²/s \cdot 102m \cdot (40kg/m³ - 20kg/m³)}{\ln (\frac{7.5m}{2.5m})}

Next Step Substitute values of Constants

∴

m r = \frac{2 \cdot 3.1416 \cdot 0.8m²/s \cdot 102m \cdot (40kg/m³ - 20kg/m³)}{\ln (\frac{7.5m}{2.5m})}

Next Step Prepare to Evaluate

∴

m r = \frac{2 \cdot 3.1416 \cdot 0.8 \cdot 102 \cdot (40 - 20)}{\ln (\frac{7.5}{2.5})}

Next Step Evaluate

∴

m r = 9333.73723112873kg/s

LAST Step Rounding Answer

∴

m r = 9333.7372kg/s

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary Formula Elements

Variables

Constants

Functions

Mass Diffusing Rate

Mass Diffusing Rate is the proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species.

Symbol: m_r

Measurement: Mass Flow RateUnit: kg/s

Note: Value can be positive or negative.

Diffusion Coefficient When A Diffuse with B

Diffusion Coefficient when A Diffuse with B is the magnitude of the molar flux through a surface per unit concentration gradient out-of-plane.

Symbol: D_ab

Measurement: DiffusivityUnit: m²/s

Note: Value can be positive or negative.

Length of Cylinder

Length of Cylinder is the vertical height of the Cylinder.

Symbol: l

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Mass Concentration of Component A in Mixture 1

Mass Concentration of Component A in Mixture 1 is the concentration of component A per unit volume in mixture 1.

Symbol: ρ_a1

Measurement: DensityUnit: kg/m³

Note: Value can be positive or negative.

Mass Concentration of Component A in Mixture 2

The Mass Concentration of component A in Mixture 2 is the concentration of component A per unit volume in mixture 2.

Symbol: ρ_a2

Measurement: DensityUnit: kg/m³

Note: Value can be positive or negative.

Outer Radius of Cylinder

The Outer Radius of Cylinder is a straight line from the center of the Cylinder's base to outer surface of the Cylinder.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Inner Radius of Cylinder

The Inner Radius of Cylinder is a straight line from the center of the cylinder's base to inner surface of the Cylinder.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

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

ln

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

Syntax: ln(Number)

Credits

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Created by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

Nishan Poojary has created this Formula and 500+ more formulas!

Verifier Image

Verified by Sagar S Kulkarni

Dayananda Sagar College of Engineering (DSCE), Bengaluru

Sagar S Kulkarni has verified this Formula and 200+ more formulas!

Other Formulas to find Mass Diffusing Rate

Go Mass Diffusing Rate through Solid Boundary Plate

m r = \frac{D ab \cdot (ρ a1 - ρ a2) \cdot A}{t p}

Go Mass Diffusing Rate through Solid Boundary Sphere

m r = \frac{4 \cdot π \cdot r i \cdot r o \cdot D ab \cdot (ρ a1 - ρ a2)}{r o - r i}

Other formulas in Molar Diffusion category

Go Chapman Enskog Equation for Gas Phase Diffusivity

D AB = \frac{1.858 \cdot (10^{- 7}) \cdot (T^{\frac{3}{2}}) \cdot ({((\frac{1}{M A}) + (\frac{1}{M b}))}^{\frac{1}{2}})}{P T \cdot {σ AB}^{2} \cdot Ω D}

Go Diffusivity by Stefan Tube Method

D AB = \frac{[R] \cdot T \cdot P BLM \cdot ρ L \cdot ({h 1}^{2} - {h 2}^{2})}{2 \cdot P T \cdot M A \cdot (P A1 - P A2) \cdot t}

See More

How to Evaluate Mass Diffusing Rate through Hollow Cylinder with Solid Boundary?

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary evaluator uses Mass Diffusing Rate = (2*pi*Diffusion Coefficient When A Diffuse with B*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder) to evaluate the Mass Diffusing Rate, Mass Diffusing Rate through Hollow Cylinder with Solid Boundary is defined as amount of particles diffusing through Hollow Cylinder with Solid Boundary per unit time. Mass Diffusing Rate is denoted by m_r symbol.

How to evaluate Mass Diffusing Rate through Hollow Cylinder with Solid Boundary using this online evaluator? To use this online evaluator for Mass Diffusing Rate through Hollow Cylinder with Solid Boundary, enter Diffusion Coefficient When A Diffuse with B (D_ab), Length of Cylinder (l), Mass Concentration of Component A in Mixture 1 (ρ_a1), Mass Concentration of Component A in Mixture 2 (ρ_a2), Outer Radius of Cylinder (r₂) & Inner Radius of Cylinder (r₁) and hit the calculate button.

FAQs on Mass Diffusing Rate through Hollow Cylinder with Solid Boundary

What is the formula to find Mass Diffusing Rate through Hollow Cylinder with Solid Boundary?

The formula of Mass Diffusing Rate through Hollow Cylinder with Solid Boundary is expressed as Mass Diffusing Rate = (2*pi*Diffusion Coefficient When A Diffuse with B*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder). Here is an example- 9333.737 = (2*pi*0.8*102*(40-20))/ln(7.5/2.5).

How to calculate Mass Diffusing Rate through Hollow Cylinder with Solid Boundary?

With Diffusion Coefficient When A Diffuse with B (D_ab), Length of Cylinder (l), Mass Concentration of Component A in Mixture 1 (ρ_a1), Mass Concentration of Component A in Mixture 2 (ρ_a2), Outer Radius of Cylinder (r₂) & Inner Radius of Cylinder (r₁) we can find Mass Diffusing Rate through Hollow Cylinder with Solid Boundary using the formula - Mass Diffusing Rate = (2*pi*Diffusion Coefficient When A Diffuse with B*Length of Cylinder*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/ln(Outer Radius of Cylinder/Inner Radius of Cylinder). This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

What are the other ways to Calculate Mass Diffusing Rate?

Here are the different ways to Calculate Mass Diffusing Rate-

Mass Diffusing Rate=(Diffusion Coefficient When A Diffuse with B*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)*Area of Solid Boundary Plate)/Thickness of Solid Plate
Mass Diffusing Rate=(4*pi*Inner Radius*Outer Radius*Diffusion Coefficient When A Diffuse with B*(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2))/(Outer Radius-Inner Radius)

Can the Mass Diffusing Rate through Hollow Cylinder with Solid Boundary be negative?

Yes, the Mass Diffusing Rate through Hollow Cylinder with Solid Boundary, measured in Mass Flow Rate can be negative.

Which unit is used to measure Mass Diffusing Rate through Hollow Cylinder with Solid Boundary?

Mass Diffusing Rate through Hollow Cylinder with Solid Boundary is usually measured using the Kilogram per Second[kg/s] for Mass Flow Rate. Gram per Second[kg/s], Gram per Hour[kg/s], Milligram per Minute[kg/s] are the few other units in which Mass Diffusing Rate through Hollow Cylinder with Solid Boundary can be measured.

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