Average Mass Transfer Coefficient by Penetration Theory Solution

STEP 0: Pre-Calculation Summary
Formula Used
Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))
kL (Avg) = 2*sqrt(DAB/(pi*tc))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
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
Average Convective Mass Transfer Coefficient - (Measured in Meter per Second) - The Average Convective Mass Transfer Coefficient is a function of geometry of the system and the velocity and properties of the fluid similar to the heat transfer coefficient.
Diffusion Coefficient (DAB) - (Measured in Square Meter Per Second) - The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit.
Average Contact Time - (Measured in Second) - Average Contact Time is the variable used to define the time for contacting between liquid and vapor phases.
STEP 1: Convert Input(s) to Base Unit
Diffusion Coefficient (DAB): 0.007 Square Meter Per Second --> 0.007 Square Meter Per Second No Conversion Required
Average Contact Time: 11 Second --> 11 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
kL (Avg) = 2*sqrt(DAB/(pi*tc)) --> 2*sqrt(0.007/(pi*11))
Evaluating ... ...
kL (Avg) = 0.0284647737853237
STEP 3: Convert Result to Output's Unit
0.0284647737853237 Meter per Second --> No Conversion Required
FINAL ANSWER
0.0284647737853237 0.028465 Meter per Second <-- Average Convective Mass Transfer Coefficient
(Calculation completed in 00.020 seconds)

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20 Mass Transfer Theories Calculators

Liquid Phase Mass Transfer Coefficient by Two Film Theory
Go Overall Liquid Phase Mass Transfer Coefficient = 1/((1/(Gas Phase Mass Transfer Coefficient*Henry's Constant))+(1/Liquid Phase Mass Transfer Coefficient))
Instantaneous Mass Transfer Coefficient by Penetration Theory
Go Instantaneous Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)/(pi*Instantaneous Contact Time))
Gas Phase Mass Transfer Coefficient by Two Film Theory
Go Overall Gas Phase Mass Transfer Coefficient = 1/((1/Gas Phase Mass Transfer Coefficient)+(Henry's Constant/Liquid Phase Mass Transfer Coefficient))
Average Mass Transfer Coefficient by Penetration Theory
Go Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))
Diffusivity by Instanataneous Contact Time in Penetration Theory
Go Diffusion Coefficient (DAB) = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi)
Instantaneous Contact Time by Penetration Theory
Go Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous Convective Mass Transfer Coefficient^2)*pi)
Fractional Resistance Offered by Liquid Phase
Go Fractional Resistance Offered by Liquid Phase = (1/Liquid Phase Mass Transfer Coefficient)/(1/Overall Liquid Phase Mass Transfer Coefficient)
Diffusivity by Average Contact Time in Penetration Theory
Go Diffusion Coefficient (DAB) = (Average Contact Time*(Average Convective Mass Transfer Coefficient^2)*pi)/4
Average Contact Time by Penetration Theory
Go Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi)
Overall Liquid Phase Mass Transfer Coefficient using Fractional Resistance by Liquid Phase
Go Overall Liquid Phase Mass Transfer Coefficient = Liquid Phase Mass Transfer Coefficient*Fractional Resistance Offered by Liquid Phase
Liquid Phase Mass Transfer Coefficient using Fractional Resistance by Liquid Phase
Go Liquid Phase Mass Transfer Coefficient = Overall Liquid Phase Mass Transfer Coefficient/Fractional Resistance Offered by Liquid Phase
Fractional Resistance Offered by Gas Phase
Go Fractional Resistance Offered by Gas Phase = (1/Gas Phase Mass Transfer Coefficient)/(1/Overall Gas Phase Mass Transfer Coefficient)
Overall Gas Phase Mass Transfer Coefficient using Fractional Resistance by Gas Phase
Go Overall Gas Phase Mass Transfer Coefficient = Gas Phase Mass Transfer Coefficient*Fractional Resistance Offered by Gas Phase
Gas Phase Mass Transfer Coefficient using Fractional Resistance by Gas Phase
Go Gas Phase Mass Transfer Coefficient = Overall Gas Phase Mass Transfer Coefficient/Fractional Resistance Offered by Gas Phase
Mass Transfer Coefficient by Surface Renewal Theory
Go Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate)
Diffusivity by Surface Renewal Theory
Go Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/ Surface Renewal Rate
Surface Renewal Rate by Surface Renewal Theory
Go Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient (DAB)
Mass Transfer Coefficient by Film Theory
Go Convective Mass Transfer Coefficient = Diffusion Coefficient (DAB)/Film Thickness
Film Thickness by Film Theory
Go Film Thickness = Diffusion Coefficient (DAB)/Convective Mass Transfer Coefficient
Diffusivity by Film Theory
Go Diffusion Coefficient (DAB) = Convective Mass Transfer Coefficient*Film Thickness

25 Important Formulas in Mass Transfer Coefficient, Driving Force and Theories Calculators

Convective Mass Transfer Coefficient through Liquid Gas Interface
Go Convective Mass Transfer Coefficient = (Mass Transfer Coefficient of Medium 1*Mass Transfer Coefficient of Medium 2*Henry's Constant)/((Mass Transfer Coefficient of Medium 1*Henry's Constant)+(Mass Transfer Coefficient of Medium 2))
Logarithmic Mean Partial Pressure Difference
Go Logarithmic Mean Partial Pressure Difference = (Partial Pressure of Component B in Mixture 2-Partial Pressure of Component B in Mixture 1)/(ln(Partial Pressure of Component B in Mixture 2/Partial Pressure of Component B in Mixture 1))
Logarithmic Mean of Concentration Difference
Go Logarithmic Mean of Concentration Difference = (Concentration of Component B in Mixture 2-Concentration of Component B in Mixture 1)/ln(Concentration of Component B in Mixture 2/Concentration of Component B in Mixture 1)
Convective Mass Transfer Coefficient
Go Convective Mass Transfer Coefficient = Mass Flux of Diffusion Component A/(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)
Liquid Phase Mass Transfer Coefficient by Two Film Theory
Go Overall Liquid Phase Mass Transfer Coefficient = 1/((1/(Gas Phase Mass Transfer Coefficient*Henry's Constant))+(1/Liquid Phase Mass Transfer Coefficient))
Convective Mass Transfer Coefficient for Simultaneous Heat and Mass Transfer
Go Convective Mass Transfer Coefficient = Heat Transfer Coefficient/(Specific Heat*Density of Liquid*(Lewis Number^0.67))
Gas Phase Mass Transfer Coefficient by Two Film Theory
Go Overall Gas Phase Mass Transfer Coefficient = 1/((1/Gas Phase Mass Transfer Coefficient)+(Henry's Constant/Liquid Phase Mass Transfer Coefficient))
Heat Transfer Coefficient for Simultaneous Heat and Mass Transfer
Go Heat Transfer Coefficient = Convective Mass Transfer Coefficient*Density of Liquid*Specific Heat*(Lewis Number^0.67)
Average Mass Transfer Coefficient by Penetration Theory
Go Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))
Convective Mass Transfer Coefficient of Flat Plate in Combined Laminar Turbulent Flow
Go Convective Mass Transfer Coefficient = (0.0286*Free Stream Velocity)/((Reynolds Number^0.2)*(Schmidt Number^0.67))
Convective Mass Transfer Coefficient of Flat Plate Laminar Flow using Reynolds Number
Go Convective Mass Transfer Coefficient = (Free Stream Velocity*0.322)/((Reynolds Number^0.5)*(Schmidt Number^0.67))
Fractional Resistance Offered by Liquid Phase
Go Fractional Resistance Offered by Liquid Phase = (1/Liquid Phase Mass Transfer Coefficient)/(1/Overall Liquid Phase Mass Transfer Coefficient)
Convective Mass Transfer Coefficient of Flat Plate Laminar Flow using Drag Coefficient
Go Convective Mass Transfer Coefficient = (Drag Coefficient*Free Stream Velocity)/(2*(Schmidt Number^0.67))
Convective Mass Transfer Coefficient of Flat Plate Laminar Flow using Friction Factor
Go Convective Mass Transfer Coefficient = (Friction Factor*Free Stream Velocity)/(8*(Schmidt Number^0.67))
Liquid Phase Mass Transfer Coefficient using Fractional Resistance by Liquid Phase
Go Liquid Phase Mass Transfer Coefficient = Overall Liquid Phase Mass Transfer Coefficient/Fractional Resistance Offered by Liquid Phase
Fractional Resistance Offered by Gas Phase
Go Fractional Resistance Offered by Gas Phase = (1/Gas Phase Mass Transfer Coefficient)/(1/Overall Gas Phase Mass Transfer Coefficient)
Gas Phase Mass Transfer Coefficient using Fractional Resistance by Gas Phase
Go Gas Phase Mass Transfer Coefficient = Overall Gas Phase Mass Transfer Coefficient/Fractional Resistance Offered by Gas Phase
Mass Transfer Boundary Layer Thickness of Flat Plate in Laminar Flow
Go Mass Transfer Boundary Layer Thickness at x = Hydrodynamic Boundary Layer Thickness*(Schmidt Number^(-0.333))
Mass Transfer Stanton Number
Go Mass Transfer Stanton Number = Convective Mass Transfer Coefficient/Free Stream Velocity
Average Sherwood Number of Combined Laminar and Turbulent Flow
Go Average Sherwood Number = ((0.037*(Reynolds Number^0.8))-871)*(Schmidt Number^0.333)
Local Sherwood Number for Flat Plate in Turbulent Flow
Go Local Sherwood Number = 0.0296*(Local Reynolds Number^0.8)*(Schmidt Number^0.333)
Local Sherwood Number for Flat Plate in Laminar Flow
Go Local Sherwood Number = 0.332*(Local Reynolds Number^0.5)*(Schmidt Number^0.333)
Average Sherwood Number of Internal Turbulent Flow
Go Average Sherwood Number = 0.023*(Reynolds Number^0.83)*(Schmidt Number^0.44)
Sherwood Number for Flat Plate in Laminar Flow
Go Average Sherwood Number = 0.664*(Reynolds Number^0.5)*(Schmidt Number^0.333)
Average Sherwood Number of Flat Plate Turbulent Flow
Go Average Sherwood Number = 0.037*(Reynolds Number^0.8)

Average Mass Transfer Coefficient by Penetration Theory Formula

Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))
kL (Avg) = 2*sqrt(DAB/(pi*tc))

What is Penetration Theory?

The “Penetration Theory” or “Higbie’s model” assumes that each liquid element at the gas-liquid interface is exposed to the gas for a short time. The basic assumptions of the theory are: (1) Mass transfer from the gas into a liquid element occurs under unsteady-state conditions once they are in contact; (2) Each of the liquid elements stays in contact with the gas for same time period; and (3) Equilibrium exists at the gas-liquid interface. This theory was considered an improvement from the two-film theory since mass transfer occurs under unsteady-state conditions in many industrial processes. The Penetration Theory expresses the liquid-side mass transfer coefficient in terms of the contact time and the molecular diffusivity of the gas in the liquid.

How to Calculate Average Mass Transfer Coefficient by Penetration Theory?

Average Mass Transfer Coefficient by Penetration Theory calculator uses Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time)) to calculate the Average Convective Mass Transfer Coefficient, The Average Mass Transfer Coefficient by Penetration Theory formula is used to calculate the average mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory. Average Convective Mass Transfer Coefficient is denoted by kL (Avg) symbol.

How to calculate Average Mass Transfer Coefficient by Penetration Theory using this online calculator? To use this online calculator for Average Mass Transfer Coefficient by Penetration Theory, enter Diffusion Coefficient (DAB) (DAB) & Average Contact Time (tc) and hit the calculate button. Here is how the Average Mass Transfer Coefficient by Penetration Theory calculation can be explained with given input values -> 0.028465 = 2*sqrt(0.007/(pi*11)).

FAQ

What is Average Mass Transfer Coefficient by Penetration Theory?
The Average Mass Transfer Coefficient by Penetration Theory formula is used to calculate the average mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory and is represented as kL (Avg) = 2*sqrt(DAB/(pi*tc)) or Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time)). The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit & Average Contact Time is the variable used to define the time for contacting between liquid and vapor phases.
How to calculate Average Mass Transfer Coefficient by Penetration Theory?
The Average Mass Transfer Coefficient by Penetration Theory formula is used to calculate the average mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory is calculated using Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time)). To calculate Average Mass Transfer Coefficient by Penetration Theory, you need Diffusion Coefficient (DAB) (DAB) & Average Contact Time (tc). With our tool, you need to enter the respective value for Diffusion Coefficient (DAB) & Average Contact 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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