Hagen Poiseuille Based Flux for Membrane Separation Calculator

✖Membrane porosity is defined as the void volume fraction of a membrane. It is the volume of the pores divided by the total volume of the membrane.ⓘ Membrane Porosity [ε]			+10% -10%
✖Pore diameter is defined as the distance between two opposite walls of a pore.ⓘ Pore Diameter [d]			+10% -10%
✖Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process.ⓘ Applied Pressure Driving Force [ΔP_m]			+10% -10%
✖Liquid viscosity is defined as the measure of a fluid's resistance to flow or its internal friction when subjected to an external force.ⓘ Liquid Viscosity [μ]			+10% -10%
✖Tortuosity is an intrinsic property of a porous material usually defined as the ratio of actual flow path length to the straight distance between the ends of the flow path.ⓘ Tortuosity [Τ]			+10% -10%
✖Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane.ⓘ Membrane Thickness [l_mt]			+10% -10%

✖Flux through membrane is defined as the rate of movement or transfer of a substance per unit area across a porous barrier known as a membrane.ⓘ Hagen Poiseuille Based Flux for Membrane Separation [J_wM]

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Hagen Poiseuille Based Flux for Membrane Separation

Formula

`"J"_{"wM"} = ("ε"*"d"^2*"ΔP"_{"m"})/(32*"μ"*"Τ"*"l"_{"mt"})`

Example

`"0.006944m³/(m²*s)"=("0.35"*("6.3245μm")^2*"300000Pa")/(32*"0.0009Kg/ms"*"280"*"75μm")`

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Hagen Poiseuille Based Flux for Membrane Separation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness)
J_wM = (ε*d^2*ΔP_m)/(32*μ*Τ*l_mt)
This formula uses 7 Variables

Variables Used

Flux through Membrane - (Measured in Cubic Meter per Square Meter per Second) - Flux through membrane is defined as the rate of movement or transfer of a substance per unit area across a porous barrier known as a membrane.
Membrane Porosity - Membrane porosity is defined as the void volume fraction of a membrane. It is the volume of the pores divided by the total volume of the membrane.
Pore Diameter - (Measured in Meter) - Pore diameter is defined as the distance between two opposite walls of a pore.
Applied Pressure Driving Force - (Measured in Pascal) - Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process.
Liquid Viscosity - (Measured in Pascal Second) - Liquid viscosity is defined as the measure of a fluid's resistance to flow or its internal friction when subjected to an external force.
Tortuosity - Tortuosity is an intrinsic property of a porous material usually defined as the ratio of actual flow path length to the straight distance between the ends of the flow path.
Membrane Thickness - (Measured in Meter) - Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane.

STEP 1: Convert Input(s) to Base Unit

Membrane Porosity: 0.35 --> No Conversion Required
Pore Diameter: 6.3245 Micrometer --> 6.3245E-06 Meter (Check conversion here)
Applied Pressure Driving Force: 300000 Pascal --> 300000 Pascal No Conversion Required
Liquid Viscosity: 0.0009 Kilogram per Meter per Second --> 0.0009 Pascal Second (Check conversion here)
Tortuosity: 280 --> No Conversion Required
Membrane Thickness: 75 Micrometer --> 7.5E-05 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J_wM = (ε*d^2*ΔP_m)/(32*μ*Τ*l_mt) --> (0.35*6.3245E-06^2*300000)/(32*0.0009*280*7.5E-05)

Evaluating ... ...

J_wM = 0.00694432296006944

STEP 3: Convert Result to Output's Unit

0.00694432296006944 Cubic Meter per Square Meter per Second --> No Conversion Required

FINAL ANSWER

0.00694432296006944 ≈ 0.006944 Cubic Meter per Square Meter per Second <-- Flux through Membrane

(Calculation completed in 00.020 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Membrane Separation » Basics of Membrane Separation Processes » Hagen Poiseuille Based Flux for Membrane Separation

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< 16 Basics of Membrane Separation Processes Calculators

Concentration of Mass at Membrane Surface

Go Solute Concentration at Membrane Surface = exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)/((Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))*Bulk Concentration

Partial Molar Volume of Water based on Solution Diffusion Model

Go Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))

Water Permeability based on Initial flux

Go Water Permeability Through Membrane = Volumetric Water Flux Through Membrane/(Applied Pressure Driving Force*(1-(([R]*Temperature*Molecular Weight)/(Initial Volume*Applied Pressure Driving Force))))

Time of Dialysis using Hollow Fiber Haemodialyser

Go Time of Dialysis = (Volume of blood/Volumetric Rate of Blood)*ln(Initial Concentration In Blood/Final Concentration In Blood)*((1-(e^-No of Transfer Units))^-1)

Hagen Poiseuille Based Flux for Membrane Separation

Go Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness)

Liquid Viscosity Based On Hagen Poiseuille Equation

Go Liquid Viscosity = (Pore Diameter^2*Membrane Porosity*Applied Pressure Driving Force)/(32*Flux through Membrane*Tortuosity*Membrane Thickness)

Tortuosity Factor of Pores

Go Tortuosity = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Membrane Thickness)

Pressure Difference across Pore based on Poiseuille's Law

Go Pressure Difference Across Pore = (Liquid Flow through Pore*128*Viscosity of Liquid*Length of Pore)/(pi*(Membrane Pore Diameter)^(4))

Liquid Flow through Pore Based On Poiseuilles Law

Go Liquid Flow through Pore = ((pi*(Membrane Pore Diameter)^4)/(128*Viscosity of Liquid*Length of Pore))*Pressure Difference Across Pore

Liquid Viscosity based on Poiseuille's Law

Go Viscosity of Liquid = (Pressure Difference Across Pore*pi*(Membrane Pore Diameter)^(4))/(Liquid Flow through Pore*128*Length of Pore)

Liquid Viscosity based on Membrane Resistance

Go Liquid Viscosity = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Flux through Membrane)

Membrane Flux Based on Resistance

Go Flux through Membrane = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Liquid Viscosity)

Resistance to flow in Membranes

Go Membrane Flow Resistance of Unit Area = Applied Pressure Driving Force/(Liquid Viscosity*Flux through Membrane)

Applied Pressure Driving Force Based on Permeability of Membrane

Go Applied Pressure Driving Force = Flux through Membrane/Water Permeability Through Membrane

Water Permeability through Membrane

Go Water Permeability Through Membrane = Flux through Membrane/Applied Pressure Driving Force

Membrane Flux Based on Water Permeability

Go Flux through Membrane = Water Permeability Through Membrane*Applied Pressure

Hagen Poiseuille Based Flux for Membrane Separation Formula

Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness)
J_wM = (ε*d^2*ΔP_m)/(32*μ*Τ*l_mt)

On what Factors does Membrane Flux Depends upon ?

The membrane flux depends on a number of factors, including:

Membrane pore size
Membrane Thickness
Membrane Material
Pressure difference
Temperature
Concentration of solutes
Membrane fouling

How to Calculate Hagen Poiseuille Based Flux for Membrane Separation?

Hagen Poiseuille Based Flux for Membrane Separation calculator uses Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness) to calculate the Flux through Membrane, Hagen Poiseuille Based Flux for Membrane Separation is defined as the amount of permeate collected per unit area per unit time. Flux through Membrane is denoted by J_wM symbol.

How to calculate Hagen Poiseuille Based Flux for Membrane Separation using this online calculator? To use this online calculator for Hagen Poiseuille Based Flux for Membrane Separation, enter Membrane Porosity (ε), Pore Diameter (d), Applied Pressure Driving Force (ΔP_m), Liquid Viscosity (μ), Tortuosity (Τ) & Membrane Thickness (l_mt) and hit the calculate button. Here is how the Hagen Poiseuille Based Flux for Membrane Separation calculation can be explained with given input values -> 0.017361 = (0.35*6.3245E-06^2*300000)/(32*0.0009*280*7.5E-05).

FAQ

What is Hagen Poiseuille Based Flux for Membrane Separation?

Hagen Poiseuille Based Flux for Membrane Separation is defined as the amount of permeate collected per unit area per unit time and is represented as J_wM = (ε*d^2*ΔP_m)/(32*μ*Τ*l_mt) or Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness). Membrane porosity is defined as the void volume fraction of a membrane. It is the volume of the pores divided by the total volume of the membrane, Pore diameter is defined as the distance between two opposite walls of a pore, Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process, Liquid viscosity is defined as the measure of a fluid's resistance to flow or its internal friction when subjected to an external force, Tortuosity is an intrinsic property of a porous material usually defined as the ratio of actual flow path length to the straight distance between the ends of the flow path & Membrane thickness is defined as the difference between the internal and outernal boundary of the membrane.

How to calculate Hagen Poiseuille Based Flux for Membrane Separation?

Hagen Poiseuille Based Flux for Membrane Separation is defined as the amount of permeate collected per unit area per unit time is calculated using Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness). To calculate Hagen Poiseuille Based Flux for Membrane Separation, you need Membrane Porosity (ε), Pore Diameter (d), Applied Pressure Driving Force (ΔP_m), Liquid Viscosity (μ), Tortuosity (Τ) & Membrane Thickness (l_mt). With our tool, you need to enter the respective value for Membrane Porosity, Pore Diameter, Applied Pressure Driving Force, Liquid Viscosity, Tortuosity & Membrane Thickness and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Flux through Membrane?

In this formula, Flux through Membrane uses Membrane Porosity, Pore Diameter, Applied Pressure Driving Force, Liquid Viscosity, Tortuosity & Membrane Thickness. We can use 2 other way(s) to calculate the same, which is/are as follows -

Flux through Membrane = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Liquid Viscosity)
Flux through Membrane = Water Permeability Through Membrane*Applied Pressure

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