Pressure Difference across Pore based on Poiseuille's Law Calculator

✖Liquid flow through pore based on Poiseuille's law is defined as the laminar flow of an incompressible and Newtonian fluid through a long cylindrical pore of constant cross-section.ⓘ Liquid Flow through Pore [q]			+10% -10%
✖Viscosity of liquid is a measure of its resistance to flow. It is defined as the shear stress required to produce a unit rate of shear strain.ⓘ Viscosity of Liquid [μ_l]			+10% -10%
✖Length of pore is the distance between the two ends of the pore. It is an important parameter in Poiseuille's law, which describes the flow rate of liquid through a pore.ⓘ Length of Pore [l]			+10% -10%
✖Membrane Pore diameter based on Poiseuille's law is defined as the radius of a cylindrical pore that would produce the same flow rate.ⓘ Membrane Pore Diameter [d_p]			+10% -10%

✖Pressure difference across pore is the difference in pressure between the two ends of the pore. It is a driving force for the flow of liquid through the pore.ⓘ Pressure Difference across Pore based on Poiseuille's Law [ΔP]

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Formula

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Pressure Difference across Pore based on Poiseuille's Law

Formula

`"ΔP" = ("q"*128*"μ"_{"l"}*"l")/(pi*("d"_{"p"})^(4))`

Example

`"99944.21Pa"=("0.0000000002453m³/s"*128*"0.01Pa*s"*"0.1m")/(pi*("0.0001m")^(4))`

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Pressure Difference across Pore based on Poiseuille's Law Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Difference Across Pore = (Liquid Flow through Pore*128*Viscosity of Liquid*Length of Pore)/(pi*(Membrane Pore Diameter)^(4))
ΔP = (q*128*μ_l*l)/(pi*(d_p)^(4))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Pressure Difference Across Pore - (Measured in Pascal) - Pressure difference across pore is the difference in pressure between the two ends of the pore. It is a driving force for the flow of liquid through the pore.
Liquid Flow through Pore - (Measured in Cubic Meter per Second) - Liquid flow through pore based on Poiseuille's law is defined as the laminar flow of an incompressible and Newtonian fluid through a long cylindrical pore of constant cross-section.
Viscosity of Liquid - (Measured in Pascal Second) - Viscosity of liquid is a measure of its resistance to flow. It is defined as the shear stress required to produce a unit rate of shear strain.
Length of Pore - (Measured in Meter) - Length of pore is the distance between the two ends of the pore. It is an important parameter in Poiseuille's law, which describes the flow rate of liquid through a pore.
Membrane Pore Diameter - (Measured in Meter) - Membrane Pore diameter based on Poiseuille's law is defined as the radius of a cylindrical pore that would produce the same flow rate.

STEP 1: Convert Input(s) to Base Unit

Liquid Flow through Pore: 2.453E-10 Cubic Meter per Second --> 2.453E-10 Cubic Meter per Second No Conversion Required
Viscosity of Liquid: 0.01 Pascal Second --> 0.01 Pascal Second No Conversion Required
Length of Pore: 0.1 Meter --> 0.1 Meter No Conversion Required
Membrane Pore Diameter: 0.0001 Meter --> 0.0001 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔP = (q*128*μ_l*l)/(pi*(d_p)^(4)) --> (2.453E-10*128*0.01*0.1)/(pi*(0.0001)^(4))

Evaluating ... ...

ΔP = 99944.2113035313

STEP 3: Convert Result to Output's Unit

99944.2113035313 Pascal --> No Conversion Required

FINAL ANSWER

99944.2113035313 ≈ 99944.21 Pascal <-- Pressure Difference Across Pore

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Membrane Separation » Basics of Membrane Separation Processes » Pressure Difference across Pore based on Poiseuille's Law

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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

Pressure Difference across Pore based on Poiseuille's Law Formula

Pressure Difference Across Pore = (Liquid Flow through Pore*128*Viscosity of Liquid*Length of Pore)/(pi*(Membrane Pore Diameter)^(4))
ΔP = (q*128*μ_l*l)/(pi*(d_p)^(4))

What does Poiseuille's Law states?

Poiseuille's law states that the flow rate of a fluid through a pore is proportional to the fourth power of the pore radius and inversely proportional to the length of the pore. It is also proportional to the pressure difference between the two ends of the pore and inversely proportional to the viscosity of the fluid.

How to Calculate Pressure Difference across Pore based on Poiseuille's Law?

Pressure Difference across Pore based on Poiseuille's Law calculator uses Pressure Difference Across Pore = (Liquid Flow through Pore*128*Viscosity of Liquid*Length of Pore)/(pi*(Membrane Pore Diameter)^(4)) to calculate the Pressure Difference Across Pore, Pressure difference across pore based on Poiseuille's law is defined as the pressure difference required to drive a fluid through the pore at a given flow rate. Pressure Difference Across Pore is denoted by ΔP symbol.

How to calculate Pressure Difference across Pore based on Poiseuille's Law using this online calculator? To use this online calculator for Pressure Difference across Pore based on Poiseuille's Law, enter Liquid Flow through Pore (q), Viscosity of Liquid (μ_l), Length of Pore (l) & Membrane Pore Diameter (d_p) and hit the calculate button. Here is how the Pressure Difference across Pore based on Poiseuille's Law calculation can be explained with given input values -> 99944.21 = (2.453E-10*128*0.01*0.1)/(pi*(0.0001)^(4)).

FAQ

What is Pressure Difference across Pore based on Poiseuille's Law?

Pressure difference across pore based on Poiseuille's law is defined as the pressure difference required to drive a fluid through the pore at a given flow rate and is represented as ΔP = (q*128*μ_l*l)/(pi*(d_p)^(4)) or 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 Poiseuille's law is defined as the laminar flow of an incompressible and Newtonian fluid through a long cylindrical pore of constant cross-section, Viscosity of liquid is a measure of its resistance to flow. It is defined as the shear stress required to produce a unit rate of shear strain, Length of pore is the distance between the two ends of the pore. It is an important parameter in Poiseuille's law, which describes the flow rate of liquid through a pore & Membrane Pore diameter based on Poiseuille's law is defined as the radius of a cylindrical pore that would produce the same flow rate.

How to calculate Pressure Difference across Pore based on Poiseuille's Law?

Pressure difference across pore based on Poiseuille's law is defined as the pressure difference required to drive a fluid through the pore at a given flow rate is calculated using Pressure Difference Across Pore = (Liquid Flow through Pore*128*Viscosity of Liquid*Length of Pore)/(pi*(Membrane Pore Diameter)^(4)). To calculate Pressure Difference across Pore based on Poiseuille's Law, you need Liquid Flow through Pore (q), Viscosity of Liquid (μ_l), Length of Pore (l) & Membrane Pore Diameter (d_p). With our tool, you need to enter the respective value for Liquid Flow through Pore, Viscosity of Liquid, Length of Pore & Membrane Pore Diameter 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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