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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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 00.020 seconds)

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< Basics of Membrane Separation Processes Calculators

Hagen Poiseuille Based Flux for Membrane Separation

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

Liquid Viscosity based on Membrane Resistance

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

Membrane Flux Based on Resistance

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

Resistance to flow in Membranes

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

Pressure Difference across Pore based on Poiseuille's Law Formula

LaTeX Go

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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