Pressure Difference Across Pore Based On Poiseuille's Law Calculator

Poiseuille's Law Formula:

\[ \Delta P = \frac{q \times 128 \times \mu_l \times l}{\pi \times (d_p)^4} \]

Liquid Flow Through Pore (q):

m³/s

Viscosity of Liquid (μ_l):

Pa·s

Length of Pore (l):

Membrane Pore Diameter (d_p):

Pressure Difference Across Pore (ΔP):

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1. What is Poiseuille's Law?

Poiseuille's Law describes the laminar flow of an incompressible, Newtonian fluid through a long cylindrical pipe of constant cross-section. It relates the pressure difference across the pipe to the flow rate, fluid viscosity, pipe length, and pipe diameter.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law formula:

\[ \Delta P = \frac{q \times 128 \times \mu_l \times l}{\pi \times (d_p)^4} \]

Where:

\( \Delta P \) — Pressure difference across pore (Pa)
\( q \) — Liquid flow through pore (m³/s)
\( \mu_l \) — Viscosity of liquid (Pa·s)
\( l \) — Length of pore (m)
\( d_p \) — Membrane pore diameter (m)
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: The equation shows that pressure difference is directly proportional to flow rate, viscosity, and length, but inversely proportional to the fourth power of pore diameter.

3. Importance of Pressure Difference Calculation

Details: Calculating pressure difference across pores is crucial in membrane filtration processes, biomedical applications, microfluidics, and understanding fluid transport through porous materials.

4. Using the Calculator

Tips: Enter all values in SI units. Liquid flow should be in cubic meters per second, viscosity in Pascal-seconds, length and diameter in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of Poiseuille's Law?
A: The fluid must be incompressible and Newtonian, flow must be laminar, the pipe must be straight and cylindrical with constant cross-section, and there must be no slip at the wall.

Q2: Why is the diameter raised to the fourth power?
A: The fourth power relationship comes from the integration of the velocity profile across the pipe cross-section and reflects the strong dependence of flow resistance on pipe diameter.

Q3: What is the range of validity for Poiseuille's Law?
A: The law is valid for laminar flow conditions, typically when the Reynolds number is less than 2000. For turbulent flow, different equations apply.

Q4: How does viscosity affect pressure difference?
A: Higher viscosity fluids require greater pressure differences to achieve the same flow rate through a given pore, as viscosity represents the fluid's resistance to flow.

Q5: Can this be used for non-circular pores?
A: The standard equation is for circular cross-sections. For non-circular pores, equivalent hydraulic diameters or specialized equations for specific geometries must be used.