Liquid Flow Through Pore Based On Poiseuilles Law Calculator

Poiseuille's Law Formula:

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

Membrane Pore Diameter (d_p):

Viscosity of Liquid (μ_l):

Pa·s

Length of Pore (l):

Pressure Difference Across Pore (ΔP):

Liquid Flow Through Pore (q):

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1. What is Poiseuille's Law?

Poiseuille's Law describes the laminar flow of an incompressible and Newtonian fluid through a long cylindrical pore of constant cross-section. It provides a mathematical relationship between the flow rate and various parameters including pore diameter, fluid viscosity, pore length, and pressure difference.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law formula:

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

Where:

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

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

3. Importance of Liquid Flow Calculation

Details: Accurate calculation of liquid flow through pores is crucial for membrane filtration processes, biomedical applications, microfluidics, and various industrial processes involving fluid transport through porous materials.

4. Using the Calculator

Tips: Enter all values in SI units. Membrane pore diameter and length should be in meters, viscosity in Pascal-seconds, and pressure difference in Pascals. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What types of fluids does Poiseuille's Law apply to?
A: Poiseuille's Law applies to Newtonian fluids (constant viscosity) undergoing laminar flow through cylindrical pores.

Q2: Why is the flow rate proportional to the fourth power of pore diameter?
A: This strong dependence comes from the combination of the cross-sectional area (proportional to d²) and the average velocity (also proportional to d²) in laminar flow.

Q3: What are typical values for membrane pore diameters?
A: Membrane pore diameters can range from nanometers to micrometers, depending on the application and membrane type.

Q4: When is Poiseuille's Law not applicable?
A: The law doesn't apply to turbulent flow, non-Newtonian fluids, very short pores, or when the pore diameter approaches the mean free path of the fluid molecules.

Q5: How does temperature affect the flow rate?
A: Temperature primarily affects the viscosity of the liquid. As temperature increases, viscosity typically decreases, leading to increased flow rates.