Liquid Viscosity Based On Poiseuille's Law Calculator

Poiseuille's Law Formula:

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

Pressure Difference Across Pore (ΔP):

Pascal

Membrane Pore Diameter (dₚ):

Meter

Liquid Flow Through Pore (q):

m³/s

Length of Pore (l):

Meter

Viscosity of Liquid (μₗ):

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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 flow rate to the pressure difference, fluid viscosity, and pipe dimensions.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law formula:

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

Where:

\( \mu_l \) — Viscosity of liquid (Pascal Second)
\( \Delta P \) — Pressure difference across pore (Pascal)
\( d_p \) — Membrane pore diameter (Meter)
\( q \) — Liquid flow through pore (m³/s)
\( l \) — Length of pore (Meter)
\( \pi \) — Archimedes' constant (3.14159...)

Explanation: The equation calculates the viscosity of a liquid based on the flow characteristics through a cylindrical pore under laminar flow conditions.

3. Importance of Viscosity Calculation

Details: Viscosity measurement is crucial in various industries including pharmaceuticals, petroleum, food processing, and chemical manufacturing. It helps determine flow properties, mixing characteristics, and product quality.

4. Using the Calculator

Tips: Enter all values in SI units. Pressure difference in Pascals, pore diameter and length in meters, and flow rate in cubic meters per second. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of Poiseuille's Law?
A: The fluid must be Newtonian, incompressible, and flow must be laminar through a straight, cylindrical pipe of constant cross-section.

Q2: What is a typical viscosity range for common liquids?
A: Water at 20°C has viscosity of about 0.001 Pa·s, while honey can have viscosity around 10 Pa·s, and motor oils range from 0.1-1 Pa·s.

Q3: When is Poiseuille's Law not applicable?
A: It doesn't apply to turbulent flow, non-Newtonian fluids, short pipes, or pipes with varying cross-sections.

Q4: How does temperature affect viscosity?
A: For most liquids, viscosity decreases with increasing temperature. The relationship is typically exponential.

Q5: What are the practical applications of this calculation?
A: Membrane characterization, filtration system design, microfluidics, blood flow analysis, and industrial process control.