Liquid Viscosity Based On Hagen Poiseuille Equation Calculator

Hagen Poiseuille Equation:

\[ \mu = \frac{d^2 \cdot \varepsilon \cdot \Delta P_m}{32 \cdot J_{wM} \cdot \tau \cdot l_{mt}} \]

Pore Diameter (d):

Membrane Porosity (ε):

Applied Pressure Driving Force (ΔP_m):

Flux through Membrane (J_wM):

m³/m²/s

Tortuosity (τ):

Membrane Thickness (l_mt):

Liquid Viscosity (μ):

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1. What is the Hagen Poiseuille Equation?

The Hagen Poiseuille equation describes the pressure drop in an incompressible and Newtonian fluid in laminar flow through a long cylindrical pipe of constant cross section. It provides a mathematical relationship between flow rate, pressure gradient, pipe dimensions, and fluid viscosity.

2. How Does the Calculator Work?

The calculator uses the Hagen Poiseuille equation:

\[ \mu = \frac{d^2 \cdot \varepsilon \cdot \Delta P_m}{32 \cdot J_{wM} \cdot \tau \cdot l_{mt}} \]

Where:

\( \mu \) — Liquid viscosity (Pa·s)
\( d \) — Pore diameter (m)
\( \varepsilon \) — Membrane porosity
\( \Delta P_m \) — Applied pressure driving force (Pa)
\( J_{wM} \) — Flux through membrane (m³/m²/s)
\( \tau \) — Tortuosity
\( l_{mt} \) — Membrane thickness (m)

Explanation: The equation calculates liquid viscosity based on membrane characteristics and flow parameters, accounting for pore geometry and flow resistance.

3. Importance of Liquid Viscosity Calculation

Details: Accurate viscosity measurement is crucial for understanding fluid behavior, designing flow systems, predicting pressure drops, and optimizing processes in chemical engineering, biomedical applications, and filtration systems.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Pore diameter and membrane thickness should be in meters, applied pressure in pascals, and flux in cubic meters per square meter per second. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for the Hagen Poiseuille equation?
A: The equation is valid for laminar flow (Re < 2300) of Newtonian fluids through straight, circular pipes with constant cross-section.

Q2: What are typical viscosity values for common liquids?
A: Water at 20°C has viscosity of ~0.001 Pa·s, while honey has ~10 Pa·s, and motor oils range from 0.1-1 Pa·s.

Q3: How does temperature affect viscosity?
A: For liquids, viscosity typically decreases with increasing temperature. This relationship can be described by various models like the Arrhenius equation.

Q4: What is the significance of tortuosity in membrane flow?
A: Tortuosity accounts for the fact that fluid paths through porous media are longer and more winding than the straight-line distance through the material.

Q5: Can this equation be used for non-Newtonian fluids?
A: No, the Hagen Poiseuille equation is specifically derived for Newtonian fluids. Non-Newtonian fluids require different flow equations.