Coefficient Of Permeability From Analogy Of Laminar Flow (Hagen Poiseuille Flow) Calculator

Formula Used:

\[ K_{H-P} = \frac{C \times (d_m^2) \times (\gamma / 1000)}{\mu} \]

Shape Factor (C):

Mean Particle Size (d_m):

Unit Weight of Fluid (γ):

N/m³

Dynamic Viscosity (μ):

Pa·s

Coefficient of Permeability (K_H-P):

m/s

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1. What is the Coefficient of Permeability from Analogy of Laminar Flow?

The Coefficient of Permeability from Analogy of Laminar Flow (Hagen-Poiseuille flow) estimates the hydraulic conductivity of porous media by drawing an analogy to laminar flow through circular pipes. It reflects the combined effect of porous medium and fluid properties on flow characteristics.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ K_{H-P} = \frac{C \times (d_m^2) \times (\gamma / 1000)}{\mu} \]

Where:

\( K_{H-P} \) — Coefficient of Permeability (m/s)
\( C \) — Shape Factor (dimensionless)
\( d_m \) — Mean Particle Size of the Porous Medium (m)
\( \gamma \) — Unit Weight of Fluid (N/m³)
\( \mu \) — Dynamic Viscosity of the Fluid (Pa·s)

Explanation: The equation accounts for the geometric properties of the porous medium and the physical properties of the fluid to determine permeability.

3. Importance of Permeability Calculation

Details: Accurate permeability estimation is crucial for groundwater flow analysis, contaminant transport studies, geotechnical engineering, and petroleum reservoir characterization.

4. Using the Calculator

Tips: Enter shape factor (dimensionless), mean particle size in meters, unit weight of fluid in N/m³, and dynamic viscosity in Pa·s. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of permeability values?
A: Permeability values range from 10⁻¹² m/s for clay to 10⁻¹ m/s for gravel, depending on the porous medium characteristics.

Q2: How does particle size affect permeability?
A: Permeability increases with the square of mean particle size, making it highly sensitive to changes in grain size distribution.

Q3: What factors influence the shape factor?
A: The shape factor depends on porosity, packing arrangement, grain shape, and grain-size distribution of the porous medium.

Q4: When is the Hagen-Poiseuille analogy applicable?
A: This analogy is most applicable for laminar flow conditions through porous media with relatively uniform particle sizes.

Q5: How does fluid viscosity affect permeability?
A: Permeability is inversely proportional to dynamic viscosity - more viscous fluids result in lower permeability values.