Hagen Poiseuille Flow Or Mean Particle Size Of Porous Medium Laminar Flow Through Conduit Calculator

Formula Used:

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

Coefficient of Permeability (Hagen-Poiseuille):

m/s

Dynamic Viscosity of the Fluid:

Pa·s

Shape Factor:

Unit Weight of Fluid:

N/m³

Mean Particle Size of the Porous Medium:

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1. What is the Hagen-Poiseuille Flow Equation?

The Hagen-Poiseuille equation describes laminar flow through conduits and porous media. It provides a relationship between flow parameters and the mean particle size of the porous medium, helping in the analysis of fluid flow through granular materials.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The equation calculates the mean particle size based on permeability, fluid properties, and shape characteristics of the porous medium.

3. Importance of Mean Particle Size Calculation

Details: Determining the mean particle size is crucial for understanding flow characteristics through porous media, designing filtration systems, and analyzing groundwater flow in soil mechanics.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure values are positive and within reasonable physical ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the shape factor?
A: The shape factor accounts for the geometry and packing of particles in the porous medium, affecting flow characteristics.

Q2: How does fluid viscosity affect the result?
A: Higher viscosity fluids experience greater resistance to flow, which influences the calculated particle size.

Q3: What are typical values for permeability coefficient?
A: Permeability varies widely depending on the material, from 10⁻¹² m/s for clay to 10⁻¹ m/s for gravel.

Q4: When is this equation most applicable?
A: This equation is most accurate for laminar flow conditions through homogeneous porous media.

Q5: How does unit weight affect the calculation?
A: Unit weight represents the fluid's density and gravity effects, influencing the driving force for flow through the medium.