Effective Particle Diameter By Ergun Given Frication Factor Calculator

Ergun Equation:

\[ D_{eff} = \frac{f_f \times L_b \times U_b^2 \times (1 - \epsilon)}{g \times H_f \times \epsilon^3} \]

Factor of Friction:

Length of Packaged Bed:

Superficial Velocity:

m/s

Void Fraction:

Acceleration due to Gravity:

m/s²

Head of Fluid:

Effective Particle Diameter (D_eff):

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1. What is the Ergun Equation?

The Ergun equation is used to calculate the pressure drop for flow through a packed bed of solids. It provides a relationship between various parameters including friction factor, bed length, superficial velocity, void fraction, and effective particle diameter.

2. How Does the Calculator Work?

The calculator uses the Ergun equation rearranged to solve for effective particle diameter:

\[ D_{eff} = \frac{f_f \times L_b \times U_b^2 \times (1 - \epsilon)}{g \times H_f \times \epsilon^3} \]

Where:

\( D_{eff} \) — Effective particle diameter (m)
\( f_f \) — Factor of friction (dimensionless)
\( L_b \) — Length of packaged bed (m)
\( U_b \) — Superficial velocity (m/s)
\( \epsilon \) — Void fraction (dimensionless)
\( g \) — Acceleration due to gravity (m/s²)
\( H_f \) — Head of fluid (m)

Explanation: The equation calculates the effective particle diameter based on the pressure drop characteristics through a packed bed.

3. Importance of Effective Particle Diameter Calculation

Details: Accurate calculation of effective particle diameter is crucial for designing packed bed reactors, filtration systems, and other industrial processes involving fluid flow through particulate media.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive and within reasonable physical limits.

5. Frequently Asked Questions (FAQ)

Q1: What is void fraction?
A: Void fraction is the fraction of the total volume that is occupied by voids or empty space between particles.

Q2: How is superficial velocity different from actual velocity?
A: Superficial velocity is the velocity the fluid would have if the bed were empty, while actual velocity accounts for the reduced flow area due to particles.

Q3: What factors affect the friction factor?
A: The friction factor depends on Reynolds number, particle shape, size distribution, and bed porosity.

Q4: When is the Ergun equation applicable?
A: The Ergun equation is applicable for laminar, transitional, and turbulent flow through packed beds.

Q5: What are typical values for void fraction in packed beds?
A: Void fraction typically ranges from 0.3 to 0.5 for randomly packed spheres, but can vary depending on particle shape and packing method.