Ergun Equation Calculator
Water flowing at 0.01 m/s through a 1 m deep bed of 3 mm spheres (ε = 0.4) loses 1484.37 Pa of pressure.
Enter a valid number for “Particle diameter d_p”.
Ergun Equation Formula
ΔP/L = 150μV₀(1 − ε)²/(ε³d²) + 1.75ρV₀²(1 − ε)/(ε³d)
d = φ_s d_p, V₀ superficial velocity
Worked Example
Water at 0.01 m/s through a 1 m bed of 3 mm spheres with ε = 0.4:
- ΔP/L = 150 μV₀(1 − ε)²/(ε³ (φd)²) + 1.75 ρV₀²(1 − ε)/(ε³ φd)
- ΔP/L = 937.5 + 546.875 = 1484.375 Pa/m
Viscous (Kozeny–Carman) term: 937.5 Pa/m · Inertial (Burke–Plummer) term: 546.875 Pa/m · Particle Reynolds number d V ρ/(μ(1 − ε)): 50
GATE tip
V₀ is the superficial (empty-column) velocity; the interstitial velocity is V₀/ε.
More Fluid Mechanics and Mechanical Operations Calculators
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Minimum Fluidization Velocity Calculator
Re_mf = √(33.7² + 0.0408 Ar) − 33.7
Ar = d_p³ρ_f(ρ_p − ρ_f)g/μ², U_mf = Re_mf μ/(ρ_f d_p)
Example: 500 µm sand (2650 kg/m³) fluidized by air: Minimum fluidization velocity U_mf = 0.198901 m/s.
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Size Reduction Energy Calculator
W = 10 W_i (1/√P₈₀ − 1/√F₈₀)
Rittinger E ∝ 1/L₂ − 1/L₁; Kick E ∝ ln(L₁/L₂); sizes in µm
Example: Grinding from 10 mm to 1 mm with W_i = 13 kWh/t: Specific energy W = 2.81096 kWh/t.
Frequently asked questions
Why is voidage so important?
The viscous term scales with (1 − ε)²/ε³: dropping ε from 0.4 to 0.35 raises it by about 70 %.
When does the inertial term dominate?
At particle Reynolds numbers above about 1000, the 1.75 term outweighs the 150 term.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Ergun Equation Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/ergun-equation-calculator/
IEEE
Scientific Converters, "Ergun Equation Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/ergun-equation-calculator/