Swamee-Jain Friction Factor Calculator
The Swamee-Jain equation gives you friction factor in one shot - no iteration required. It's an explicit approximation of the Colebrook-White equation, accurate to within 3%. This calculator also runs the full iterative Colebrook-White solution so you can see exactly how close they are.
Calculate Friction Factor (Swamee-Jain vs Colebrook-White)
Results
What Is the Swamee-Jain Equation?
The Colebrook-White equation is the gold standard for turbulent pipe flow friction factor - but it's implicit: friction factor appears on both sides of the equation, so you have to solve it iteratively (as the Moody Chart Calculator does with Newton-Raphson iteration).
In 1976, Prabhata K. Swamee and Akalank K. Jain published an explicit approximation that gives nearly identical results in a single calculation. It's been widely used in engineering practice ever since - especially for hand calculations, spreadsheets, and embedded systems where iteration is inconvenient.
The Swamee-Jain Formula
f = 0.25 / [log₁₀(ε/D/3.7 + 5.74/Re⁰·⁹)]² - f - Darcy friction factor (dimensionless)
- ε/D - relative roughness (dimensionless)
- Re - Reynolds number (dimensionless)
Valid range: Re between 5,000 and 10⁸, ε/D between 10⁻⁶ and 5×10⁻². Accuracy: within ±3% of the Colebrook-White solution.
The Colebrook-White Equation (for comparison)
1/√f = -2.0 × log₁₀(ε/D/3.7 + 2.51/(Re × √f)) This implicit equation is solved iteratively - this calculator uses Newton-Raphson iteration (same as the main Moody Chart Calculator) converging to tolerance 10⁻¹⁰.
Worked Example
Commercial steel pipe (ε/D = 0.0001), Re = 100,000.
f_SJ = 0.25 / [log₁₀(0.0001/3.7 + 5.74/100000⁰·⁹)]²
= 0.25 / [log₁₀(2.703×10⁻⁵ + 5.74/35,938)]²
= 0.25 / [log₁₀(2.703×10⁻⁵ + 0.0001598)]²
= 0.25 / [log₁₀(0.0001868)]²
= 0.25 / [-3.7285]²
f_SJ ≈ 0.01796
Colebrook-White: f_CW ≈ 0.01795 - difference < 0.1%
Frequently Asked Questions
Is Swamee-Jain accurate enough for real engineering?
Yes, for nearly all practical applications. A 3% error in friction factor translates to less than 3% error in pressure drop - well within the uncertainty of most pipe roughness estimates. For water mains and HVAC design, Swamee-Jain is entirely appropriate. Use Colebrook-White for high-stakes, precision-critical work.
What is the Churchill equation, and is it better than Swamee-Jain?
The Churchill (1977) equation is another explicit friction factor approximation, valid across all flow regimes (including laminar and transitional). It's slightly more complex than Swamee-Jain but is more accurate in the transitional zone. For turbulent flow only, Swamee-Jain is simpler and nearly as accurate as Churchill.
Can Swamee-Jain be used for laminar flow?
No. Swamee-Jain is only valid for turbulent flow (Re > 4,000, ideally Re > 5,000). For laminar flow (Re < 2,300), use f = 64/Re - try our Laminar Flow Friction Factor Calculator.
Related Tools
📊 Moody Chart Calculator
Full Colebrook-White solution with interactive Moody diagram visualization.
🌊 Reynolds Number Calculator
Find Re to use as input to this Swamee-Jain calculator.
📏 Relative Roughness Calculator
Find ε/D from pipe material and diameter.
➡️ Laminar Friction Factor
For Re < 2300: use f = 64/Re instead.