Swamee-Jain Friction Factor Calculator
Enter pipe roughness ε, diameter D and Reynolds number Re to compute the Darcy friction factor from the explicit Swamee-Jain formula, avoiding iterative Colebrook solving.
Input Data
Results
At a glance:In the Darcy-Weisbach head-loss formula h_f = f·(L/D)·v²/(2g), the hardest term to find is the Darcy friction factor f. In the turbulent regime f depends on relative roughness ε/D and Reynolds number Re via the implicit Colebrook-White equation, which must be solved iteratively. Swamee and Jain (1976) proposed an explicit approximation that returns f in one step: f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re^0.9)]², where f is the Darcy friction factor (dimensionless), ε the absolute roughness (m), D the diameter (m) and Re the Reynolds number. The ε/(3.7D) term dominates fully-rough turbulence (f depends only on roughness), while 5.74/Re^0.9 captures the viscous sublayer's contribution in smooth-pipe turbulence; summing them covers the entire transitional turbulent region. For commercial steel ε=0.00015 m, D=0.1 m, Re=1e5: ε/(3.7D)≈4.05e-4, 5.74/Re^0.9≈1.82e-4, sum≈5.87e-4, log₁₀≈−3.231, squared≈10.44, f=0.25/10.44≈0.0239 — matching the Moody chart within ~1%.
Formula
Swamee-Jain: f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re^0.9)]².
ε roughness (m), D diameter (m), Re Reynolds number (dimensionless).
Turbulent range 4000<Re<10⁸; laminar uses f = 64/Re.
$$f = \dfrac{0.25}{\left[\log_{10}\!\left(\dfrac{\varepsilon}{3.7D} + \dfrac{5.74}{Re^{0.9}}\right)\right]^{2}}$$How to Use
- Enter the absolute pipe roughness ε (m; steel ≈ 0.00015).
- Enter the diameter D (m) and the Reynolds number Re.
- The tool returns the Darcy friction factor f from the Swamee-Jain formula.
Case Studies
Water main friction factor
Commercial steel ε=0.00015 m, D=0.1 m, Re=1e5.
f = 0.25/[log₁₀(0.00015/0.37 + 5.74/1e5^0.9)]² ≈ 0.0239.
Plug into Darcy-Weisbach to estimate head loss per meter of pipe.
Smooth vs rough regimes
At low Re the 5.74/Re^0.9 term dominates (smooth-pipe behavior).
At very high Re the ε/(3.7D) term dominates (fully rough, f independent of Re).
Swamee-Jain smoothly blends both without iteration.
FAQ
When do I use Swamee-Jain instead of Colebrook?
Whenever you want f quickly without iteration. Swamee-Jain is explicit and within ~1% of Colebrook for 4000<Re<10⁸ and 10⁻⁶<ε/D<10⁻² — fine for most engineering estimates and spreadsheet calculations.
What about laminar flow?
For Re<2000 (laminar) the friction factor is f=64/Re, which does not depend on roughness. Swamee-Jain applies only to turbulent flow.
Is this the Darcy or Fanning factor?
It returns the Darcy-Weisbach factor, 4× the Fanning factor. Use it directly in h_f=f·(L/D)·v²/(2g).
How do I get the Reynolds number?
Re = ρvD/μ = vD/ν, where ρ is density, v the mean velocity, D the diameter, μ dynamic and ν kinematic viscosity.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.