Calculate Darcy and Fanning friction factors for pipe flow. Moody chart calculation with Colebrook-White equation, Reynolds number, pipe material roughness, and head loss per meter.
The Darcy friction factor (f) is a dimensionless parameter used in the Darcy-Weisbach equation to calculate pressure drop and head loss in pipe flow. For laminar flow (Re < 2100), f = 64/Re. For turbulent flow, f depends on both the Reynolds number and the relative roughness ε/D, described by the implicit Colebrook-White equation.
The Moody chart is a graphical way to read friction factor against Reynolds number for different roughness values. This calculator replaces that lookup with a direct numerical estimate and also reports Darcy and Fanning factors, Reynolds number, and head loss per length.
Pipe flow calculations usually need more than a single friction number. Seeing the Reynolds number, roughness, and resulting head loss together makes it easier to size piping or compare operating conditions without switching between a chart and a worksheet.
Reynolds Number: Re = vD/ν Laminar (Re < 2100): f = 64/Re Turbulent (Colebrook-White): 1/√f = −2 log₁₀(ε/(3.7D) + 2.51/(Re√f)) Swamee-Jain (explicit approximation): f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re⁰·⁹)]² Darcy-Weisbach: h_f = f × (L/D) × v²/(2g) Pressure drop: ΔP = f × (L/D) × ρv²/2 Fanning factor: f_F = f_D / 4
Result: f = 0.0218, Re = 202,390 (Turbulent)
4" commercial steel pipe (ε = 0.045 mm) with water at 2 m/s: Re = 2 × 0.1016 / 1.004e-6 = 202,390 (turbulent). Swamee-Jain: f = 0.0218. Head loss: 0.0047 m per meter of pipe.
The Moody chart, published by Lewis Moody in 1944, plots the Darcy friction factor versus Reynolds number for various relative roughnesses. It consolidates decades of experimental and theoretical work into a single, universally used tool. The chart reveals four distinct flow regimes: laminar (f = 64/Re), critical/transitional (unstable), smooth turbulent (f depends on Re only), and fully rough (f depends on ε/D only).
Derived in 1939, the Colebrook-White equation bridges the smooth and rough turbulent regimes with a single implicit formula. Its implicit nature was acceptable in 1939 (solved by trial-and-error or nomographs), but modern computers and explicit approximations (Swamee-Jain 1976, Haaland 1983) make iterative solution unnecessary. The Swamee-Jain approximation used here is accurate to within 1% for 5×10³ < Re < 10⁸ and 10⁻⁶ < ε/D < 5×10⁻².
Friction factor is the key input for pipe system sizing — the single most common calculation in fluid engineering. A 10% error in f translates to 10% error in pressure drop, which affects pump sizing, energy costs, and system capacity. For a typical water distribution system operating millions of hours, even small accuracy improvements in friction factor calculation yield significant cost savings.
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The Darcy friction factor (f_D) is 4× the Fanning friction factor (f_F). Both are correct but used in different regional and disciplinary traditions. Always verify which convention a reference or textbook uses. The Darcy-Weisbach equation uses the Darcy factor.
The Colebrook-White equation has f on both sides: 1/√f = −2 log(ε/(3.7D) + 2.51/(Re√f)). This requires iterative solution (Newton-Raphson or fixed-point iteration). Explicit approximations like Swamee-Jain avoid this iteration with minimal accuracy loss.
Between Re ≈ 2100 and 4000, flow can be either laminar or turbulent depending on disturbances. The friction factor is unpredictable in this range. Pipe design should avoid operating in the transition zone if possible.
At very high Reynolds numbers, the viscous sublayer becomes thinner than the roughness elements, so turbulent eddies interact directly with surface features. This is why the Moody chart lines become horizontal (fully rough regime) at high Re.
No. The pipe friction factor (Darcy/Fanning) relates to fluid shear stress in internal flow. The coefficient of friction (μ) for solid surfaces relates to contact friction. Different physics, different definitions, same word "friction."
Temperature mainly affects viscosity (and thus Reynolds number). Water at 20°C has ν = 1.004×10⁻⁶ m²/s; at 80°C, ν = 0.365×10⁻⁶ m²/s — nearly 3× lower, which triples Re. Higher Re generally means higher friction factor for turbulent flow.