Darcy Friction Factor Calculator

The Darcy friction factor (also called the Darcy-Weisbach friction factor) is a dimensionless number that quantifies the resistance to flow caused by pipe wall friction. It is a key input in the Darcy-Weisbach equation (h_l = f × (L/D) × V²/2g) used to calculate head loss and pressure drop in pipe systems. Accurate friction factor values are essential for pump sizing, pipe network design, and energy efficiency analysis.

For laminar flow (Re < 2300), the friction factor is calculated exactly using f = 64/Re — a simple analytical formula. For turbulent flow (Re > 4000), the Colebrook-White equation is used: 1/√f = −2 log(k/(3.7D) + 2.51/(Re√f)). Because this equation is implicit, this calculator uses the Mileikovskyi-Tkachenko explicit approximation, which achieves accuracy within 0.00072%. The transition zone (2300 < Re < 4000) is treated as transitional flow.

The Colebrook-White equation is the industry-standard formula for computing the Darcy friction factor in turbulent pipe flow. It accounts for both the pipe's relative roughness (k/D) and the Reynolds number. Because it's implicit in f, engineers often use explicit approximations like Swamee-Jain or Mileikovskyi-Tkachenko for computational efficiency. This calculator uses the Mileikovskyi-Tkachenko approximation, valid for 2320 ≤ Re ≤ 10⁹ and 0 ≤ k/D ≤ 0.65.

Relative roughness (k/D) is the ratio of the pipe's absolute surface roughness (k) to its hydraulic diameter (D). A higher relative roughness means more surface irregularities relative to pipe size, increasing the friction factor and therefore energy losses. Smooth pipes (low k/D) approach the smooth-pipe limit on the Moody chart, while fully rough pipes see friction dominated entirely by roughness, independent of Reynolds number.

The Darcy friction factor (f) and the Fanning friction factor (f_F) are both used in pipe flow, but they differ by a factor of 4: f = 4 × f_F. The Darcy factor is used in the Darcy-Weisbach head loss equation, while the Fanning factor appears in momentum transfer and heat transfer formulations. Always verify which convention a source uses before applying values, as mixing them up leads to a 4× error in pressure drop calculations.

Typical absolute roughness values: PVC and drawn tubing ≈ 0.0015 mm (very smooth), commercial steel ≈ 0.046 mm, wrought iron ≈ 0.046 mm, galvanized iron ≈ 0.15 mm, cast iron ≈ 0.26 mm, concrete ≈ 0.3–3 mm (varies widely with finish), and riveted steel ≈ 0.9–9 mm. Smoother pipes yield lower friction factors at the same Reynolds number, reducing energy losses in fluid systems.

Once you have the Darcy friction factor f, plug it into: h_l = f × (L/D) × (V²/2g), where h_l is head loss (m), L is pipe length (m), D is hydraulic diameter (m), V is average flow velocity (m/s), and g is gravitational acceleration (9.81 m/s²). For pressure drop, use: ΔP = f × (L/D) × (ρV²/2), where ρ is fluid density (kg/m³). These equations apply to fully developed, steady-state, incompressible flow.

This calculator handles the full practical range of Reynolds numbers. For Re < 2300 (laminar flow), it uses the exact analytical formula f = 64/Re. For Re between 2300 and 4000 (transitional flow), results are approximate as flow behavior is unpredictable in this region. For Re ≥ 4000 up to 10⁹ (turbulent flow), the Mileikovskyi-Tkachenko approximation of the Colebrook-White equation is applied with relative roughness k/D up to 0.65.