CastorPrep

Friction factor calculator (Colebrook / Moody)

The Darcy friction factor from Reynolds number and relative roughness — the Colebrook equation the Moody diagram is drawn from.

Free, right in your browser. Every result shows its work.

Don't have it? Use the Reynolds number calculator.

Result

Darcy friction factor, f
0.01851
Fanning friction factor (f/4)
0.004628
Flow regime
turbulent (Re > 4,000)
Swamee–Jain (explicit) check
0.01845
  1. 1.Colebrook: 1/√f = −2 log₁₀[ (ε/D)/3.7 + 2.51/(Re√f) ]
  2. 2.Start from Swamee–Jain: f₀ = 0.25 / [log₁₀((ε/D)/3.7 + 5.74/Re^0.9)]² = 0.018452
  3. 3.Iterate to convergence (12 iterations): f = 0.018514

How it's tested on the exam

Shows up on: PE Mechanical (Thermal & Fluid Systems) · PE Mechanical (HVAC & Refrigeration) · PE Civil (Water Resources & Environmental)

  • Darcy vs Fanning. The Moody diagram gives the Darcy factor; the Fanning factor is one quarter of it. Use Darcy in h_f = f(L/D)(V²/2g).
  • Relative roughness is ε/D with both in the same unit. Commercial steel is about 0.00015 ft (0.045 mm); dividing that by a diameter in inches is off by 12.
  • Laminar flow ignores roughness. Below Re ≈ 2,000, f = 64/Re regardless of the pipe.
  • Reading the diagram vs solving the equation. On the exam, a careful diagram read is usually close enough; when two choices are within a few percent, the equation settles it.

Worked example

Find the Darcy friction factor at Re = 100,000 in a pipe with ε/D = 0.0001.

  1. 1.Turbulent (Re > 4,000), so solve Colebrook: 1/√f = −2 log₁₀(ε/3.7D + 2.51/(Re√f))
  2. 2.Start from Swamee–Jain (f = 0.01845) and iterate to convergence

f ≈ 0.01851

Where it is in the Handbook

  • Hydraulics, Fluids, and Pipe Flow — Darcy-Weisbach Equation — PE Mechanical Reference Handbook
  • Hydraulics — Head Loss Due to Flow (Darcy-Weisbach Equation) — PE Civil Reference Handbook
  • Hydraulics, Fluids, and Pipe Flow — Flow in Closed Conduits (Moody diagram) — PE Mechanical Reference Handbook

Section names as printed in the current NCEES PE Reference Handbooks (Mechanical 2.1, Civil 2.2); numbering can shift between versions. On exam day you'll use your own approved calculator — here's which models NCEES allows.