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Moody Chart Reader

// FRICTION FACTOR • REYNOLDS • ROUGHNESS

● Turbulent Darcy fD
A friction factor reader. Not a piping design, and not a hydraulic model of your system. Colebrook-White is a curve fit to experimental data that scatters by roughly ±15%, and it describes steady, fully developed, isothermal, single-phase flow in a straight circular pipe. The roughness you type is the largest uncertainty on the page and it is a guess. Open for the full scope limits.

What this tool actually does

Educational and informational use only. This page is for learning, screening and sanity checking a number you got somewhere else. It is not an engineering deliverable.

Solves the Colebrook-White equation iteratively for the Darcy friction factor at a given Reynolds number and relative roughness, plots the point on a Moody diagram, and reports the laminar branch (f = 64/Re) and the Prandtl-von Kármán smooth-pipe limit alongside it. The arithmetic is checked: the tool ships a physics suite reachable from the console, and the spec pins Colebrook reference values and the back-substitution residual.

Darcy, not Fanning. The two differ by a factor of four, and using one where the other belongs is the most common error in this calculation. The Fanning value is shown next to it so the mistake is visible rather than silent.

What the correlation itself cannot tell you

  • The scatter is in the data, not the solver. Colebrook is fitted to Nikuradse and Colebrook-White pipe measurements, and the underlying spread is about ±15%. A friction factor read to six digits is arithmetic precision, not physical accuracy.
  • Roughness in service is unknown. The published 0.045 mm for commercial steel is a new, clean pipe. Corrosion, scale, biofilm, wax and deposits move ε by an order of magnitude over the life of a line, and there is no way to recover the real value except by measuring pressure drop on the actual pipe.
  • Equivalent sand-grain roughness is not a surface finish. It is a fitted parameter from pipe experiments. Ra, Rz and machining callouts do not convert to ε, and treating them as though they do produces a confident wrong answer.
  • The transition region is not predictable. Between roughly Re 2000 and 4000 the flow may be laminar, turbulent or intermittent depending on disturbances upstream. The chart draws a band there because no correlation applies inside it.
  • Friction factor is not pressure drop. Getting f right and the length, diameter, density or velocity wrong is the usual route to a wrong answer.

Not modelled at all

  • Minor losses: fittings, valves, bends, tees, entrances, exits, expansions and contractions. In a short run these commonly exceed the straight-pipe loss this tool computes.
  • Two-phase flow, slurries, non-Newtonian fluids, and anything with entrained solids or gas.
  • Compressible flow where density changes materially along the pipe, and choked flow.
  • Entrance-length effects, non-isothermal flow, and viscosity varying along a heated or cooled line.
  • Non-circular ducts beyond a hydraulic-diameter approximation, partially full pipes and open channels.
  • Transients: water hammer, surge, pump start and stop, valve slam.
  • Elevation, pump curves, NPSH, cavitation and flashing.

Nothing on this page checks whether the pipe can hold the pressure, whether the material suits the fluid, or whether the velocity will erode it.

Never use this for

  • Piping design, rating, wall-thickness selection or flexibility analysis under ASME B31.1, B31.3 or any equivalent code.
  • Relief and blowdown system sizing or any overpressure protection case under API 520 and API 521.
  • Fire protection hydraulics under NFPA 13, NFPA 20 or NFPA 24.
  • Gas distribution or transmission design, custody transfer, or emissions and regulatory reporting.
  • Contractual pressure drop, pump acceptance testing, or any performance guarantee.
  • Safety-instrumented functions, or any case where a wrong flow rate has a safety consequence.

What to use instead when it matters

Size real systems in hydraulic software that carries the fittings, the elevation profile and the pump curve, using a roughness bracketed between new and fouled rather than a single value. Where the answer governs a purchase, a guarantee or a safety case, have it reviewed by a qualified mechanical or process engineer working to the governing code, and confirm the result against measured pressure drop as soon as the line exists.

No warranty. No liability. You assume all risk. This page and its outputs are provided as-is and as-available, without warranty of any kind, express or implied, including accuracy, completeness, timeliness, reliability, fitness for a particular purpose, merchantability, engineering or professional suitability, regulatory or code acceptability, or non-infringement. To the maximum extent permitted by law, the author accepts no liability for any loss, injury, death, damage, cost or claim arising from use of or reliance on this page.

Independent verification required. Check every value against a published Moody diagram, a recognised hydraulics reference, and a qualified engineer before it informs any design, operation or purchase. The governing code and professional judgement control; where this page disagrees with them, this page is wrong.

Consequential damages excluded. To the maximum extent permitted by law, in no event will the author or maintainers be liable for any direct, indirect, incidental, special, exemplary, punitive or consequential damages, including loss of use, data, profits or business interruption, however caused and on any theory of liability, whether in contract, strict liability or tort including negligence, arising out of or in connection with this page, even if advised of the possibility of such damage.

Indemnity. By using this page you agree to indemnify and hold harmless the author and maintainers against any claim, demand, loss or expense arising out of your use of it or of anything derived from it.

Severability. If any part of this notice is held unenforceable, the remainder continues to apply, and the unenforceable part is limited to the least extent necessary rather than struck out.

Moody Diagram
Laminar (f=64/Re)
Smooth (Prandtl)
Constant ε/D (Colebrook)
Controls
Chart Overlays
Current Values
Turbulent Flow
Re (inertia/viscosity) 1.00×10⁵
fD (Darcy friction) 0.0198
fF (Fanning = fD/4) 0.00495
ε/D (rel. roughness) 0.001
Equation Colebrook
Input Parameters
Reynolds Number (Re) 100,000
Relative Roughness (ε/D) 0.001
Flow Regime Classification
Regime Turbulent
Classification Logic Re > 4000 → Turbulent
Equation Used
Colebrook-White Equation
1/√f = -2·log₁₀(ε/(3.7D) + 2.51/(Re·√f))
Solution Method
Algorithm Fixed-point iteration
Initial Guess (Swamee-Jain) 0.01985
Convergence Tolerance 1×10⁻¹⁰ (relative)
Iteration Log
Final Result
Darcy Friction Factor (fD) 0.019829
Fanning Friction Factor (fF) 0.004957
Iterations Required 6
Converged ✓ Yes
Verification
Back-substitution check LHS = RHS ✓
Residual 2.3×10⁻¹²

Colebrook is a data fit, not a law. The friction factor above carries the roughly ±15% scatter of the experiments behind the correlation, and the roughness you entered is almost certainly not the roughness of a pipe in service. Add minor losses, bracket the roughness between new and fouled, and have anything that governs a design, a purchase or a safety case reviewed by a qualified engineer.