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CORRELATION GUIDE / VERSION 1

Refrigerant-side single-phase friction-factor correlations

Explains website options, friction-factor definitions, applicability ranges, and the relationship between explicit correlations and the Colebrook reference.

2026-08-28Darcy friction factorCircular tube
Distinguish available options from reference material

The current solver exposes 14 single-phase pressure-drop options. The reference table lists 15 literature correlations. Wood (1966) is unavailable because it degenerates to a zero friction factor at ε/D=0; three other correlations remain reference-only because their applicability ranges are unavailable.

1. Options available in the current solver

Solver optionImplementation ID

2. Quick comparison of literature correlations

Ranks follow the current source compilation and have not yet been independently recomputed by this website on a common grid. The correlations below are reference material and are not necessarily available in Solver Settings.

RankCorrelationFormula summaryPublished range

3. History, definitions, and laminar-flow basis

Single-phase pipe-flow friction factors developed from experimental pressure-drop laws into dimensionless definitions and engineering correlations. The Hagen–Poiseuille relation established the basis for fully developed laminar pipe flow; the work of Weisbach and Darcy led to the modern Darcy–Weisbach pressure-drop form; Fanning established another widely used coefficient convention. Modern literature must therefore distinguish Darcy and Fanning friction factors.

Darcy friction factorΔp = f_D (L/D) (ρu²/2)

This guide and the Moody diagram use the Darcy friction factor.

Fanning friction factorf_D = 4f_F

Always confirm which convention a paper or software package uses.

Fully developed laminar flow in a circular tube

Re = ρuD/μ　　f_D = 64/Re　　f_F = 16/Re

The current model treats Re < 2000 as laminar. Do not directly extrapolate this relation to developing entrances, non-circular ducts, non-Newtonian fluids, or two-phase flow.

4. Development of the Moody diagram and Colebrook relation

Moody's 1944 chart was not a single new correlation, but a graphical synthesis of accepted pipe-resistance research: the laminar branch came from the Hagen–Poiseuille relation, rough-pipe behavior drew on Nikuradse's experiments, the implicit Colebrook relation connected smooth- and rough-pipe regimes, and Moody presented these results through the Darcy friction factor, Reynolds number, and relative roughness.

RegionRange used hereTreatment
LaminarRe < 2000f_D = 64/Re, independent of relative roughness.
Critical zone2000 ≤ Re ≤ 4000Flow is unstable; no universally unique friction-factor curve applies.
TurbulentRe > 4000Depends on both Re and ε/D.
Moody diagram showing Darcy friction factor versus Reynolds number and relative roughness
Redrawn Moody diagram; the vertical axis is the Darcy friction factor and the gray area marks the critical zone.

Colebrook

1/√f_D = −2log₁₀[ε/(3.7D) + 2.51/(Re√f_D)]

Colebrook is implicit and requires iteration. Explicit correlations primarily reduce repeated computation cost, but introduce approximation error relative to the selected reference.

5. Usage guidance

  1. Confirm whether the Darcy or Fanning convention is used.
  2. Check the Re and ε/D range over the entire tube calculation, not only at the inlet.
  3. Interpret critical-zone results cautiously and compare against experiments or an independent reference.
  4. After changing a correlation, rerun benchmark cases rather than comparing names alone.

6. Principal references