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Directions

Hover over the diagram to explore values. Click anywhere to pin a point and calculate equivalent parameters.

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Details

The diagram plots the Fanning friction factor \( f_F \) versus the Reynolds number \( Re \) on logarithmic axes for a family of relative roughness values \( \epsilon / D \).

Laminar flow (\( Re < 2300 \)):

\( f_F = \dfrac{16}{Re} \)

Turbulent flow (Colebrook–White equation, solved by Newton–Raphson iteration):

\( \dfrac{1}{\sqrt{4 f_F}} = -2.0 \, \log_{10}\!\left( \dfrac{\epsilon / D}{3.7} + \dfrac{2.51}{Re \, \sqrt{4 f_F}} \right) \)

Darcy–Fanning relation:

\( f_D = 4 \, f_F \)

Implied relative roughness for a pinned point (inverted Colebrook–White equation):

\( \dfrac{\epsilon}{D} = 3.7 \left[ 10^{-1 / \left( 2 \sqrt{f_D} \right)} - \dfrac{2.51}{Re \, \sqrt{f_D}} \right] \)

Symbols:

• \( Re \) — Reynolds number (dimensionless)
• \( f_F \) — Fanning friction factor (dimensionless)
• \( f_D \) — Darcy friction factor (dimensionless)
• \( \epsilon \) — pipe surface roughness (m)
• \( D \) — pipe inner diameter (m)
• \( \epsilon / D \) — relative roughness (dimensionless)

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About

This simulation was generated by Professor David L. Silverstein and Dr. Loyal Murphy of the University of Mississippi using Google Gemini. It was modified for LearnChemE using Claude AI.