Swamee–Jain Friction Factor

Colebrook and White's 1939 equation is the accepted description of turbulent friction, but it has f on both sides and must be iterated: a genuine nuisance in the slide-rule era and still an irritation in a spreadsheet. In 1976 Prabhata Swamee and Akalank Jain published this explicit fit that lands within about 1% of Colebrook across the whole practical range, and it has been the default in hydraulic software ever since. Commercial steel (ε = 0.045 mm) at 100 mm bore and Re = 100 000 gives f ≈ 0.0202, matching a Moody chart read to the width of a pencil line.

Watch the roughness values: ε is absolute, in the same length units as D, and it varies enormously (0.0015 mm for drawn tubing, 0.045 mm for new commercial steel, 0.15 mm for galvanised, 0.26 mm for cast iron, 3 mm for riveted steel). New-pipe roughness is also optimistic; a domestic-water steel line ten years into service can have several times the design ε from tuberculation, which is exactly why plant hydraulic models drift from reality and why Hazen–Williams C values are quietly downgraded as systems age.