Duct Static-Pressure Loss
Friction loss in a round duct run — Swamee-Jain friction factor on standard air, with in. w.g. per 100 ft for the ASHRAE-chart crowd.
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The engineering
The ASHRAE friction chart is Darcy-Weisbach in disguise, and this card computes it directly: velocity from flow and diameter, Reynolds number on your air properties, then the Swamee-Jain explicit fit for the friction factor (laminar 64/Re below Re = 2,300, which you will essentially never see in a real duct). The default ε = 0.09 mm is medium-smooth galvanized spiral — the roughness the ASHRAE chart assumes. Bump it to ~0.9 mm for fully-stretched flex duct, or worse if it sags.
The friction-rate row is what you actually design to: the classic equal-friction method sizes trunks around 0.8–1 Pa/m (≈ 0.1 in. w.g./100 ft), and much past 2 Pa/m you start buying noise and fan energy. Remember this is straight-run friction only — elbows, takeoffs, transitions, and dampers go in as fitting losses (C·½ρV²) on top, and in short residential runs the fittings usually dominate.
Rectangular duct? Convert to equivalent round first (ASHRAE's D_e = 1.30·(a·b)^0.625/(a+b)^0.25) and run it through this card — the friction rate carries over at equal flow.
Where this math comes from
Julius Weisbach wrote the head-loss law in its modern form in 1845 and Henry Darcy's Dijon pipe experiments (1857) put wall roughness into it — but for a century HVAC designers couldn't use it directly, because the friction factor needed iteration. Cyril Colebrook's 1939 transition formula and Lewis Moody's 1944 chart tamed the physics; what ductwork needed was a chart in duct units.
D. K. Wright Jr. delivered exactly that in 1945 with 'A New Friction Chart for Round Ducts' — cfm, duct diameter, and inches of water per 100 feet on one log-log sheet, built on Colebrook with galvanized-duct roughness baked in. ASHRAE adopted and refined it, and it has anchored the Duct Design chapter of the Fundamentals Handbook ever since. Swamee and Jain's 1976 explicit fit is what lets this card skip both the chart and the iteration.
- 1845Julius WeisbachHead-loss equation in the modern f·(L/D)·V²/2g form.
- 1857Henry DarcyDijon experiments make wall roughness part of the friction law.
- 1939Cyril ColebrookImplicit transition formula for f across the turbulent range.
- 1945D. K. Wright Jr.Publishes the round-duct friction chart that became the ASHRAE standard.
- 1976P. K. Swamee & A. K. JainExplicit friction-factor fit — the equation this card evaluates; ASHRAE Fundamentals carries the modern chart.
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