Tools › Building Systems › Ducts and Airflow › Duct Sizing › Example

Four-segment supply duct: Colebrook friction against the Moody chart and the ASHRAE equal-friction diameter

ToolDuct Sizing
SourceAmerican Society of Heating, Refrigerating and Air-Conditioning Engineers (2021). ASHRAE Handbook: Fundamentals. ASHRAE, Peachtree Corners, GA. Chapter 21, Duct Design (friction chart and the table of circular equivalents of rectangular ducts); Moody, L. F. (1944). "Friction Factors for Pipe Flow." Transactions of the ASME, Vol. 66, No. 8, pp. 671–684.
LevelUndergraduate

Problem

A galvanized-steel supply run (absolute roughness 0.0003 ft) carries 2,000 cfm through 40 ft of 18-in round duct, then 1,400 / 800 / 400 cfm through 30 / 25 / 20 ft of 16 / 12 / 10-in duct, each segment with its summed fitting coefficient; the terminal loses 0.05 in. w.g. and the equipment 0.5 in. w.g. Find the friction factor and pressure loss of each segment, the round diameter each segment would need at a design friction rate of 0.08 in. w.g. per 100 ft, and the fan static pressure.

Inputs to Enter

  • Air density 0.075 lb/ft³, material galvanized (ε = 0.0003 ft), design friction 0.08 in. w.g./100 ft
  • Segments S1–S4: length 40 / 30 / 25 / 20 ft, airflow 2,000 / 1,400 / 800 / 400 cfm, round D 18 / 16 / 12 / 10 in, ΣC 1.2 / 0.6 / 0.6 / 1.5
  • Terminal loss 0.05 in. w.g., equipment loss 0.5 in. w.g.
Open the Duct Sizing tool (loaded with this example)

Answers

  • Segment 1: V = 1,132 fpm, Re = 174,474, ε/D = 2 × 10⁻⁴ → Colebrook f = 0.01743 (Moody chart 0.01742)
  • Segment 1 equal-friction round diameter at 0.08 in. w.g./100 ft: 18.54 in (ASHRAE friction chart: 18 to 19 in)
  • Segment 1 losses: p_v 0.0797 in. w.g., friction 0.0370, fittings 0.0957, total 0.1327 in. w.g.
  • Duct run 0.333 in. w.g.; with the terminal 0.383; fan static pressure 0.883 in. w.g.

Notes

The tool's default inputs are this run; press Submit. A further check of the Huebscher equivalent diameter: a 20 × 10 in rectangular duct gives D_e = 1.30 · 200^0.625 / 30^0.25 = 15.23 in against the ASHRAE table's 15.2 in (enter Rect W 20, Rect H 10 on a segment).