Duct Sizing: Method

Friction, Fittings and the Equal-Friction Method

Friction loss

Air moving through a duct loses pressure to wall friction by the Darcy equation, Δp = f (L/D) ρV²/2: the friction factor f times the length in diameters times the velocity pressure. The friction factor depends on the Reynolds number and the relative roughness ε/D through Colebrook's implicit relation, which the tool solves by iteration; at the Reynolds numbers of HVAC ducts (10⁴ to 10⁶) f lies between 0.015 and 0.03 and is governed more by the roughness than by the velocity. The roughness classes are ASHRAE's: galvanized steel with normal seams about 0.0003 ft, smooth aluminum or plastic 0.0001 ft, lined or fully extended flexible duct 0.003 ft, and compressed flexible duct an order of magnitude rougher still, which is why a sagging flex run can double a branch's loss.

Rectangular ducts

The velocity comes from the actual area. For friction a rectangular duct of sides a and b behaves like a round duct of Huebscher's equivalent diameter D_e = 1.30 (ab)^0.625/(a + b)^0.25, which carries the same flow at the same friction rate; it is not the hydraulic diameter 4A/P, which overstates the capacity of a flat duct.

Fittings

Elbows, transitions, branches and dampers lose pressure in proportion to the velocity pressure, Δp = C ρV²/2, with C from the ASHRAE or SMACNA fitting tables (a smooth radius elbow 0.1 to 0.3, a mitered elbow without vanes about 1.2, an abrupt entry 0.5). The coefficients of a segment's fittings are entered as their sum, referred to the velocity in that segment.

Equal-friction sizing

The common design method sizes every segment so that the friction rate is the same, typically 0.08 to 0.10 in. w.g. per 100 ft (0.8 to 1.0 Pa/m) for low-pressure supply ducts, which keeps velocities moderate and balances the branches roughly. For each segment the tool solves for the round diameter at which the entered design rate is met at that segment's flow; a segment whose actual rate is far above the design rate is undersized, far below it is oversized. Velocities above about 2,500 ft/min (12.7 m/s) in occupied-space ducts are flagged for noise.

Fan pressure

The sum of the segment losses along the index run (fan to the farthest or highest-loss terminal) plus the terminal's own loss is the external static pressure the distribution needs; adding filters, coils and other equipment losses gives the fan static pressure to select the fan at the total airflow. Return ducts are sized the same way and their loss added.

Not included

Static regain and the velocity-reduction methods, system-effect factors at the fan inlet and outlet, leakage, thermal effects on density along the run, and acoustic calculations beyond the velocity flag.