Duct design is one of the few areas where the easy method is also the right one for most jobs. The equal friction approach — size every duct to the same pressure loss per metre — gets you a balanced, quiet system without iteration, and it is what the majority of commercial low-pressure work uses.
Pick a friction rate, then size everything to it
Around 0.8–1.0 Pa/m (roughly 0.08–0.1 in. w.g. per 100 ft) is the usual starting point. Lower means physically bigger ducts, more sheet metal and more building space, but a smaller fan running cheaper for the life of the building. Higher saves capital and costs energy forever. Given how long ducts last and how fan power scales, the cheap-to-run end of that range is usually the right commercial decision.
Then check velocity, because that is what actually limits you
A friction rate on its own will happily hand you a duct that whistles. Noise, not pressure drop, is the real constraint. Keep branch ducts near occupied spaces under about 5 m/s, main ducts under roughly 8–10 m/s, and treat anything above 10 m/s as needing acoustic attention. Plant rooms tolerate far more than an open-plan office does — the limit is about the room, not the duct.
Round is better, but rectangular fits
Round duct has the lowest perimeter per unit area, so it is the cheapest to make and the lowest loss. Rectangular exists because buildings have ceilings. Convert with the equivalent diameter relation De = 1.30(ab)0.625/(a+b)0.25, which matches friction loss at equal airflow — not equal cross-sectional area, which is the common mistake. A flat duct is hydraulically smaller than a square one of the same area, so keep the aspect ratio under about 4:1; past that you are paying for sheet metal and fan energy to move the same air.
Fittings cost more than straight duct
A long radius elbow is cheap; a mitred one without turning vanes can cost as much as many metres of straight duct. Sudden expansions, tight takeoffs and anything immediately at a fan discharge are worse still — a fan needs several diameters of straight duct to develop a proper profile, and the "system effect" of not giving it that can eat a surprising fraction of the fan's rated performance.
Flexible duct is not free
Fully stretched, flex duct has roughly 30 times the roughness of galvanised steel. Compressed — which is how it usually ends up installed — it is dramatically worse, and a few metres of sagging flex can undo the whole balancing exercise. Use short, taut runs only.
Working it through
Size the ducts on the Duct Sizing tool, get the airflow the space actually needs from Coil Load & SHR and Ventilation Rate, and check the fan speed and power consequences on Pump Affinity Laws — the fan laws are the same relations, and power goes as the cube of speed.