The core idea
A duct's job is to move a set volume of air (m³/h) with the least wasted energy and noise. For a given airflow Q, velocity v in the duct follows directly from the cross-sectional area A:
v = Q / A, with A = πD²/4 for a round duct.
Because area grows with the square of diameter, the relationship is steep: doubling the diameter quadruples the area and cuts velocity to one quarter. Friction losses in straight ducts scale roughly with the square of velocity, so halving the velocity cuts friction to about a quarter. That is why a slightly fatter duct is almost always cheaper to run than a small one pushed hard.
Practical design velocities: supply/extract trunk ducts in homes 3–5 m/s, branch runs 2–3 m/s. Above about 6–7 m/s in residential systems, noise and pressure drop grow quickly.
Real-world example
A home MVHR (heat-recovery ventilation) system must deliver 400 m³/h. In a Ø160 mm duct: A = 0.0201 m², so v = 400/3600 / 0.0201 ≈ 5.5 m/s — acceptable for a short trunk run. In a Ø125 mm duct the same air moves at ≈ 9 m/s: the friction penalty is about 2.7× higher and the duct will likely whistle at the vents. Sizing up one standard diameter at the trunk buys quiet, low-loss distribution for the life of the building.
Common pitfall
Sizing ducts by "what fits in the ceiling void" rather than by velocity. Squeezing a run into whatever space is left often doubles the velocity — and since losses scale with v², the fan must work disproportionately harder, costing noise and energy for decades. Check the velocity first, then negotiate the routing.