Fan Affinity Laws (Speed / Diameter Change)
For a fixed fan changing speed: airflow scales with speed (Q2 = Q1 r), static with the square (SP2 = SP1 r^2), power with the cube (BHP2 = BHP1 r^3). 10,000 CFM / 1.0 in wg / 5.0 BHP from 900 to 1200 rpm -> 13,333 CFM, 1.78 in wg, 11.85 BHP; slowing to r 0.75 cuts power 58%, the VFD payback in one line. The fan curve governs.
Formula and source
r = N2/N1; Q2 = Q1 r; SP2 = SP1 r^2; BHP2 = BHP1 r^3.
The fan affinity (fan) laws for a speed change from AMCA / ASHRAE Handbook - Fundamentals, by name.
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