Fan Affinity Laws (Speed Change)
How far airflow, static pressure, and horsepower move when a fan's speed changes.
Example
You enter
- Baseline airflow Q1 (cfm) 10000
- Baseline static pressure SP1 (in wg) 1
- Baseline brake horsepower BHP1 (hp) 5
- Baseline speed N1 (rpm) 900
- New speed N2 (rpm) 1200
You get
- Speed ratio r = N2/N1 1.3333
- New airflow Q2 = Q1 r 13,333 cfm
- New static SP2 = SP1 r² 1.78 in wg
- New power BHP2 = BHP1 r³ 11.85 hp
Checked against published worked examples from: Twin City Fan.
Details, formula, and sources
ScopeFor 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 or tabler = N2/N1; Q2 = Q1 r; SP2 = SP1 r^2; BHP2 = BHP1 r^3.
Source and editionThe fan affinity (fan) laws for a speed change from AMCA / ASHRAE Handbook - Fundamentals, by name.
Free accessThe affinity laws (flow proportional to speed, pressure to speed squared, power to speed cubed) are standard published fan-engineering relations.
What governsEstimate. AHJ and licensed professional govern.
API field namesq1_cfm, sp1_inwg, bhp1_hp, n1, n2, r, q2_cfm, sp2_inwg, bhp2_hp
- Affinity laws Q2 = Q1 r, SP2 = SP1 r^2, BHP2 = BHP1 r^3, r = N2/N1AMCA / ASHRAE Fundamentals
- Same fan and system same fan on the same system curve; efficiency shifts not capturedfan engineering
- Design aid the manufacturer's fan curve and ratings governscope of this tile