Fan laws: terms and equations

When the working conditions differ from those stated on the performance curves (speed and diameter); adjustment should be made using the following formulae before reference to the performance curves.

In the following formulae index “1” indicates the value on the curves and index “2” the value to be calculated.

Terms:
Dynamic pressure Pd [Pa] = [N/m²]
Static pressure Ps [Pa]
Total pressure Pt [Pa]
Air flow q [m³/s]
Air temperature t [°C]
Axial thrust F [N] = [kgm/s²]
Rot. Frequency n [RPM]
Power P [W]
Tip speed Vt [m/s]
Diameter d [m]
Density ρ [kg/m³]
Efficiency η  

Rot. Frequency Conversion
Rot. frequency ratio is:
n2
 k =
n1
Air flow:
q2 = q1 · k
Pressure:
P2 = P1 · k2
Power:
P2 = P1 · k3

Diameter Conversion
The difference in diameter should be restricted
to 10% above or below the measured diameter, since the fan laws are only accurate
for geometrically proportioned impellers.
Diameter ratio is:
d2
k =
d1
Air flow:
q2 = q1 · k3
Pressure:
P2 = P1 · k2
Power:
P2 = P1 · k5

Temperature Conversion
Temperature ratio is:
T1
k =
; where T = t + 273
T2
Air flow is not influenced by temperature.

Pressure:
P2 = P1 · k
Power:
P2 = P1 · k

Other Useful Formulae
Total pressure:
Pt = Ps + Pd
Dynamic pressure:
8 · q2 · ρ
Pd =
d4· π2
Tip speed:
n · π · d
Vt =
60
Axial thrust:
ρ · q2 · 4
F =
d2 · π
Efficiency:
pt · q
ρ =
p