Fan laws used to calculate axial fan performance

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	P_d	[Pa] = [N/m²]
Static pressure	P_s	[Pa]
Total pressure	P_t	[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	V_t	[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:

P_t

P_s

+ P_d

Dynamic pressure:

		8 · q² · ρ
P_d	=
		d⁴· π²

Tip speed:

		n · π · d
V_t	=
		60

Axial thrust:

		ρ · q² · 4
F	=
		d² · π

Efficiency:

		p_t · q
ρ	=
		p

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Fan laws: terms and equations