2.2. Definition of Mach Number

The Mach number describes the ratio of the air velocity v to the velocity of sound c :

Ma = \frac{v}{c}

For fans, this is additionally rewritten to the circumferential Mach number, which relates the velocity of the blade ends u to the speed of sound:

 Ma_{\mathrm{u}} =\frac{u}{c}

For peripheral Mach numbers Ma_{\mathrm{u}} greater than 0.15, significant differences in fan ratings can occur if Ma_{\mathrm{u}} does not remain the same for the test and specified conditions.

When the fan pressure increases, the average density of the fan also increases, while the ratio of the density at the inlet to the average density of the fan decreases. The similarity of the velocity triangle is then no longer given and the losses increase.

This is also the reason why, as Ma_{\mathrm{u}} increases, fan performance and efficiency first increase and then tend to deteriorate. This effect depends on the type of fan, the design of the fan impeller and the location of the operating point on the fan curve.