7.2. Fan Acoustics

The sound emission of a fan impeller is determined by its geometry and operating data. An exact theoretical calculation of the sound level is usually not possible in advance, approximate calculations are possible with a very high technical and time effort. The sound power of a fan impeller can therefore only be estimated approximately in advance by simple means and shows the following dependencies on the volume flow, the pressure difference, the diameter, the density and the circumferential speed:

 L_W\thicksim V\cdot\Delta p^2

With:

 V\thicksim u\cdot D^2
 \Delta p\thicksim\rho\cdot u^2 

applies: 
 L_W\thicksim\rho^2\cdot D^2\cdot u^2

The sound power level of a fan impeller is linearly dependent on the volume flow and quadratically dependent on the pressure increase. If these dependencies are further subdivided, a quadratic dependency on the diameter and a dependency of the 5th power on the circumferential speed become apparent.
Formulas for a rough estimation of the sound power level are:

L_W=L_{W,spez_1}+10\cdot\log_{\frac{V}{V_{ref}}}+20\cdot\log_{\frac{\Delta p}{p_{ref}}}

L_W=L_{W,spez_2}+50\cdot\log_{\frac{u_2}{u_1}}+20\cdot\log_{\frac{\rho_2}{\rho_1}}+20\cdot\log_{\frac{D_2}{D_1}}

The summand  L_{W,spez_1} results from the individual geometry of the fan wheel. With this method, similar to the proportionality laws of air technology, it is possible to estimate on the basis of measured data how a wheel of the same series will behave in other sizes and operating ranges. In the range of highest efficiency, the sound power is usually lower than when the fan is operated outside this range.