# Generalised fan sound power formula

From Section 14.6, assuming that dipole sources predominate, and that the Reynolds number exponent has an average value of -0.5, we may state fan sound power level:

Oc fan power x (Mach number)3 x (Reynolds number) 0 5 <x N3D5 x N3D3 x -0.5 D-1,

Or fan sound power level SWL oc N5 5D7.

This of course is an average of the extreme variations which could occur but is unlikely to lead to drastic errors for small vari­ations in speed and diameter.

Converting to a logarithmic decibel scale we may say in the general case:

Fan sound power level SWL (dBW re 10-12 watts)

= X + 55 log — + 70 log — Equ 14.28

N, D1 H

Where:

X = constant for a particular design of fan operat­

Ing at a particular point on its characteristic

N1 = original fan speed (rev/min)

N2 = final fan speed (rev/min)

D-i = model fan diameter (m or mm)

D2 = final fan diameter (m or mm)

This holds good over reasonable ranges of speed and size if the inherent inaccuracies and tolerances of the British Stan­dard are recognised.

Example 1:

Suppose a fan 500 mm diameter operating at 1100 rev/min has a sound power level of 76 dBW. What will this increase to at 1350 rev/min?

Increase = 55 log =4.89 dBW 1100

I. e. the new sound power level will be 81 dBW approximately (no greater accuracy is justified).

In like manner we may calculate the sound power level of a 630 mm diameter fan at 1100 rev/min in the same geometric series.

Increase = 70 log = 7.03 dBW 500

I. e. the new sound power level will be 83 dBW to nearest 1 dBW.

To assist the fan and system designer, these calculations may be plotted on a Nomogram (Figure 14.22). For ease in the ma­nipulation of the figures they can be related to a datum for a 1000 mm diameter fan at 1000 rev/min.

Thus if we have the base figure X for a 1000 mm diameter fan at 1000 rev/min at a certain point on its characteristic, A the incre­ment to be added for any other size or speed in the same fan range can be obtained.

Connect the point on rev/min scale to point on size scale. Where this intercepts A scale is the amount to be added to the X value. (The effects of variation in air density may usually be ig­nored, being of the order of 1 dB or less.)

Example 2:

For the given design of fan, X has a value of 95.5 dBW. What will be the fan sound power level of a 500 mm fan at 1100 rev/min in the same series?

Joining 500 on the size scale to 1100 the increment is -19.5 dB.

 Sound power level = 95.5-19.5 = 76 dBW Size mm A dB. Rev/Min 60 П-4000 — 3500 50 — " 2000— — 3000 1800— — 40 I 1600— — 2500 1400— 30- — 1250— — 2000 20- I 1120—— 7 1000— 10 : — 1500 900— — 800— —- 0- ; 710— — -10- — 630— —1000 560— — 20“ [-900 500—— J— 800 450— -30- R §—700 400— L -40- 1-600 355—— L 315— -50- §-500 280— E_ -60- 250—— §—400 224—— -70- L 200— 180— -80- ^-300 160— : -90- — 250

In reverse manner, knowing the sound power level of a particu­lar fan at a particular speed, we can calculate X.

Example 3:

A 710 mm fan at 1800 rev/min has a sound power level of 99 dBW.

Increment A = +3.5 dB

 J_X

 20

.-. X + A = 99 dBW or X = 95.5 dBW.

Posted in Fans Ventilation A Practical Guide