THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

392 14. Machinery Noise ControlFigure 14.13 illustrates that peak levels occur in the range of 15 ◦ –45 ◦ from theaxis of the jet. The ordinate of Figure 14.13 giving the relative sound pressure levelconstitutes a directivity index DI θ .Example Problem 9Find the radiated overall sound pressure level at a radial distance of 15 m from thenozzle of Problem Example 7 at angular positions of 0 ◦ ,45 ◦ ,90 ◦ , and 180 ◦ .SolutionWe make use of Equation (14.45) and the results of Problem Example 7. The soundpressure level at r = 15misL p = L W + 10 log [Q(θ,φ)] − 20 log r − 11= 107.6 − 20 log(15) − 11 + DI θ = 73.1 + DI θ dBFrom Figure 14.13, the DI θ = 0atθ = 0 ◦ , and L p = 73.1 + 0 = 73.1 dB. At 45 ◦ ,DI 45 ◦ is approximately +3 dB, and L p (45 ◦ ) = 73.1 + 3 = 74.1 dB. Similarly forthe other angles, we haveDB 90 ◦ =−5dB, L p (90) ◦ = 73.1 − 5 = 68.1 dBDI 180 ◦ =−10 dB, L P (180 ◦ ) = 73.1 − 10 = 63.1 dBIt becomes apparent from the above example that the jet has a strong directionalcharacter that must be accounted for in determining the sound level pressures.Gas jets also manifest a strong frequency dependence. A first-order estimatefor the peak frequency can be obtained for a given power level from the empiricalrelationf peak = St × VD(14.46)whereSt = Stouhal number, a constant = 0.15 for a wide variety of nozzlediameters and operating conditionsV = average exit velocity of the nozzle, m/sD = nozzle diameter, mExample Problem 10Given a 5-cm diameter nozzle with an exit velocity of 344 m/s, determine the peakfrequency of the air blowdown.