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

390 14. Machinery Noise ControlExample Problem 7An air jet, operating through a choked 1-cm diameter nozzle, exhausts into theatmosphere. Determine the overall acoustical power and the sound power levelL W at 20 ◦ C.SolutionBecause the nozzle is choked, the average velocity of the air jet must be equalto the speed of sound at 344 m/s. The density of air at atmospheric pressure is1.204 kg/m 3 is found from the ideal gas relation,ρ = p aRT1.01325 × 105= = 1.204 kg/m3287 × (20 + 273.2)and the area of the nozzle is πD 2 /4 = π(10 –2 ) 2 /4 = 7.85 (10) –5 m 2 . FromFigure 14.12, the radiation efficiency factor εM 5 is found to be approximately3 × 10 –5 . Inserting these values into Equation (14.43) we findP = ε M5 ρ 0 V 3 A2= 3.0 × 10−5 × 1.204 × 344 3 × 7.85 × (10) −52= 0.0577 Wthus giving us the sound power level,( ) 0.0577L W = 10 log = 107.6 dB (14.44)10 −12From this last example, the acoustical power can be calculated to the first orderon the basis of the nozzle diameters and exit velocities. However, the acousticalpower of the air jet may have an accuracy of ±5 dB or thereabouts. But what if thegas jet is hot and extremely turbulent, as in the case of a gas burner? This situationcan be resolved by applying a first-order correction for the temperature:( ) TCorrection due to temperature = T = 20 logT awhere T and T a are the absolute temperatures of the gas jet and the ambient air,respectively.Example Problem 8Consider the nozzle described in Problem Example 7 above. What would be thetotal radiated acoustical power level L W if the temperature of the jet is to be raisedfrom 20 ◦ Cto260 ◦ C?