A turbofan's bypass duct exhausts air (density

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Sound in a moving, absorbing fluid: sources, refraction and loss

Problem

A turbofan's bypass duct exhausts air (density ρ0=1.204 kg m−3\rho_0=1.204\,\mathrm{kg\,m^{-3}}, sound speed c0=343.2 m s−1c_0=343.2\,\mathrm{m\,s^{-1}}) at speed U=120 m s−1U=120\,\mathrm{m\,s^{-1}} through a circular nozzle of diameter D=1.5 mD=1.5\,\mathrm{m}. Model the exhaust as a cold subsonic jet whose kinetic-energy flux is 12ρ0U3(πD2/4)\tfrac12\rho_0U^3\left(\pi D^2/4\right), and use the quoted order-of-magnitude jet-noise efficiency (Lighthill scaling) η≡Pkinetic-energy flux∼10−4M5,M=U/c0.\eta\equiv\frac{P}{\text{kinetic-energy flux}}\sim 10^{-4}M^5,\qquad M=U/c_0. ((a)) Estimate the kinetic-energy flux of the exhaust. ((b)) Estimate the total acoustic power PP radiated. ((c)) Treating the nozzle as a point source radiating equally in all directions, estimate the sound intensity level 100 m100\,\mathrm{m} away (reference intensity 10−12 W m−210^{-12}\,\mathrm{W\,m^{-2}}).

Browse the problem library