1 
2 oA 2 
% Po” | fT3, @| 9[(1 - 3cos* 0) + 4cos?@ sin? 6] 
Ny aU TT eT ea [65] 
p Bmp ,o'r |3cos? 6-1| 
In general, the sound pressure from randomly oriented multipoles predominates over the fluctu- 
ating Bernoulli pressure in the induction near field as long as the magnitudes of the particle 
motions induced by the multipoles are small compared to the distance from the multipoles. 
The dependence of the ratio of the sound power radiated to the mechanical power 
dissipated (the so-called ‘‘efficiency of conversion of mechanical power to sound power’’) 
on the Mach number and other factors may also be used to estimate the relative contributions 
of sources, dipoles, and quadrupoles. Except for secondary effects, this efficiency is propor- 
tional to M, for sources, Mo for dipoles, and Mo for quadrupoles. 
For jets the efficiency of conversion of mechanical power to sound power has been de- 
fined in terms of the total mechanical power of the jet. The efficiency of conversion to sound 
for aboundary layer, however, is more conveniently expressed in terms of the time rate of 
energy dissipation by the boundary layer; namely, the drag times the free-stream velocity. In 
terms of the drag coefficient Ces the efficiency of conversion to sound for the dipole and quad- 
rupole radiation from a boundary layer may be written, respectively: + 
acoustic power per unit area 
0g = Mg (Bs Mo) [66] 
ie 3 
5 Pol Cr 
acoustic power per unit area M590. (R [67] 
ur ay 1 3 ee, Iq (R, io) 
Baye 
Thus, in ranges of conditions in which each multipole source predominates, data may be con- 
solidated and 7, and ily evaluated. These efficiencies would be expected to show secondary 
Mach number effects and Reynolds number dependences through the functions g,(#, Mg) and 
Iq (FR, Mo), especially at low Reynolds numbers. 
For a uniformboundary layer, the rate of energy dissipation bythe layer should be a 
more realistic standard thanthe total power of the jet as used to compare jet noise data. 
Thus, the efficiency 1g would not be expected to be the same as the acoustic efficiency as 
defined for a jet. The presence of high viscous dissipation of energy very near the boundary 
would tend to make 1g lower than jet efficiencies. But the fact that much of the energy dissi- 
pated in a jet is in a region with lower Mach number than that used to define the jet sound 
conversion efficient, would tend to make Ng higher than jet efficiencies. The separation of 
the contributions of the fluctuating forces and the fluctuating stresses and the evaluation of 
22 
