E. J. Skudrzyk and G. P. Haddle 269 
would be expected to become acoustically effective), the noise level turns out 
to be -158 db relative tol d/cm?. This value may be considered as the equivalent 
of zero flow-noise level for the condition of the experiment. The other curves 
should then intersect with the zero flow-noise level, —158 db, at speeds equal 
to the corresponding critical values; and this indeed seems to be what happens 
if we allow for a small experimental error and for the fact that the energy of 
the background and that of the flow noise add up to the resultant noise level so 
as to change the shape of the curves at lower noise levels. Paint covers the 
smaller roughnesses, but in doing this seemsto increase the larger roughnesses 
with paint streaks. Yet the density of the larger roughnesses is relatively small 
and the roughness noises seem to be masked by the boundary-layer noise. This 
conclusion follows from the slope of the curve, which is only 18 db per speed 
octave. 
We may conclude that the roughness noise equals the boundary-layer noise 
at 24 kc at a speed that is about six times as great as the critical speed if the 
surface is densely covered with roughnesses, and at a correspondingly higher 
speed if the roughnesses are widely spaced from one another. 
Figures 14.8 and 14.9 show measurements obtained with buoyant units. The 
units were about 5 yards in length and 19 in. in diameter. Each was equipped 
with six hydrophones and a seven-channel tape recorder. Theory predicts that 
the spectral level of the low frequencies is proportional to the thickness of the 
boundary layer and is borne out by the experiments. The low-frequency noise 
level increases with the distance from the head of the buoyant unit. The high- 
frequency noise level, on the other hand, is considerably weaker at the rear of 
the buoyant unit where the boundary layer is very thick. The boundary layer of 
the buoyant units or of a vehicle of a similar shape is very thin at its head. For 
a buoyant unit the thickness is about a thousandth of an inch. The flow is there- 
fore laminar. The turbulence starts when the head merges into the cylindrical 
section. The noise that is received at a stagnation point is entirely due to the 
sound radiated from the turbulent zones into this area and to the eddies shed by 
the surface roughnesses. If the head of the unit is not highly polished, then the 
flow velocities become large enough an inch or two from the stagnation point, 
and the surface roughnesses generate eddies. Because of the laminar nature of 
the boundary layer in this part of the unit, the eddies decay very rapidly, but 
they do generate flow noise. This can easily be tested by performing measure- 
ments with hydrophones of different sizes. The received flow noise depends on 
the size of the hydrophone and consequently is at least partially nearfield noise. 
The flow becomes turbulent at the minimum pressure point which is very near 
to the joint between the cylindrical sectionand the head of the unit. In this region 
the velocities are 50% larger than the velocity of the vehicle and the turbulence 
is still very unstable and bumpy. The noise levels are therefore considerably 
larger than those which would correspond to the stable turbulence of the bound- 
ary layer. The region near this joint is particularly critical for the generation 
of flow noise. Toward the rear, one to two yards away from this joint, the tur- 
bulence has already decreased to its normal value and the noise level is approxi- 
mately the same as the noise level in the test section of the water tunnel. 
