E. J. Skudrzyk and G. P. Haddle 265 
penetrate the laminar boundary sublayer [16], that is, when the fluctuating ve- 
locity v* exceeds the value five. This Reynolds-number condition leads to the 
equivalent result that in a turbulent boundary layer, the surface OU ESI 
become effective whenever this height in inches becomes equal to 6- 10-* divided 
by the velocity of the vehicle Up in knots: 
h [inches] = 6 
ee [knots] (26) 
If the boundary layer is not turbulent, v* has to be replaced by the true velocity 
Uph/d at the peaks of roughnesses, and the corresponding Reynolds-number con- 
dition becomes 
Uh 
5h (27) 
or 
h? _ Sv _ 4.2. 1074 (28) 
Oo HS wp 
where UJ) is in knots and 6 is in inches. For a boundary layer of a thickness of 
10-2 in. (as on the spherical head of a buoyant unit) and a speed of 42 knots, 
h/5= 0.1, or h= 1074 in., which is in good agreement with the experimental 
results. 
The eddies shed by the surface roughnesses may be expected to depend on 
the velocity gradient near the wall. They will be independent of whether the 
—_- — — 
5 
HYDROPHONE NO 3 8-014: ot SOtps 
1/2 in DIA 3 ft from entrance of tes} section 
DBS re/ dyne/ cm?/ cps 
1 ' ' 10 100 
FREQUENCY IN KC 
Fig. 14.4. Flow-noise spectra as a function of speed. 
