262 Lecture 14 
The results of the preceding paragraph can also be deduced from the sta - 
tistical theory given by Corcos, Cuthbert, and Von Winkle [15]. The integral of 
Eq. (15) is identical with the solution of the equation given in [15], if the trans- 
verse correlation length is small in comparison to the width of the hydrophone. 
But the statistical solution cannot be evaluated in closed form when the width 
of the hydrophone becomes larger than the correlation length. 
However, it is easy to see that the hydrophone area can be subdivided into 
strips of width equal to the transverse correlation length of the pressure fluc- 
tuations. The contributions of all the strips willthen be uncorrelated and random 
in phase, and they will add energy. The sensitivity of a rectangular hydrophone 
that is broad in comparison to the transverse correlation length will, therefore, 
be given by 
sinkl, 5 [2 sink] [6 
SF — = }7 eee Y ZI 
e kl, l, (0) 9 Kl, Ty cay 
Doubling the dimensions of the hydrophone then decreases its flow-noise output 
by 9 db, and doubling the frequency decreases the flow-noise output by 6 db. For 
minimum flow-noise sensitivity, the strips should beof optimum shape; but none 
of them should be rectangular, and it is immaterial whether they are symmetri- 
cal or not. The strips can be of the shape shown in Fig. 14.2, but the length J; of 
each strip has to decrease by more thana space wavelength A,, of the turbulence 
per each unit increase of correlation length 6,. For a frequency of 20 kc, a 
correlation length 5, equal to 0.1 in., and a velocity of 600 in./sec, 
al; 600 
CL ee OURS EY Ly (22) 
dy 20,000-.0.1 3 
Thus, the angle @ should be 45° at the greatest. The ends of the hydrophone 
should be somewhat tapered in the direction ofthe flow, as indicated. A properly 
DIRECTION OF FLOW 
Fig. 14.2. Optimum shading of a hydrophone. 
