NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 83 



When cavitation be^-ins, p = o, v = 2a , . The value of ^ + —v- 

 at large distances from the disk may be taken as ^" , where p^ is the 



r 



atmospheric pressure in pounds per square foot. Hence we find 



^^l_4«^^ u=^Jb (13) 



As numerical data we may take />o= (22X 12)', p = .oS. Then 



t/ = 2ioo - foot-seconds. (14) 



a . 



In the case of an ellipsoid 6 inches by 1/16 inch, the velocity U is 

 about 22 foot-seconds. For smaller disks of the same minor axis the 

 velocity U should be larger in inverse ratio to the size of the major 

 axis. 



The upper limit of 22 foot-seconds here found for the critical 

 velocity is not surprisingly above the actual range of 10 to 20 foot- 

 seconds found by Mr. Hunsaker. But a noteworthy result shown on 

 his diagrams is that the critical velocity does not vary proportionately 

 to the reciprocal of the diameter of the disk — it is practically con- 

 stant — and had we taken to test the theory his smallest disk, we should 

 have had an upper limit decidedly above the experimental value. This 

 lack of accord between his experiments and the present theory can 

 hardly be regarded as surprising. His disks were all equally sharp 

 upon the edge, and all considerably sharper than an ellipsoid of the 

 same length and breadth, particularly in the smaller disks. Once the 

 edge is sharp enough to start cavitation at a given velocity of the gen- 

 eral stream, the motion becomes such that we can no longer expect our 

 theory to hold, and it is entirely possible that the thickness of the disk 

 is unimportant above a certain value. The effect of a 6-inch disk 

 1/16 of an inch thick may not dift'er appreciably from that of one 

 1/32 of an inch thick. The effects of the changing density of 

 the air and of viscosity might also, and probably would, be of some 

 importance. On the whole we may consider the correlation of 

 experiment and theory as fairly satisfactory; at least it is good 

 enough to indicate strongly the existence of a critical velocity for 

 these disks at reasonably small velocities of the stream. 



