NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS QI 



for a value of the "Reynolds Number" - - =2500. Here D is 



diameter of pipe, V is velocity, and v the coefficient of kinematic vis- 

 cosity. A very rough calculation for the square 4-foot wind tunnel, 

 using the above figure, indicates a critical velocity of 1/16 mile per 

 hour. For the 3-inch pipes of the honeycomb, the critical velocity is 

 about I mile per hour. Our experiments were conducted well above 

 these speeds. 



Similarly there is a limiting velocity for the flow of air at atmos- 

 pheric pressure to be deduced from St. Venant's equation for motion 

 of a compressible fluid. 



For air at ordinary temperatures this limiting velocity is about 

 770 miles per hour. 



A more practical condition which may occur at ordinary speeds may 

 account for the existence of an apparent critical velocity at which 

 the fluid refuses to turn a corner due to its inertia. Thus, for true 

 stream line motion about a disk, the air is required to turn sharply over 

 the edge and close in on the back of the disk. The stream line has a 

 finite radius of curvature and a finite velocity at any point, and there 

 is consequently a centrifugal force on each particle of the fluid. 

 Unless the pressure gradient is sufficient to balance this centrifugal 

 force, the curvature of the stream line cannot be maintained. A dead 

 water then forms at the rear of the disk which is dragged away by 

 the viscosity of the moving air in contact with it, thus setting up a 

 turbulent wake. A considerable increase in resistance might be 

 expected to take place when turbulence is set up. 



Our experiments show an abrupt change near 13 feet per second 

 for thin disks, with unstable flow for velocities between 10 and 20 feet 

 per second. This range is of the same order of magnitude as the 

 critical velocity for a flat ellipsoid deduced by Mr. E. B. Wilson in the 

 prefatory note above. 



NOTE ON AN EMPIRICAL EQUATION TO EXPRESS THE EXPERIMENTAL 



RESULTS 



Within the limits of these experiments the normal resistance of a 

 thin disk may be represented by the expression 



in which 



R is total force on disk in pounds, 



D, diameter in feet, and 



V, wind velocity in feet per second. 



