NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 25 



assuming" that equation (lo) may be relied on for great accuracy 

 when the size D changes over a very large range ; and it seems 

 possible that it may sometimes be desirable to make experiments 

 guided by equation ( 1 1 ) which holds for any series of geometrically 

 similar bodies, whatever the speeds may be. 



The conditions for dynamical similarity given by equations (12) 

 can evidently not be satisfied if we work with only a single medium ; 

 for if vm = v and Cm = C, we have Sm = S and Dm=D, so that no scale 

 reduction is possible while preserving dynamical similarity. This 

 difficulty may, in principle, be surmounted by running the model in 

 water if the original is to run in air. Suppose, for instance, that the 

 original is an air-ship which is to run 40 miles an hour in air, and let 

 the model be run in water at such a temperature that its kinematic 

 viscosity is 1/15 that of the air. We then have v= i^vm and the first 

 of equations (12) gives us 



iSD„,Sni = DS. (14) 



The second condition requires that the speed of the model shall be 

 the same fraction of the speed of sound in water as 40 miles per 

 hour is of the speed of sound in air. Since sound travels about four 

 times as fast in water as in air, the model must move at the very high 

 rate of 160 miles per hour, or about 235 feet per second. With this 

 condition that Sm=4S, and the previous condition stated by equation 

 (14), we have 



A model to 1/60 scale run in water will then be dynamically similar 

 to the original in air, if it is run four times as fast. Having thus 

 satisfied equations (12) we may use equation (13) ; and if we set 

 p,„ = 8oop we have 



R,n 800 V 4 / 32 



The resistance of the original in air will therefore be about one- 

 quarter of the resistance of the dynamically similar 1/60 scale model 

 in water. How soon it will seem worth while to attempt experiments 

 of this sort cannot be predicted, but the notion of dynamical similarity 

 shows how the problem may be attacked. 



The Pitot Tube 

 Hitherto we have let R be the total head resistance of a solid body, 

 but if D is the diameter of the impact opening of a Pitot tube, ^^ "^^7 



