A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



roughness element has little effect on transition, if Ukk/v is less than 300. 

 If the free stream velocity XJ were used, the corresponding value of Uk/v 

 would be about 800. The numerical values obviously depend on the shape 

 of the elements, although systematic data are not available. 



There are only a few experiments on distributed roughness on a flat 

 plate, and these are difficult of analysis because of the necessary experi- 

 mental treatment of the leading edge. Thus Holstein [14], using a "plate" 

 consisting of a structure of wood about 11 feet long and 1.4 inches thick 

 with an elliptical nose piece about 7.09 inches long, left the nose piece 



100 



300 



500 700 



Ukk/v 



900 



Fig. A,5j. Relation between Reynolds number of spherical roughness 

 elements and transition Reynolds number of a plate [23]. 



smooth and roughened the remainder of the surface by attaching emery 

 paper of various degrees of roughness. The value of Re^ for the smooth 

 plate varied with the speed, perhaps because of variation of the turbu- 

 lence with speed. Furthermore, the plate was not aerodynamically smooth 

 since fine emery paper often increased the transition Reynolds number. 

 Holstein believed that the paper covered up the surface waviness. The 

 average value of Re^ was about 650,000 corresponding to a turbulence 

 of 1.0 per cent, or more probably to departures from aerodynamic 

 smoothness. 



The emery paper had a thickness of about 0.3 mm and the sharp step 

 at the leading edge of the paper was smoothed with plasticine over a 



< 16 ) 



