A, 5 • SURFACE ROUGHNESS AND WAVINESS 



so long as transition is forward of the smooth plate position but down- 

 stream from and not too close to the roughness element. The dotted up- 

 ward branches in Fig. A,5c correspond to transition at the roughness 

 element. The location of these branches is determined by the parameter 

 Xk/k, where Xk is the position of the roughness element. 



The results of Fage [13] analyzed in this way are shown in Fig. A,5d; 

 typical results of Sttiper [19], discussed at some length in [17], are shown 



1.5 



1.3 



1.1 



X0.9 





0.7 



0.5 



0.3 



0.2 0.4 0.6 0.8 



k/5* 



1.0 



Fig. A,5c. Effect of single cylindrical roughness element on the transition Reynolds 

 number of a plate. Measurements of Tani, Hama, and Mituisi \15\ and Tani and 

 Hama \18\. 



in Fig. A,5e. A few results by Scherbarth as reported by Quick [20] are 

 plotted in Fig. A,5f. These refer to flat ridges 20 mm wide and varying in 

 height from 0.1 to 1.0 mm. 



Tani and his collaborators repeated Dryden's analysis using the origi- 

 nal data found in Japan and applying corrections for the small departures 

 of the pressure from uniformity [21], These revised values, the data of 

 Fig. A,5f, results of more recent measurements by Tani, luchi, and 

 Yamamoto [22\ and results obtained by Feindt [9] on a hollow cylinder 

 with axis parallel to the wind are shown in Fig. A,5g. These data cover 



( 11 > 



