A,12 • SCHLICHTING'S PROCEDURE 



transition occurs when Ee^* reaches the critical value computed for the 

 local velocity distribution which is in turn determined by the local pres- 

 sure gradient. The location of transition is then computed by the following 

 procedure : 



1. Compute the theoretical pressure distribution over the body from po- 

 tential flow theory. The result is expressed as a plot of u^/U vs. s/c' 

 where u^ is the velocity at a distance s measured along the surface from 

 the stagnation point, U is the stream velocity at a great distance, and 



10^ 



(^-f)=^ 



10- 



102 



0.2 



0.4 



0.6 



0.8 



s/c' 



Fig. A,12f. Variation of displacement-thickness Reynolds number for elliptic 

 cylinder as function of cylinder Reynolds number and local position. 



c' is the distance from leading to trailing edge measured along the 

 surface. Fig. A, 12a and A, 12b show this curve for an elhptic cyhnder 

 of fineness ratio 4 and a Joukowski airfoil respectively. 

 Compute by Pohlhausen's method (4-term polynominal approximation 

 to the velocity distribution) the displacement thickness 5* of the 

 boundary layer. Compute also the Pohlhausen parameter X. There 

 result curves of (5*/c) \/Uc/v and X vs. s/c' as shown in Fig. A,12c 

 and A,12d. 



From the stability calculations and the values of X, plot the critical 

 Reynolds numbers (i^es*)cr corresponding to each X vs. s/c'. The rela- 

 tion of (i^e«*)cr to X as used by Schlichting is shown in Fig. A,12e. 

 From the values of (6*/c) ^Uc/v = {U/ue){Re&*/Rei), where Re is 



(35 > 



