A,3 • PRESSURE GRADIENT ON FLAT PLATE 



agreement with 

 nondimensional 

 where du^/dx is 

 ness defined by 

 distribution in 

 yields a critical 



the theory. The computed effect is very large. A suitable 

 measure of the pressure gradient is X = i8^/v){dujdx) 

 the velocity gradient and 5 is the boundary layer thick- 

 the Pohlhausen four-term approximation to the velocity 

 the boundary layer. For -3 < X < 3, stability theory 

 Reynolds number Res* based on displacement thickness 



Ap/q 



•0.05-0.10 





^'W^Vl%^^'^-'^/'^^ 



C 



o 

 E 



CD 

 > 



CD 



Fig. A,3. Effect of pressure gradient on laminar boundary layer oscillations. Oscil- 

 lograms of u' at y = 0.021 in., C/ = 95 ft/sec. Time interval between dots, -g^o sec. 



(see Art. 6 and IV, C) approximately proportional to e°-^^. The actual 

 values are 160, 575, and 4000 for X equal to —3, 0, and 3, respectively, 

 corresponding to values of Ret for zero pressure gradient of 8500, 110,000, 

 and 5,300,000. The critical Reynolds number for transition is, however, 

 considerably greater than that at which amplification of disturbances 

 begins and by an unknown ratio which may vary with X. 



Liepmann made some measurements of the influence of pressure gradi- 

 ent on transition [8] on the convex surface of a plate of 20-foot radius of 



<7> 



