26 



Substituting only the first three boundary conditions a, b, and c into Equa- 

 tion [59] and its derivatives to form a system of simultaneous equations for 

 evaluating the coefficients, results in the following quadratic equation for 

 the shearing-stress distribution 



f -v-[-f)-<i + .>(f; 



•60 



where a = — 4^, a pressure-gradient parameter. Using all five boundary con- 

 ditions yields the following quadratic equation for the shearing-stress 

 distribution 



= 1 



+ -{fj.-(4 + 3a)(-f)' + (3 + .2^(|,) 4 



[61 



Schubauer and Klebanoff 25 found indifferent correlation between their experi- 

 mental results and either of Fediaevsky's equations. Agreement is good at the 



beginning of the adverse pressure gradi- 

 ent and near the point of separation 

 but is extremely poor at the inter- 

 mediate stations. 



In an attempt to improve on 

 the Fediaevsky formulations, Ross and 

 Robertson 27 considered the shearing- 

 stress distribution to depend on its 

 previous history of development along 

 the boundary layer. Fediaevsky's bound- 



ary condition (d) is altered to gx = ___i 

 •> dy Si 



at y = 6, in order to obtain a constant 

 slope at the outer edge of the boundary 

 layer travelling downstream from i, the 

 initial position of the adverse pres- 

 sure gradient. This requirement makes 

 the shearing-stress distribution depend 

 on conditions upstream. Using a modi- 

 fied polynomial expression for r and 

 incorporating the revised boundary con- 

 dition (d), together with the other 

 four Fediaevsky conditions, Ross and 

 Robertson derived the following 

 expression: 















\s>. 







+ . 



V' 







IK \p. 



.I 1 



V 



V 







// v> \ 

 / / V* 



// v- 









y in inches 



Figure 12 - Shearing- Stress 



Distributions in an Adverse 



Pressure Gradient as 



Measured by Schubauer and 



Klebanoff, Reference 25, 



At Various Stations 



