12 



effect in his analysis. The empirical equation fitting his test points is 



given as 



-± djufjzi = 0.OO89477 - 0.00461 [20] 



U 2 dx 



for 77 < 0.8. When-^ ^x^ is ex P anded to *aJ + 27? ("u dx")' U is seen that 

 the rate of variation of 77, dri/dx, and the nondimensional pressure gradient 

 -jj- -T- are both included in Equation [20]. The variation of 77 is calculated 

 from the auxiliary equation, [20], when used simultaneously with the 

 von Karman momentum equation. Gruschwitz considered separation to occur at 

 77 > 0.8 which is equivalent to H > 1 .85. 



Prom test data covering a wider range of Reynolds numbers, 

 1 x 10 3 < R 9 < 3.5 x 10 4 , Kehl 6 incorporated the effect of Reynolds number in 

 the Gruschwitz equation and obtained 



6 d(U 2 7?) n nn o oUT , 0-0164 0.85 r? , i 



— z ST ■ 0-00894r7 -T^J e + (V300T [21 ] 



Using H rather than 77 as the single parameter for the shape of the 

 velocity profiles, von Doenhoff and Tetervin made an empirical study of the 

 variation of H in pressure gradients in order to obtain an auxiliary equation. 

 From a collection of NACA and other test data representing a range of Reynolds 

 numbers, 1 x 10 3 < R < 7 x 10 4 roughly, they considered the rate of change of 

 H to vary as follows 



^ = f. 2 . , 5( „. 1 . 286) .^(|g)]e"» ( »- 2 -' [22] 



where r //>U 2 is taken from the flat plate formula of Squire and Young 11 

 w o 



T w n r 1 



u2 " L5-890 log 10 (4.075 R 9 ) 



\ [23 



Von Doenhoff and Tetervin considered separation to occur in the range 

 1 .8 < H < 2.6. It is to be noted that the pressure-gradient parameter is 

 — -pp and the parameter representing the Reynolds-number effect is r /pU 2 , the 

 local-skin-frictlon coefficient. Although these parameters are satisfactory 

 in themselves for describing the flow, their combination into a single term in 

 the empirical equation seems objectionable for analysis. 



