Huang and von Kerezek 
-0. 653 
a 
o 
ii] 
0. 0306 (G - 30) 
2st DS 
4 
Q 
i" 
1535. (ft -‘0.°7) ce 
The skin friction coefficient C,, is given by the two-dimensional 
formula 
niet tig 
H. +1 
Q fe) 
0. 0146 ( om ) 
Ce S i 
log, 4 (2R 6, ) SS log) (2R 0, ) + 0. 4343] 
Hap» = PLAsaY dog R + 0. 9698 
fe) 10 B44 (4) 
Q = 0.9058 - 1.818 log,,H 
Q. a Q(H,) 
where Rg, = R,U, 6), and Ry, = VL/2» (recall U, and 6,, are 
non-dimensional). 
This is Granville's (24) formula and is an extension of the Von 
Karmann-Schoenherr flat-plate skin-friction formula to flows with 
a pressure gradient. This skin friction formula was chosen over 
others, for instance the Ludweig-Tillman formula, because it is 
more accurate at high Reynolds numbers. With the Mager 25 profile 
assumptions for the crossflow, the crossflow momentum integral 
equation is transformed into an equation for the angle 6 that the 
shear stress makes with the streamline direction. Then 6 is de- 
fined by 
tan B = 
where Cy = Ty2/PU%/2) and Twz2 is the wall shear stress in the 
crossflow (e.g. normal to the surface streamlines) direction. 
The shear stress magnitude is then given by 
C =" G a: . 
CIN SRR Se 
1968 
