z-Momentum Equation 



T— ^ r 7— t: 1- V -r K„w cot 6 + KiU esc 6 + K„,uw 



h dx h„ dz 9y 2 1 21 



2 TT 



^ cot e CSC 9 8(p/p) _ CSC 9 9(p/p) _^ d_ / 9w _ -^ 



dx 



dz dy \ 8y 



(Ic) 



where u, v, and w = velocity components in the x, y, and z directions, respectively 



X, y, and z = nonorthogonal boundary- layer coordinates, as given in 

 Reference 6 



P 



P 



h^, h2 



K^2' ^2^ 



= fluid density 



= pressure on the body 



= metric coefficients 



= geodesic curvatures of the curves z = constant and 

 X = constant, respectively 



= functions of the geodesic curvatures and metric coefficients 



= angle between the coordinates x and z 

 = kinematic viscosity of the fluid 



u V , v w = Reynolds stresses 



The eddy-viscosity concept is used to relate the Reynolds stresses to the mean 

 velocity profiles by 



e . -;t— , inner regxon < y < y 



idy — — c 



(2) 



e du 



O -TT- 



3y 



, outer region y < y 



where e . = ^ 



1 



du \ . / 9w \ , „ -5- / 9u \ / 9w 



1 1/2 



which is the eddy viscosity in the inner region 



