20 



dx dy p dx fdy \d y ^^l\ pf dx \_ \ /J 



pr dy \_\ "^ )\ T dx 



u^a + ui± ^1^ =J^± \rl^ -iJi]]^ ± J. \r(~p7~')\ 

 dy dy p dy r (9» |_ \dci; dy/j pr dy \_ \ /J 



pr dx \ \ n r dy 



[ 



and the equations of continuity 



d{ru) ^ d(rv) ^ q 

 dx dy 



[56] 



djru') + d(rv') ^ q [57] 



dx dy 



The unprimed quantities refer to the mean flow and the primed quantities to the fluctuation 

 flow. The bars over the various products indicate averages in accordance with the Reynolds 

 concept. Specifically, u, v, q,, primed or unprimed, represent components of velocity in the 

 X, y, and <f> directions, respectively. As before, x is the distance along the meridian profile 

 and y is the distance perpendicular to the profile. ^S is the angle between any meridian plane 

 and some reference meridian plane. 



Eliminating terms of negligible magnitude in [55] gives the following equations of 

 motion for the axisymmetric boundary layer on a body of revolution 



dx dy p dx pr dx pr dy 



=IJL 



dy 



where — — . 



a = p«'^ 



is the negative value of a Reynolds normal stress and 



[58] 

 [59] 



T = n iJH - pu'v' [60] 



dy 



is the total shearing stress. 



Integrating the boundary-layer equations, [58], across the boundary layer in the y- 

 direction from y = to y = S and incorporating the equation of continuity, [56], gives the dif- 



