10 



A non-dimensional form of the momentum equation, [31], convenient for calculation 

 purposes is 



where I is the axial distance from the nose, 



dl = cos a dx [37] 



L is the length of the body and ff^ is the body Reynolds number given by 



[38] 



Transition to turbulent flow is assumed to occur instantaneously at a transition point 



(Z/L)j which then becomes the upper limit of integration in Equation [36] when the integration 



is performed for the complete laminar boundary layer. 



TRANSITION 



As the boundary layer thickens downstream on the body, the laminar flow tends to be- 

 come unstable and undergo transition to turbulent flow under the stimulus of disturbances in 

 the flow. The transition zone may be considered to extend from the point where the charac- 

 teristic shape of the mean-velocity profile of the laminar boundary layer begins to change to 

 the point where the characteristic shape of the mean-velocity profile of the turbulent boundary 

 layer first appears. For most drag calculations the zone of transition is short enough to be 

 adequately represented by a transition point. The position of transition depends largely upon 

 the interaction of the boundary-layer flow with random disturbances in the flow. Significant 

 parameters of the boundary-layer flow affecting the position of transition are the boundary- 

 layer Reynolds number representing the ratio of inertial forces to viscous forces, the pres- 

 sure gradient in the downstream direction, and the curvature of the surface. The source of 

 random disturbances may be the turbulence in the free stream, the roughness of the surface 

 or noise being transmitted through the fluid. 



As shown theoretically by ToUmien" and Schlichting^ among others (see summary in 

 Reference 12) and verified experimentally by Schubauer and Skramstad^ and Liepmann,^^ the 

 laminar boundary layer exhibits stability characteristics which are governed largely by the 

 boundary-layer Reynolds number and by the jaressure gradient. Random disturbances of van- 

 ishingly small amplitude have certain frequencies amplified and other frequencies damped by 

 the laminar flow in the boundary layer. The amplified fluctuations combine into regular waves 

 termed ToUmien-Schlichting waves which increase in amplitude downstream at a rate deter- 

 mined by the Reynolds number and the pressure gradient of the boundary layer. Intermittent 



