B,9 • VELOCITY, PRESSURE, AND TEMPERATURE DISTRIBUTIONS 



while the laminar recovery factors on plates are higher than those on 

 cones and other models. These high values of the recovery factor can be 

 attributed to heat conduction effects in the leading edge region of the 

 flat plate. 



The foregoing relations between temperature and velocity will be 

 referred to in Art. 12 in connection with the relation between the tem- 

 perature profile and the velocity profile. If Pr = 1, the relations become 

 especially simple, as shown by Eq. 9-5 with heat transfer and by Eq. 9-7 

 without heat transfer. If Pr 7^ 1, the viscous dissipation and the heat 

 conduction render such a general relationship between temperature and 



1.0 



0.8 





0.6 



0.4 



0.2 



0.2 



0.4 



0.6 



0.8 



1.0 



y/5 



Fig. B,9c. Velocity profile across turbulent boundary layer. The free stream Mach 

 number is 4.93 and there is no heat transfer. The data are drawn after Lobb, Winkler, 

 and Persh [18] and private communications. 



velocity very difficult, and a basic approach to the problem must involve 

 the detailed mechanism of turbulence. However, without turning to this 

 approach a relation between the temperature at the wall and the velocity 

 and temperature at y = d was made possible by introducing a recovery 

 factor Te. For no heat transfer such a relation was found to be that of 

 Eq. 9-9a, and this agreed rather well with measurements. The question 

 may be asked as to what form the relation might take if it were general- 

 ized to include the heat transfer and to cover all positions in the boundary 

 layer. To this end and by similar reasoning, we could introduce a variable 

 recovery factor r{y) which satisfies Eq. 9-9a at the limit and becomes 

 r{y) = 1 for Pr = 1. It is expected that a relation between T° and T^, 



<95> 



