G • COOLING BY PROTECTIVE FLUID FILMS 

 where 



vV-i'-""'- 



(s) 



2 pwi'w / w 



Mw = M« (If) 



1 + 5 ^ - AM fr 



(s)' 



(4-48) 



(4-49) 



and 



C^ = 1 / c/da: (4-50) 



From the assumption that the Prandtl number is equal to unity it 

 can be shown that the simple relation between skin friction and heat 

 transfer is 



Ch = ~\ = % (4-51) 



and 



Ck = ^ (4-52) 



Once local or average skin friction is determined from Eq. 4-47, the 

 appropriate heat transfer coefficients can be determined from Eq. 4-51 

 and 4-52. In the case where the Prandtl number is not equal to unity 

 the effect of transpiration cooling on the relation between the coefficients 

 of skin friction and heat transfer may be found in [29]. 



In [30] the heat transfer and skin friction coefficients have been ob- 

 tained from measured data for turbulent boundary layers at very low 

 Mach numbers. In these tests both suction and injection were applied at 

 the plane boundary of the stream. Skin friction coefficients were deter- 

 mined from plots of the momentum thickness against longitudinal station, 

 where the momentum thickness was determined by obtaining the velocity 

 profiles at various stations. The heat transfer was determined by direct 

 measurement. The Reynolds number range of this data was about 9 X 10* 

 to 3.3 X 10^ and the temperature difference between the wall and the free 

 stream was about 30°F. 



In order to make a comparison between the theoretically derived local 

 skin friction and heat transfer coefficients and the appropriate data in [30], 

 the empirical constants K and D in Eq. 4-47 are determined by letting 

 Cf = Cf, T^/T^ — 1, ilf« = 0, and ^w = and comparing the resulting 

 expression with the following von Karman incompressible local skin fric- 

 tion law 



4.15 log {cjRe:) + 1.7 = c7^ (4-53) 



from which K = 0.393 and D = 6.53. 



< 458 ) 



