Figure 8 - Logarithmic Plot of Velocity Profiles in Pressure Gradients s 

 Illustrating w The Law of the Wall" (Ludwieg and Tillmann, Reference 18) 



Then [38] reduces to 



P u 2 P u 2 l \ ' 



[40] 



Comparing the exponents of y in [34] and [40], it is seen that the exponent 

 obtained by Ludwieg and Tillmann has a constant value of 1 .705 while that of 

 the equation just derived depends on H , which varies with Reynolds number. 

 From Figure 11 showing the variation of H Q with R $ , the exponent k/R +l is 

 found equal to* 1 .639 for R g = 1 .5 x 10 3 , and 1 .800 for R $ = 4 x 10 4 . These 

 values compare favorably with the value 1 .705 of Ludwieg and Tillmann. 



