B,20 • EQUILIBRIUM BOUNDARY LAYERS 



wall, but the requirement of nearness is considerably relaxed over that 

 required to derive C/ from the initial slope of a velocity distribution. 



Ludwieg and Tillmann [89], who first confirmed the validity of the 

 law of the wall in a region of adverse pressure gradient by means of their 

 heated-element measurements of c/, deduced the following formula for 



^J J^QCeTSH^^g 0.268 ^^^ ^^ 



where H is the form parameter and Ree = U^d/v. This formula gives c/ 

 reasonably well where the velocity profiles conform to the i?-parameter 

 family of Fig. B,19a. 



Ue 



Fig. B,19d. Chart for experimental determination of turbulent 

 skin friction coefficient, after Clauser [83]. 



B,20. Equilibrium Boundary Layers According to Clauser. 



Since the velocity profile beyond the immediate region of the wall is 

 affected by the pressure gradient, a universal representation on the basis 

 of the velocity-defect law, as shown by Fig. B,16, is not in general ob- 

 tained. However, by means of an experiment in which long lengths of 

 two-dimensional turbulent boundary layer could be subjected to various 

 adverse pressure gradients, Clauser [83] showed that the pressure dis- 

 tribution could be adjusted to give similar boundary layer profiles when 

 plotted on the basis of the defect law. The form of the function was 

 different from that for constant pressure flow and also different for each 

 separate pressure distribution, but the significant fact was that the same 

 functional relation applied over an essentially arbitrary number of cross 

 sections for any one pressure distribution. He termed the resulting bound- 

 ary layer an "equilibrium boundary layer" on the grounds that the same- 

 ness of the function g in the case of a pressure gradient implied the same 

 similarity of major flow characteristics as was maintained in constant 



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