B • TURBULENT FLOW 



inherently an indistinctly defined region, but taking the conventionally 

 defined sharp limit given by 



V 



Slan 



11.5 



Ur 



the effect of roughness begins when h/bi^^ = ^ and the fully rough regime 

 sets in when /c/6iam is between 4 and 8. These figures tell us httle that 

 could not be inferred, namely that the roughness elements must be well 



20 



AU 



10 



Colebrook-White 



O 48% smooth, 47% fine grains, 5% large gr 

 O 95% uniform sand, 5% large grains 

 ■ 97.5% uniform sand, 2.5% large grains 

 A 95% smooth, 5% large grains 

 A Uniform sand 



Prandtl-Schlichting 

 sond-grain roughness 



• W. L Moore 'xr:^^?^^^^!^^ #Rand (flume) 

 n F. R. Hama ^^^^|4^ cfSarpkaya (flume) 



10 



102 



Uk/v 



103 



K 



Fig. B,23a. Effect of roughness on universal turbulent 

 velocity profile, after Clauser [72]. 



buried in the laminar sublayer to have no effect and must extend well 

 above it to completely eradicate viscosity effects. 



It may be shown rather simply that in order for a surface to remain 

 aerodynamically smooth the roughness must decrease almost inversely 

 with the free stream velocity. If the critical value is designated as k„ and 

 the limit is taken as Urht/v = 4, then 



kr.T — 4 



Ur 



= 4 



\Uj\cf 



where C/ is the smooth wall coefficient which varies with 17^ but only 

 slowly. It is also apparent from the slow variation of c/ that the require- 

 ments on k„ are nearly as stringent on a large body as on a small one. 

 Returning to Fig. B,23a it is significant that the data conform to the 



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