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Unformatted text preview: urbulent pipe flow. (a) The logarithmic overlap-velocity profile
shifts down and to the right; (b) experiments with sand-grain roughness by Nikuradse  show a systematic increase of the turbulent
friction factor with the roughness
ratio. For example, at Red 105, f 0.0180, and ys /d 0.001, a wall roughness of about
0.001d will break up the sublayer and profoundly change the wall law in Fig. 6.9.
Measurements of u(y) in turbulent rough-wall flow by Prandtl’s student Nikuradse
 show, as in Fig. 6.12a, that a roughness height will force the logarithm-law profile outward on the abscissa by an amount approximately equal to ln , where
u*/ . The slope of the logarithm law remains the same, 1/ , but the shift outward
causes the constant B to be less by an amount B (1/ ) ln .
Nikuradse  simulated roughness by gluing uniform sand grains onto the inner
walls of the pipes. He then measured the pressure drops and flow rates and correlated
friction factor versus Reynolds number in Fig. 6.12b. We see that laminar friction is
unaffected, but turbulent friction, after an onset point, increases monotonically with the
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
- Spring '08