611 comparison of laminar and turbulent pipe flow

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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 [7] 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 [7] 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 [7] 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 roughness...
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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.

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