The slope of the logarithm law remains the same 1 but

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Unformatted text preview: ratio /d. For any given /d, the friction factor becomes constant (fully rough) at high Reynolds numbers. These points of change are certain values of u*/ : u* 5 5: 70: u* u* hydraulically smooth walls, no effect of roughness on friction transitional roughness, moderate Reynolds-number effect 70: fully rough flow, sublayer totally broken up and friction independent of Reynolds number For fully rough flow, 70, the log-law downshift B in Fig. 6.12a is | v v B | e-Text Main Menu | 1 ln Textbook Table of Contents 3.5 | Study Guide (6.61) 348 Chapter 6 Viscous Flow in Ducts and the logarithm law modified for roughness becomes 1 u ln y B B 1 ln y 8.5 (6.62) The viscosity vanishes, and hence fully rough flow is independent of the Reynolds number. If we integrate Eq. (6.62) to obtain the average velocity in the pipe, we obtain V u* 1 f 1/2 or 2.44 ln 2.0 log d /d 3.7 3.2 fully rough flow (6.63) There is no Reynolds-number effect; hence the head loss varies exactly as the square of the velocity in this case. Some numerical values of friction factor may be listed: /d f 0.00001 0.0001 0.001 0.01 0.05 0.00806 0.0120 0.0196 0.0379 0.0716 The fricti...
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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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