56 at low turbulent reynolds numbers this explains

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Unformatted text preview: re sharply than the laminar formula (6.47). Thus the quickest way to reduce required | e-Text Main Menu | Textbook Table of Contents | Study Guide 346 Chapter 6 Viscous Flow in Ducts pumping pressure is to increase the pipe size, although, of course, the larger pipe is more expensive. Doubling the pipe size decreases p by a factor of about 27 for a given Q. Compare Eq. (6.56) with Example 5.7 and Fig. 5.10. The maximum velocity in turbulent pipe flow is given by Eq. (6.48), evaluated at r0 umax 1 Ru* ln B (6.58) u* Combining this with Eq. (6.49), we obtain the formula relating mean velocity to maximum velocity V umax (1 1.33 f) 1 (6.59) Some numerical values are Red 4000 104 105 106 107 108 V/umax 0.790 0.811 0.849 0.875 0.893 0.907 The ratio varies with the Reynolds number and is much larger than the value of 0.5 predicted for all laminar pipe flow in Eq. (6.43). Thus a turbulent velocity profile, as shown in Fig. 6.11, is very flat in the center and drops off sharply to zero at the wall....
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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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