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Unformatted text preview: averaging period taken to be longer than any significant period of the
fluctuations themselves. The mean values of turbulent velocity and pressure are illustrated in Fig. 6.7. For turbulent gas and water flows, an averaging period T 5 s is
usually quite adequate.
The fluctuation u is defined as the deviation of u from its average value
u u u (6.9) also shown in Fig. 6.7. It follows by definition that a fluctuation has zero mean value  v v u  eText Main Menu  1
T T (u u ) dt u u 0 0 Textbook Table of Contents  Study Guide (6.10) 334 Chapter 6 Viscous Flow in Ducts u p
p = p + p′
u = u + u′ u′ p
u
p′ Fig. 6.7 Definition of mean and
fluctuating turbulent variables:
(a) velocity; (b) pressure. t t (a) (b) However, the mean square of a fluctuation is not zero and is a measure of the intensity of the turbulence
u 1
T 2 T u 2 dt 0 (6.11) 0 Nor in general are the mean fluctuation products such as u and u p zero in a typical turbulent flow.
Reynolds’ idea was to split each property into mean plus fluctuating variables
u u u w w w p p p (6.12) Substitute these in...
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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
 Sakar

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