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Unformatted text preview: dx h
y h gz) (6.80) This may be nondimensionalized as a friction factor:
f 8w
V2 24
Vh 24
Reh (6.81) These are exact analytic laminarflow results, so there is no reason to resort to the
hydraulicdiameter concept. However, if we did use Dh, a discrepancy would arise. The
hydraulic diameter of a wide channel is b→∞ y = +h
y
2h u ( y)
x
Y u max  v v Fig. 6.14 Fully developed flow between parallel plates.  eText Main Menu y=–h  Textbook Table of Contents  Study Guide Chapter 6 Viscous Flow in Ducts 4A Dh lim b→ 4(2bh)
2b 4h 4h (6.82) or twice the distance between the plates. Substituting into Eq. (6.81), we obtain the interesting result
Parallel plates: 96
V(4h) flam 96
ReDh (6.83) Thus, if we could not work out the laminar theory and chose to use the approximation
f 64/ReDh, we would be 33 percent low. The hydraulicdiameter approximation is
relatively crude in laminar flow, as Eq. (6.76) states.
Just as in circularpipe flow, the laminar solution above becomes unstable at about
ReDh 2000; transition occurs and turbul...
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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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