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Unformatted text preview: dx h
y h gz) (6.80) This may be nondimensionalized as a friction factor:
Reh (6.81) These are exact analytic laminar-flow results, so there is no reason to resort to the
hydraulic-diameter concept. However, if we did use Dh, a discrepancy would arise. The
hydraulic diameter of a wide channel is b→∞ y = +h
2h u ( y)
Y u max | v v Fig. 6.14 Fully developed flow between parallel plates. | e-Text 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 hydraulic-diameter approximation is
relatively crude in laminar flow, as Eq. (6.76) states.
Just as in circular-pipe 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