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Unformatted text preview: 138d, which is the
longest development length possible.
In turbulent flow the boundary layers grow faster, and Le is relatively shorter, according to the approximation for smooth walls
Le
d 1/6
4.4 Red turbulent  v v Some computed turbulent entrance lengths are thus  eText Main Menu  Textbook Table of Contents  Study Guide (6.6) Chapter 6 Viscous Flow in Ducts Red 4000 104 105 106 107 108 Le/d 18 20 30 44 65 95 Now 44 diameters may seem “long,” but typical pipeflow applications involve an L/d
value of 1000 or more, in which case the entrance effect may be neglected and a simple analysis made for fully developed flow (Sec. 6.4). This is possible for both laminar and turbulent flows, including rough walls and noncircular cross sections.
EXAMPLE 6.2
A 1 indiameter water pipe is 60 ft long and delivers water at 5 gal/min at 20°C. What fraction
2
of this pipe is taken up by the entrance region? Solution
Convert
Q (5 gal/min) 0.00223 ft3/s
1 gal/min 0.0111 ft3/s The average velocity is
Q
A V Red 0.0111 ft3/s Vd 8.17 ft/s ( /4)[( 1 /12...
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 Spring '08
 Sakar

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