Unformatted text preview: the shear stress does not equal 2 R. The momentum equation (6.26) thus becomes
pA gA L sin w L 0 5  v v This section may be omitted without loss of continuity.  eText Main Menu  Textbook Table of Contents  Study Guide Chapter 6 Viscous Flow in Ducts or p
g hf L
g A/
w z (6.70) This is identical to Eq. (6.27) except that (1) the shear stress is an average value integrated around the perimeter and (2) the length scale A/ takes the place of the pipe
radius R. For this reason a noncircular duct is said to have a hydraulic radius Rh, defined by
Rh crosssectional area
wetted perimeter A (6.71) This concept receives constant use in openchannel flow (Chap. 10), where the channel cross section is almost never circular. If, by comparison to Eq. (6.29) for pipe flow,
we define the friction factor in terms of average shear
fNCD 8 w hf f (6.72) V2 where NCD stands for noncircular duct and V Q/A as usual, Eq. (6.70) becomes L V2
4Rh 2g (6.73) This is equivalent to Eq. (6.30) for pipe flow except that d is replaced by 4Rh. Therefore we customarily define the h...
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 Spring '08
 Sakar
 Fluid Dynamics, eText Main Menu, Osborne Reynolds

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