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Unformatted text preview: on the wall shear because there are two
shear stresses, the inner stress being greater than the outer. It is better to define f with
respect to the head loss, as in Eq. (6.73),
f hf Dh 2g
L V2 Q
(a2 b2) where V (6.94) The hydraulic diameter for an annulus is
Dh 4 (a2
2 (a b2)
b) 2(a b) (6.95) It is twice the clearance, rather like the parallel-plate result of twice the distance between plates [Eq. (6.82)].
Substituting hf, Dh, and V into Eq. (6.94), we find that the friction factor for laminar flow in a concentric annulus is of the form
ReDh a4 b)2(a2 b2)
(a2 b2)2/ln (a/b) (a
b4 (6.96) The dimensionless term is a sort of correction factor for the hydraulic diameter. We
could rewrite Eq. (6.96) as
Concentric annulus: f 64
Reeff 1 Reeff ReDh (6.97) | v v Some numerical values of f ReDh and Deff/Dh 1/ are given in Table 6.3.
For turbulent flow through a concentric annulus, the analysis might proceed by patching together two logarithmic-law profiles, one going out from the inner wall to meet
the other coming i...
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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