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Chapt06

# However if we did use dh a discrepancy would arise

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Unformatted text preview: ent flow results. For turbulent flow between parallel plates, we can again use the logarithm law, Eq. (6.21), as an approximation across the entire channel, using not y but a wall coordinate Y, as shown in Fig. 6.14: u(Y) u* 1 ln Yu* B 0 Y h (6.84) This distribution looks very much like the flat turbulent profile for pipe flow in Fig. 6.11b, and the mean velocity is V 1 h h u dY u* 1 ln hu* 1 B (6.85) 0 Recalling that V/u* (8/f)1/2, we see that Eq. (6.85) is equivalent to a parallel-plate friction law. Rearranging and cleaning up the constant terms, we obtain 1 f 1/2 2.0 log (ReDh f 1/2) 1.19 (6.86) where we have introduced the hydraulic diameter Dh 4h. This is remarkably close to the pipe-friction law, Eq. (6.54). Therefore we conclude that the use of the hydraulic diameter in this turbulent case is quite successful. That turns out to be true for other noncircular turbulent flows also. Equation (6.86) can be brought into exact agreement with the pipe law by rewriting it in the form 1 f 1/2 2.0 log (0.64 ReDh f 1/2) 0.8 (6.87) Thus the turb...
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