Reynolds Equation and Mixing Length Model Turbulent Flow Between Two Parallel Plates
Equation (3) now becomes
,
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(6)
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Integrating (6) and noting that , we find
,
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(7)
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At the centerline , equation (7) implies
,
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(8)
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Eliminating between (7) and (8), the result is
,
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(9)
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Introducing the dimensionless variable
, equation (9) may be restated as
,
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(10)
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where
,
and .
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(11)
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Alternatively introducing , equation (9) becomes
,
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(12)
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For high Reynolds number flows as ,
equations (10) and (12) imply
,
(as ,
(core region)).
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(13)
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,
(as ,
(surface layer)).
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(14)
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