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Unformatted text preview: ENU 4133 – Duct Flows – Part 2 February 24, 2010 Duct Flows Coverage I Reynolds number regimes (Section 6.1) I Internal viscous flows & development length (Section 6.2) I Friction factors (Section 6.3 + notes) I Solution for laminar round tube flow (Section 6.4) I Friction factors in turbulent flows (Section 6.6) – equations, roughness, Moody chart I Solving duct flow problems (Section 6.7 + examples) I Noncircular ducts (Section 6.8) I Minor losses (form losses) (Section 6.9 + notes) Section 6.5 – covered later. Section 6.10 – not explicitly covered. Sections 6.11 and 6.12 – not covered. Friction Factors in Turbulent Flow (6.6) Analytical determination of smooth tube friction factors for turbulent flow has not yet been achieved and may well be impossible. Empricial estimates are generally preferred. One semiempirical model determined that f is wellapproximated by a function of the form: 1 √ f = A log 10 Re √ f + B (1) Turbulence theory (studied later in this course) would predict: 1 √ f = 1 . 99log 10 Re √ f 1 . 02 (2) Comparison to actual data, however, gives: 1 √ f = 2log 10 Re √ f . 8 (3) Friction Factor Approximations Such an implicit equation can be difficult to use. White recommends the following: For Re < 10 5 , the Blasius friction factor (also semiempirical): f ≈ . 316 Re 1 / 4 (4) Otherwise, the Haaland correlation with roughness set to zero: f ≈ 1 . 8log 10 Re 6 . 9 2 (5) Other references give different equations and different ranges of applicability. Friction Factor Approximations (2) Todreas & Kazimi instead suggest: For Re < 30 , 000: f ≈ . 316 Re 1 / 4 (6) For 30 , 000 < Re < 1 , 000 , 000 (McAdams): f ≈ . 184 Re 1 / 5 (7) McAdams works well for nuclearrelevant flows. When using an approximation such as these, you should be clear about which...
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 Spring '11
 Schubring
 Fluid Dynamics, Dh, Friction Factors

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