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Unformatted text preview: ENU 4133 Duct Flows February 17, 2011 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. Reynolds Number Regimes (6.1) Laminarturbulent transitions depend most strongly on Reynolds number: Re = VL (1) For internal flows, the velocity scale used is the average velocity . In round tube/pipe flow, the length scale is the diameter: Re round tube = V ave D = mD A = 4 m D (2) In round pipes, for a Reynolds number below 2100 (or 2000 or 2300), laminar flow prevails and the simple NS solution from Chapter 4 applies. Above this, intermittent or sustained turbulence prevails. Other geometries: different Re crit values . Turbulent Flows (6.1) Turbulence: stochastic fluctuations of flow velocity (in 3D) as functions of time and space (3D). Instantaneous, local velocity traces: Internal Viscous Flow (6.2) For the most parts, internal flow, wallbounded flow, and duct flow are synonymous. With few exceptions, nuclearrelevant flows are internal flows. Development Length (6.2) Function of Re only. Laminar flows: L entrance = C 1 D Re (3) C 1 given as 0.06 in White, often 0.05 in other books. Turbulent flows: L entrance = 4 . 4 Re 1 / 6 D (4) Rule of thumb: L entrance , turb 30 40 D . Remark: strictly, we should clarify these as hydrodynamic development lengths; the lengths required for hydrodynamic parameters (pressure gradient, velocity profile) to reach equilibrium. In flows with heat transfer, a potentially very different thermal development length may also exist. Friction Factor Development (1) (6.3) Control volume for fully developed pipe flow: Friction Factor Development (2) 1D Continuity: Q 1 = Q 2 (5) V 1 = V 2 (6) Fully developed implies 1 = 2 (same profile shape)....
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This note was uploaded on 07/14/2011 for the course ENU 4133 taught by Professor Schubring during the Spring '11 term at University of Florida.
 Spring '11
 Schubring

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