Duct_Flow_web - ENU 4133 Duct Flows February 17, 2011 Duct...

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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 Non-circular 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) Laminar-turbulent 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 N-S 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 3-D) as functions of time and space (3-D). Instantaneous, local velocity traces: Internal Viscous Flow (6.2) For the most parts, internal flow, wall-bounded flow, and duct flow are synonymous. With few exceptions, nuclear-relevant 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) 1-D 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.

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Duct_Flow_web - ENU 4133 Duct Flows February 17, 2011 Duct...

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