{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Duct_Flow_web

# Duct_Flow_web - ENU 4133 Duct Flows Duct Flows Coverage...

This preview shows pages 1–10. Sign up to view the full content.

ENU 4133 – Duct Flows February 17, 2011

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 = ρ VL μ (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 = ρ V ave D μ = ˙ mD μ A = 4 ˙ m πμ 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 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Friction Factor Development (2) 1-D Continuity: Q 1 = Q 2 (5) V 1 = V 2 (6) Fully developed implies α 1 = α 2 (same profile shape). Steady-flow energy equation p 1 ρ g + α V 2 1 2 g + z 1 = p 2 ρ g + α V 2 2 2 g + z 2 + h f (7) p 1 - p 2 ρ g + z 1 - z 2 = h f (8) Δ p ρ g + Δ z = h f (9)
Friction Factor Development (3) x-Momentum Equation: Δ p π R 2 + ρ g π R 2 L sin φ - 2 τπ RL = ˙ m ( V 2 - V 1 ) (10) Δ pR + ρ gRL sin φ - 2 τ L = 0 (11) Δ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 25

Duct_Flow_web - ENU 4133 Duct Flows Duct Flows Coverage...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online