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Unformatted text preview: Chapter 6: Viscous Flow in Ducts 6.1 Reynolds Number Regimes 6.2 Internal vs External Fluid Flows 6.3 Head Loss – The Friction Factor 6.4 Laminar Fully Developed Pipe Flow 6.5 Turbulence Modeling 6.6 Turbulent Pipe Flow 6.7 Four Types of Pipe Flow 6.8 Flow in Noncircular Ducts* 6.9 Minor Losses Pipe Systems* 6.10 Multiple Pipe Systems* 6.11 Diffuser Performance* 6.12 Fluid Meters* * skim Flashback Control Volume Analysis V p 2 p 1 τ w τ w l CV General Approaches to Analyze Fluid Motion • Control Volume, or large scale analysis (Ch.3) ~ useful engineering estimates; 1Dimensional; provides info on average force, not force at a point • Differential or small scale analysis (Ch.4) ~ differential eqs. can be modeled numerically • Dimensional analysis (Ch.5) ~ useful to reduce the cost of experimentation General Approaches to Analyze Fluid Motion • Control Volume, or large scale analysis estimate maximum force to anchor jet engine for test; or lift on wing or pressure drop in pipe • Differential or small scale analysis infinitesmal control volume provides differential eqs: velocity, pressure and shear stress at point • Dimensional analysis concept of similitude, important to develop meaningful experiments General Approaches to Analyze Fluid Motion Control Volume, or large scale analysis Sometimes interested in effect of flow on body (e.g. drag or lift)  not the forces on each fluid particle Rare that we want to follow the ultimate path of a specific fluid particle. System vs a Control Volume A specific, identifiable quantity of matter Specific volume in space independent of the flowing fluid Governing laws of physics (determining fluid motion) are stated in terms of fluid systems not control volumes Basic Laws for a System • Conservation of Mass • Momentum Equation • The Angular Momentum Principle • The First Law of Thermodynamics • The Second Law of Thermodynamics Control Volume formulation important because it is often extremely difficult to identify and follow the same mass of fluid at all times. Which is direction is force on ball? Control Volume Interested not in the motion of a specified mass of fluid but rather the effect of fluid motion on a structure, or time to fill a holding tank, or power to pump water… Control Volume Which is direction is force on wing? “ need to relate the time derivative of a system property to the rate of change of that property in a certain region ” – White Reynolds Transport Theorem CV like freebody concept, applied to systems in solid mechanics analysis “ By examining the geometry of the system/control volume pair at t = t o and t = t o + Δ t, we will be able to obtain control volume formulation of the general laws. ” – Fox et al....
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 Summer '09
 Rohr
 Fluid Dynamics, Conservation Of Energy, Reynolds Transport Theorem, noncircular, control surface

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