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Unformatted text preview: CWR 4202 Lecture 2 Visualizing Flow The fundamental method of visualizing a flow pattern is by means of 'streamlines'. A streamline is constructed by drawing a line which is tangential to the velocity vectors of a connected series of fluid particles (Fig. 1 (a)). The streamline is thus a line representing the direction of flow of the series of particles at a given instant. Because the streamline is always tangential to the flow, it follows that there is no flow across a streamline. A set of streamlines may be arranged to form an imaginary pipe or tube. This is known as a 'streamtube' (Fig. 1(b)). Under certain specific circumstances, streamtubes can actually be identified. For example, the internal surface of a pipeline must also be a streamtube, since the vectors representing the flow adjacent to the surface must be parallel to that surface. The surface is therefore 'covered' with streamlines. Fig. 1 Definition of a streamline and streamtube. (Adapted from Andrew Chadwick, John Morfett and Martin Borthwick. Hydraulics in Civil and Environmental Engineering, Fourth Edition. 2004. Spon Press. NY, NY.) Fundamental Physical Principals of Hydraulics 1. Conservation of Mass (Continuity) 2. Conservation of Energy 3. Conservation of Momentum (Newtons 2nd Law) 1 scalar equation 1 scalar equation 1 vector equation or(3 scalar equations) Note: For most real world applications we want to reduce problems to scalar equations (more readily applied). Conservation of Mass (Continuity) Energy and Momentum Coefficients In deriving the momentum equation, it was stressed that it could only be applied directly to a large region if the velocity ( ) was constant across the region (set equal to V). The energy equation was stated to apply to a streamline with velocity . In many real fluid flow problems, V varies across a section. The velocity distribution across a section is not always known, and the mean velocity (defined as ) must be used instead of V. However, both the energy and momentum equations may still be used by introducing the energy and momentum coefficients, and, ' respectively. Portions of this material were adapted from: Andrew Chadwick, John Morfett and Martin Borthwick. Hydraulics in Civil and Environmental Engineering, Fourth Edition. 2004. Spon Press. NY, NY. ...
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- Fall '08