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Unformatted text preview: vector Fluids Lecture 8 Notes 1. Streamlines 2. Pathlines 3. Streaklines Reading: Anderson 2.11 Three types of uid element trajectories are defined: Streamlines, Pathlines, and Streaklines. They are all equivalent for steady ows, but differ conceptually for unsteady ows. Streamlines Streamline equations A streamline is defined as a line which is everywhere parallel to the local velocity vector vector V ( x, y, z, t ) = u + v + w k . Define dvectors = dx + dy + dz k as an infinitesimal arc-length vector along the streamline. Since this is parallel to vector V , we must have dvectors V = 0 + ( v dx u dy ) ( w dy v dz ) + ( u dz w dx ) k = 0 Separately setting each component to zero gives three differential equations which define the streamline. The three velocity components u , v , w , must be given as functions of x, y, z before these equations can be integrated. To set the constants of integration, it is sucient to specify some point x o , y o , z o through which the streamline passes, y y V ds V ds x o o o z...
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- Fall '05