f08_new_fall

# f08_new_fall - vector Fluids – Lecture 8 Notes 1...

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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 ﬂuid element trajectories are defined: Streamlines, Pathlines, and Streaklines. They are all equivalent for steady ﬂows, but differ conceptually for unsteady ﬂows. Streamlines Streamline equations A streamline is defined as a line which is everywhere parallel to the local velocity vector vector ˆ V ( x, y, z, t ) = u ˆ ı + v ˆ+ w k . Define dvectors = dx ˆ ı + dy ˆ + dz ˆ 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 ) ˆ ( w dy − v dz )ˆ ı + ( u dz − w dx ) ˆ 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 suﬃcient 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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## This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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f08_new_fall - vector Fluids – Lecture 8 Notes 1...

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