f08_new_fall

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online