Fluid Kinematics: Streamlines, Pathlines, and Streaklines

This lecture focuses on fluid kinematics, specifically the fundamental equations of fluid flow and their derivation from the laws of physics. The instructor discusses the distinction between Eulerian and Lagrangian approaches to fluid flow, emphasizing the importance of visualizing flow through different types of lines. The first type discussed is the streamline, defined as a line tangent to the velocity vector at every point. The instructor explains how to derive equations for streamlines using similar triangles and the Eulerian velocity field. Next, the pathline is introduced as the trajectory of a particle advected by the flow, highlighting its Lagrangian nature. The instructor elaborates on how pathlines can cross, unlike streamlines. Finally, the streakline is defined as a line made up of particles that have previously passed through a common point, illustrating its construction through examples like smoke from a chimney. The lecture concludes with a discussion on the conditions under which streamlines, pathlines, and streaklines are identical, emphasizing the significance of steady flow.