Chanel: Science of Fluids,    / scienceoffluids  
Playlist: Fluids made easy: 02 Fluid motion descriptions
   • Fluids Madeeasy Courses: 02  Fluid ...  

This talk is on the streamline equation and pathline equations for steady incompressible flows, so to answer the question: why the streamlines and pathlines would be same in a steady flow? As we frequently see the statement: the streamline and pathline would be same in the steady flows, and we see the illustrations in the steady flows, the streamlines and pathlines would be coincident, but why? This talk will give an answer to this, for which we use a simple example of a steady flow past a cylinder. The flow here is assumed as a potential flow, such that we could have an analytical solution to the flow, and thus the analytical expression for the flow field. This would allow us to build the streamline and pathline equations and the theoretical solutions to the streamlines and pathlines so that we can see the streamlines and pathlines would be same mathematically in the steady flows (and they are very different in unsteady flows, see my next talk on the streamlines and pathlines in unsteady flows).
This talk includes the following main contents:
Streamline equation for the velocity field
Pathline equation for the flow field
A steady flow: the streamline equation and solution
A steady flow: the pathline equation and solution
An explanation why the streamlines and pathlines are coincident in steady flows.