1 / 14

Stream Function & Velocity Potential

Stream Function & Velocity Potential. Stream lines/ Stream Function ( Y ) Concept Relevant Formulas Examples Rotation, vorticity Velocity Potential( f ) Concept Relevant Formulas Examples Relationship between stream function and velocity potential Complex velocity potential.

chogan
Download Presentation

Stream Function & Velocity Potential

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Stream Function & Velocity Potential • Stream lines/ Stream Function (Y) • Concept • Relevant Formulas • Examples • Rotation, vorticity • Velocity Potential(f) • Concept • Relevant Formulas • Examples • Relationship between stream function and velocity potential • Complex velocity potential

  2. Stream Lines • Consider 2D incompressible flow • Continuity Eqn • Vx and Vy are related • Can you write a common function for both?

  3. Stream Function • Assume • Then • Instead of two functions, Vx and Vy, we need to solve for only one function y - Stream Function • Order of differential eqn increased by one

  4. Stream Function • What does Stream Function y mean? • Equation for streamlines in 2D are given by y = constant • Streamlines may exist in 3D also, but stream function does not • Why? (When we work with velocity potential, we may get a perspective) • In 3D, streamlines follow the equation

  5. b Time = t + dt a Rotation • Definition of rotation Time=t y Dy Dx x Assume Vy|x< Vy|x+Dx and Vx|y> Vx|y+Dy

  6. Similarly Rotation • To Calculate Rotation Time = t + dt Dy1 a Dx

  7. a b Rotation • To Calculate Rotation • For very small time and very small element, Dx, Dy and Dt are close to zero

  8. Rotation • To Calculate Rotation • For very small q, (i.e.q ~ 0)

  9. Simplifies to Rotation • To Calculate Rotation

  10. Rotation in terms of Stream Function • To write rotation in terms of stream functions • That is • For irrotational flow (wz=0)

  11. Rotation and Potential • For irrotational flow (wz=0) • This equation is “similar” to continuity equation • Vx and Vy are related • Can we find a common function to relate both Vx and Vy ?

  12. Velocity Potential • Assume • Then • In 3D, similarly it can be shown that • f is the velocity potential

  13. Velocity Potential vs Stream Function • In 2D inviscid flow (incompressible flow OR steady state compressible flow), both functions exist • What is the relationship between them?

  14. Stream Function- Physical meaning • Statement: In 2D (viscous or inviscid) flow (incompressible flow OR steady state compressible flow), y = constant represents the streamline. • Proof • If y = constant, then dy=0 Vy • If y = constant, then Vx

More Related