1. Examples of Potential Flows SOURCE FLOW All rights reserved by don moorcroft

2. Examples of Potential Flows SOURCE FLOW x y r Cartesian coordinates Potential Function

3. Polar coordinates Cartesian coordinates

5. For a SINK flow, Q will be negative Stream Function Kundu’s book p. 69

6. All rights reserved by don moorcroft

7. Examples of Potential Flows IRROTATIONAL VORTEX The circulation along any circle around the origin is a constant As a potential flow, it is irrotational & incompressible

8. IRROTATIONAL VORTEX www.zotloeterer.com

9. IRROTATIONAL VORTEX Potential Function

10. VORTEX Stream Function

11. DOUBLET (Sources and Sinks) x y source sink Both have strength Q. The flow field can be obtained by combining the potential function for the sink φ 2 and the source φ 1. Laplace’s function is linear – linear superposition is valid. Taylor expansion

12. Similarly

14. In the same way ψ 2 and ψ 1 can be added because Laplace’s function is linear – linear superposition is valid.