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

2. Cartesian coordinates
Polar coordinates

4. For a SINK flow, Q will be negative

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

6. VORTEX

7. VORTEX
Potential Function

8. VORTEX
Stream Function

9. DOUBLET (Sources and Sinks)y
DOUBLET (Sources and Sinks)
Both have strength Q. The flow field can be obtained by combining the potential function for the sink φ2 and the source φ1. Laplace’s function is linear – linear superposition is valid.
source
sink x
Taylor expansion

10. Similarly

12. In the same way ψ2 and ψ 1 can be added because Laplace’s function is linear – linear superposition is valid.