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

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Presentation transcript:

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

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

Polar coordinates Cartesian coordinates

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

All rights reserved by don moorcroft

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

IRROTATIONAL VORTEX

IRROTATIONAL VORTEX Potential Function

VORTEX Stream Function

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

Similarly

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