In Chap. 9, we define the stream function for two-dimensional incompressible flow in the xy-plane, where

In Chap. 9, we define the stream function ψ for two-dimensional incompressible flow in the xy-plane,

where u and v are the velocity components in the x- and y-directions, respectively. 

(a) What are the primary dimensions of ψ? 

(b) Suppose a certain two-dimensional flow has a characteristic length scale L and a characteristic time scale t. Define dimensionless forms of variables x, y, u, v, and ψ. 

(c) Rewrite the equations in non dimensional form, and identify any established dimensionless parameters that may appear.

Transcribed Image Text:

u = ne ду v= V pe xe