Chapter 7, Problem 31P

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

$u=\frac{\partial \psi }{\partial y}v=-\frac{\partial \psi }{\partial x}$
where u and v ate the velocity components in the x- and y-directions, respectively. (a) What are the primary dimensions of $\psi$ ? (b) Suppose a certain two-dimensional flow has a characteristic length scale L and a characteristic time scale t. Define dimensionless forms of vat tables x, y, u, v, and $\psi$ . (c) Rewrite the equations in nondimensional form, and identify an established dimensionless parameters that may appear.