Stream function

(Difference between revisions)

Revision as of 11:04, 12 September 2005

The stream function is a scalar field variable which is constant on each streamline. It exists only in two-dimensional and axisymmetric flows.

On a streamline in two-dimensional flow

$d\psi = \frac{\partial \psi}{\partial x} dx + \frac{\partial \psi}{\partial y} dy = 0$

The equation of a streamline in two-dimensions is

$v dx - u dy = 0$

Comparing the two equations, we have

$u = - \frac{\partial \psi}{\partial y}$

$v = \frac{\partial \psi}{\partial x}$