Stream function
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(Difference between revisions)
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v = \frac{\partial \psi}{\partial x} | v = \frac{\partial \psi}{\partial x} | ||
</math> | </math> | ||
+ | |||
+ | Conversely, the stream function at any point <math>P</math> can be obtained from the velocity field by a line integral | ||
+ | |||
+ | <math> | ||
+ | \psi(P) = \psi(P_o) + \int_{P_o}^P [ v(x,y,t) dx - u(x,y,t) dy ] | ||
+ | </math> | ||
+ | |||
+ | where <math>P_o</math> is some reference point and one can assume <math>\psi(P_o) = 0</math> since the stream function is determined only upto a constant. |
Revision as of 11:11, 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
The equation of a streamline in two-dimensions is
Comparing the two equations, we have
Conversely, the stream function at any point can be obtained from the velocity field by a line integral
where is some reference point and one can assume since the stream function is determined only upto a constant.