Real Life Application
Stream function is a mathematical postulation with scalar characteristics, defined for flow fields of incompressible fluids. This function helps to describe the flow velocity components and thus plot streamlines and path lines which represent the trajectories of fluid particles.
Mathematically the stream function for a flow field can be evaluated from the continuity equation corresponding to it by assuming a scalar function whose partial derivatives (gradients in principal directions) are somehow related to the velocity components and the function is itself satisfying the continuity equation.
Based on the above procedure the stream function (ψ) for a 2D flow field has been expressed in the video.
Properties of stream function
The stream function has some properties which simplify the kinematic analysis of a flow situation. These properties are as follows:
1. Stream function is constant along a streamline
2. For irrotational flow, it follows the continuity equation
3. The difference of stream function values between corresponding to two stream lines is equal to volumetric flow rate between the two lines per unit width of the flow
4. This difference is also equal to line integral of normal velocity along any random line between any two points on those streamlines