Stream & Velocity Potential Function (Kinematics and Dynamics of Flow Part-3)

Stream Function: A stream function is an arbitrary function whose derivatives give velocity components of a particular flow situation.

The partial derivative of stream function with respect to any direction gives the velocity component at right angles to that direction. It is denoted by ψ

According to the above definition

** As ψ satisfies the coninuity equation hence, if ψ exists then it is possible case of fluid flow. **

Now let us see the rotational components of fluid particles

Here u,v,w are the velocities in x, y, z-direction respectively.

Conclusion:

1. If stream function (ψ) exists, it is a possible case of fluid flow. But we can’t decide whether the flow is rotational or irrotational.

2. If stream function satisfies Laplace equation then, it is a possible case of irrotational flow.

**If Φ satisfies above equation then it is a possible case of fluid flow.**

Now let us see the rotational components of fluid particles

Here u,v,w are the velocities in x, y, z-direction respectively.

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