**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

**Continuity Equation** for flow is given by

**** 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.

##### Putting values of u & v in terms of ψ, we get

#### This is a Laplace equation for stream function (ψ)

**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.

**Velocity Potential Function:**

##### It is a scalar function of space and time such that its negative derivative with respect to any direction gives the fluid velocity in that direction.

##### It is denoted by Φ

**Continuity Equation** for flow is given by

#### This is a Laplace equation for velocity potential function (Φ)

****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.