 # 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 ##### 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 #### 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 denoted by Φ ##### Continuity Equation for flow is given by #### **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.  #### Stream Function Ψ #### Velocity Potential Φ #### Relation between stream function and velocity potential

##### Comparing both stream function (Ψ) and velocity potential function (Φ) #### Stream Line

##### It is the line along which stream function (ψ) remains constant. #### Equipotential Line

##### It is the line along which Velocity potential (Φ) remains constant. ### I hope you like this section. Please share with friends and like my Facebook page and never miss an update.

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