Analysis of Inviscid, Incompressible, Irrotation Flows

Incompressible flow is a constant density flow.

 Let us visualize a fluid element of defined mass, moving along a streamline in an incompressible flow.

Due to constant density , we can write       

(20.1)

Irrotational Flow

• if the fluid element does not rotate as it moves along the streamline, or to be precise, if its motion is translational (and deformation with no rotation) only, the flow is termed as irrotational.

The rate of rotation of the fluid element can be measured as the average rate of rotation of two perpendicular line segments.

The average rate of rotation ω_z about z-axis is expressed in terms of the gradients of velocity components as 

Similarly, the other two components of rotation are    

ω_x , ω_y and ω_z are components of 

         

In a two-dimensional flow, ω_z is the only non-trivial component of the rate of rotation called in-plane component of vorticity and computed as 

Thus for irrotational flow,  vorticity is zero i.e.