Chapter 8 : Viscous Incompressible Flows
Lecture 25 :


Exact Solutions Of Navier-Stokes Equations

Consider a class of flow termed as parallel flow in which only one velocity term is nontrivial and all the fluid particles move in one direction only.

  • We choose $ \textit{x}$ to be the direction along which all fluid particles travel , i.e. . Invoking this in continuity equation, we get

 

 

  which means

  • Now. Navier-Stokes equations for incompressible flow become


 


 
 


So, we obtain

   which means
and (25.11)