Problem
In a one-dimensional flow field, the velocity at a point may be given in the Eulerian system by u=x+2t. Determine the displacement of a fluid particle whose initial position is xat initial time to in the Lagrangian system.
Solution
  Given u=x+2t
 
gives on integration

 
(A)
where, c is the constant of integration. C can be found by initial conditions-
For 
Therefore,  

 
(B)
Putting value of c from (B) into (A)
 
This equation represents the Lagrangian version of the fluid particle having the identity at 

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