Problem
In a onedimensional 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 x_{0 }at initial time to in the Lagrangian system.
Solution
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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