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 x0 at initial time to in the Lagrangian system.
gives on integration
where, c is the constant of integration. C can be found by initial conditions-
Putting value of c from (B) into (A)
This equation represents the Lagrangian version of the fluid particle having the identity at