In a steady two-dimensional flow, particle trajectories are given byx(t) =x0cosγt; y(t) =y0sinγta. from these trajectories determine the lagrangian particle velocity componentsu(t) =dx/dtandv(t) =dy/dt. convert these to eulerian velocity componentsu(x, y) andv(x, y). note that the eulerian velocity does not depend on time.

Answer with Explanation:

Given that

Thus by definition x component of velocity in Lagrangian system is given by

Thus by definition y component of velocity in Lagrangian system is given by

Since in eulerian system we need to eliminate time from the equations

From euations 'i' and 'ii' we can write

Applying these values in the velocity components as obtained in Lagrangian system we get

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