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In a Lagrangian system, the position of a fluid particle in a flow is described as x = x_0 e^{-kt} and y = y_0 e^{kt}, where t is time and x_0, y_0, and k are constants. The flow is

1. unsteady and one-dimensional
2. steady and two-dimensional
3. steady and one-dimensional
4. unsteady and two-dimensional

Correct answer: steady and two-dimensional

Solution

The motion is described by both x and y coordinates, so it is two-dimensional. Differentiating gives velocities that can be written in terms of position variables without explicit time dependence, indicating a steady flow.

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