Question

In a Lagrangian system, the position of a fluid particle in a flow is described as x=x₀e⁻ᵏᵗ and y=y₀eᵏᵗ, where t is the time while x₀, y₀, and k are constants. The flow is

Accepted Answer

The correct answer is (B) steady and two-dimensional. Velocity components: u=dx/dt=−kx₀e⁻ᵏᵗ=−kx, v=dy/dt=ky₀eᵏᵗ=ky. Both depend only on position (x,y), not explicitly on time, so the velocity field is steady. Since u depends on x and v depends on y (two independent spatial directions both carry flow), it is two-dimensional.

Explanation