In a Lagrangian system, the position of a fluid particle

In a Lagrangian system, the position of a fluid particle in a flow is described as x = x₀e^–kt and y = y₀e^kt where t is the time while x₀, y₀, 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

x direction scalar of velocity field,

u =	dx
	dt

u = - kx₀e^-kt
y direction scalar of velocity field

v =	dy
	dt

v = ky₀e^kt
v̄ = uî + vĵ
V̄ = - kx₀e^-ktî + ky₀e^ktĵ
u & v are non zero scalar t ≥ 0 so it is 2D flow. 2D possible flow field

	δu	+	δv	= 0
	δx		δy

	δ	(- kx₀e^-kt) +	δ	(ky₀e^kt) = 0
	δx		δy

0 + 0 = 0 continuity satisfied.

	δu	+ k²x₀e^-kt
	δt

	δv	+ k²y₀e^kt
	δt

	δu	≠ 0
	δt

	δv	≠ 0
	δt

So, flow is unsteady.