Find an expression that predicts the future shape of a line between the points (0, 0, 0) and (1, 0, 0) at t = 0 for the flow given in Problem 10.9. Problem 10.9 The Lagrangian particle paths for an...

Find an expression that predicts the future shape of a line between the points (0, 0, 0) and (1, 0, 0) at t = 0 for the flow given in Problem 10.9.

Problem 10.9

The Lagrangian particle paths for an irrotational vortex are given by

where K is a constant in m²
/s. Where will the particle located at R₀
= 1m, θ₀
= 0, Z₀
= 0 at t₀
= 0, be at t = πs?