For the flow described in Problem 10.6, sketch the streakline initiated at (0, 0, 0). Sketch the  pathline for the particle at this point at t = 0. Problem 10.6 The Lagrangian particle paths for a...

For the flow described in Problem 10.6, sketch the streakline initiated at (0, 0, 0). Sketch the  pathline for the particle at this point at t = 0.

Problem 10.6

The Lagrangian particle paths for a flow are given by

where U m/s, V m/s, ω s⁻¹
are constants. Find the location of the particle at times π/4ω, π/2ω, 3π/4ω, and π/ω initially located at X₀
= 0, Y₀
= 0, Z₀
= 0 at t = t₀
= 0. If t₀
= π/4ω, where will the particle located at X₀
= 0, Y₀
= 0, Z₀
= 0 be at times π/2ω, 3π/4ω, and π/ω?