For the flow given in Problem 10.6, where was the particle at t = −π/4ω that is currently located at X 0 = Uπ/ω, Y 0 = 0, Z 0 = 0 at t 0 = 0? Problem 10.6 The Lagrangian particle paths for a flow are...

For the flow given in Problem 10.6, where was the particle at t = −π/4ω that is currently located at X₀
= Uπ/ω, Y₀
= 0, Z₀
= 0 at t₀
= 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?