2003-14.md

course	course_year	question_number	tags	title	year
Fluid Dynamics	IB	14	IB 2003 Fluid Dynamics	1.I.6C	2003

An unsteady fluid flow has velocity field given in Cartesian coordinates $(x, y, z)$ by $\mathbf{u}=(1, x t, 0)$, where $t$ denotes time. Dye is released into the fluid from the origin continuously. Find the position at time $t$ of the dye particle that was released at time $s$ and hence show that the dye streak lies along the curve

$$y=\frac{1}{2} t x^{2}-\frac{1}{6} x^{3}$$