Consider the vortex flow of a fluid of density $\rho$ where the fluid rotates with an angular velocity $\omega$ about the $z$-axis. Determine where a unit square $S$ on the $yz$-plane should be placed if we want zero net amount of fluid flowing through this square per unit time.
I know that we can show that the velocity vector $v = \omega × r$ does not depend on $z$, so that the unit square S can have one of its sides on the y-axis at a distance a from the origin. Then we just need to establish this distance. However, I'm confused about how to actually go about this...