# Flux Integral of a Fluid Rotating about an Axis

## Homework Statement

We have a fluid with density ρ which is rotating about the z-axis with angular velocity ω. Where should a unit square, call it S, be placed in the yz-plane such that there is zero net amount of fluid flowing through it?

## Homework Equations

$$\mathbf{v}=\mathbf{\omega}\times\mathbf{r}$$
$$\int\mathbf{F}\cdot d\mathbf{S}$$

## The Attempt at a Solution

My attempt has been to try and show that the velocity vector (cross product of angular velocity and position) is independent of z. This would mean that I can position the square such that one side is on the y-axis at distance δ from the origin. Then just find the value of δ.

I'm not sure how to set-up my angular velocity vector and my position vector. Also, is my method idea correct?