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## Homework Statement

A bucket of water is rotated slowly with angular velocity w about its vertical axis..When a steady state has been reached the water rotates with a velocity field v(r) as if it were a rigid body. Calculate div(v) and interpret the result. Calculate curl (v). Can the flow be represented in terms of a velocity potential such that v = grad phi? If so, what is phi?

## Homework Equations

## The Attempt at a Solution

Not sure how to do this...

I think somewhere in my notes it says that v here should = (-wy,wx,0)

Is this right?

In which case, div(v) = 0 - what is the interpretation?? No sinks or sources??

curl v = (0,0,2w)...

Can I write it as the gradient of a scalar function? If so, what is the function?