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?
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?