- #1
jbar18
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Homework Statement
What is wrong with the following argument from Bernoulli's equation?
Suppose a fluid in a bucket is rotating under gravity with constant angular velocity W so that velocity is:
[itex]u = (-\Omega y,\Omega x, 0).[/itex]
Then:
[itex]\frac{P}{\rho} + \frac{u^2}{2} + gz = constant[/itex],
[itex]z = constant - \frac{(\Omega)^2}{2g} (x^2+y^2)[/itex]
But this implies that the highest point of the water is in the middle, which is obviously not true.
2. The attempt at a solution
I was wondering if perhaps it might have something to do with P or rho (or both) being a function of x and y? In the problem the whole pressure term seems to have been grouped with the constant, and I'm wondering if that is justifiable. Beyond that I don't know, it looks like Bernoulli's equation is just not appropriate for this situation for some reason (or else it has been applied incorrectly, but I am not sure why).
I've put this in the homework section, but I should mention that it is not assessed and I am unable to check my answer, so this is just out of interest.
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