# Fluids angular momentum

1. Sep 28, 2016

### joshmccraney

I don't typically do this, but attached is a figure with a problem statement. This is not homework because I have already solved it! My question is a subtle one.
Please see the attachments, one is the question and the other is my solution.

I know my solution is correct, but at the end of equation (2) I wrote $n = e_x$ where $e_x$ is the unit vector in the $x$ direction. At the time I am not sure why I wrote $e_x$ this way, because I now think it should be $\cos \theta e_x + \sin \theta e_y$. Any help here would be awesome in understanding why what I had was correct.

Thanks so much.

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• ###### problem.png
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2. Sep 30, 2016

### haruspex

I am not going to try to follow your intricate algebra, but I will suggest an easier way. Take moments about the sprinkler's axis and apply conservation of angular momentum. What is the tangential velocity of the jet in the ground frame?

3. Sep 30, 2016

### joshmccraney

Tangential velocity is $-r \omega + Q \cos \theta / 3 A$.

I think I know how to solve the problem assuming velocity out of the sprinkler pipe is constant (or rather averaged), but I want to make sure I can do it both ways (the way you mention above and using integrals).

4. Sep 30, 2016

### joshmccraney

Never mind, I figured it out. For others, in case they want to know, I'll attach the solution.

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