| 5 comments ]

The fluid flows into the sprayer through point O, so the fluid has no initial angular momentum. Therefore, the sprayer reaches its constant angular speed when the fluid flows out radially. In order to find the condition, it will be easier if first we observe from sprayer's rotating frame.We define a new variable, r, which equals to the distance from point O to end of pipe.


In this frame, the fluid flows out from the sprayer at velocity v. Using Bernoulli equation for rotating frame, we can get





Now observe it from ground frame. Velocity of the fluid at ground frame is a resultant of and Because velocity of fluid must be radial at ground frame, tangential component of v must be equal to ωr,




Substitute v from equation (2) to equation (1), and we get




Substitute r, and finally we get





That's my solution.
If you have any question, correction, or comment, please leave a comment below.
Thank you.

Solution - Rotating SprayerSocialTwist Tell-a-Friend

5 comments

Anonymous said... @ February 27, 2009 at 1:52 AM

in the step going to eqtn 1 why isnt their any term for pressure in thr RHS of the equation?

Anonymous said... @ February 27, 2009 at 12:56 PM

I do the question using angular momentum.. it produce a different answer..
I don't know how to write my answer in latex here.. but, my answer is
w = 6/5 (2P/(rho) a^2)^0.5
I don't know why the answer is different..

Anonymous said... @ February 27, 2009 at 1:04 PM

by the way, why the fluid velocity must be tangential in ground frame?? why not tangential like usual in simple circular motion?

Anonymous said... @ February 27, 2009 at 1:05 PM

sorry, correction for above..
by the way, why the fluid velocity must be radial in ground frame?? why not tangential like usual in simple circular motion?

Copycat91 said... @ February 28, 2009 at 8:56 AM

@1st commenter:
The pressure term in RHS of the equation is for atmospheric pressure. And it has been mentioned at the problem's text that P is much larger than atmospheric pressure.

@2nd commenter:
Hmmm... I don't know, too. But could you send your solution to my email, please?

@3rd commenter:
In order to keep angular momentum of the fluid zero when it enters and flows out from the sprayer.

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