Re: Which way will an inverse garden sprinkler rotate?

Hello Professor Quayle,

I must admit that, for a brief second, I was tempted to think that this was a hoax... as you might be aware, those of us on the other side of the pond had a certain political aspirant whose name is quite similar to yours... oh what a difference a single letter makes! So, if you'll permit me to answer another question before we move on to your question: p-o-t-a-t-o... no "e".

Okay, now that we've gotten that out of our system, I'm not terribly surprised that you haven't been able to find a consensus among the physicists you've talked to. It turns out that your question has been the subject of much heated (pardon the (bad) pun) debate for the last 40 odd years. The original problem was suggested by Feynman, which led to this being called the "Feynman Inverse Sprinkler" problem. In James Gleick's Genius, Gleick outlines Feynman's approach to the problem. Basically, the idea was that the force of the water flowing in would be balanced by an opposite force which would lead to the inverse sprinkler essentially sitting there motionless (i.e., the water coming in from all directions led to the different forces cancelling each other out).

Now, Feynman wasn't much of a sidelines kind of guy so, in a moment of inspiration, he commandeered a tank, filled it with water, put a sprinkler in there, and went to work sending compressed air in the top to force water into the sprinkler: hence, an inverse sprinkler. When he started to do this, sure enough the sprinkler stayed still. Not quite satisfied, he continued to increase the pressure until the walls of the container could no longer stand up to this and burst!

A few years down the line, some enterprising physicists at MIT decided to duplicate his results but, not being terribly fond of getting wet, they decided to try it with air instead of water. There was a web page about this that used to be out there a couple years ago and I actually managed to find the link in my original bookmarks file. Unfortunately, that link is outdated and I wasn't able to find the page off the MIT homepage. Regardless, their experiment/demonstration bore out Feynman's original thesis... their vacuum intake end had an equal force hitting both the wall and coming in, thus cancelling each other out and leading to no motion in the horizontal plane. Interestingly enough, they did detect a slight vertical motion but, since the apparatus was fixed in the vertical plane, their demo didn't address this problem.

But a couple of hotheads led by Prof. Berg of the University of Maryland weren't quite satisfied with this. So they set out on their own to see what was going on. Berg, et. al. have published their result in two articles in the American Journal of Physics (referenced below). What they basically found was that the sprinkler did, indeed, rotate in the opposite direction. Their explanation for this can be found at this UMD site (which, btw, I found from Yahoo by doing a search for "+feynman +inverse +sprinkler"). Briefly, they propose that conservation of momentum requires that the angular momentum of the sprinkler head be approximately equal and opposite to that of the fluid in the sprinkler arms. Berg goes into this in quite some detail in his 2nd paper on the topic.

So how to reconcile this with the Feynman and MIT experiments? Berg suggests that for the air experiment, various effects from turbulence might have led to null results and that the other water experiments suffered from frictional effects that led to the null results. To my mind, the apparatus (e.g., the Berg sprinklers are circular whereas the MIT one was essentially a curved tube) involved must also play some small role although I haven't the inclination of Feynman and the others to test this by flooding my basement.

I don't know how much this answer does to settle the controversy for you but I hope it does point you in the right direction. I know that there are a couple of earlier papers also published in the AJP about this problem but I think the Berg papers, especially the latest one, supercede the others (although I haven't read those others). I have the Berg paper from 1991 lying around and if you'd like to reference it, please drop me a line and I'd be more than happy to email/fax it to you. Also, please feel free to drop me a line at science@zentropy.com if you have any more questions (or corrections! :).

Best regards,

Rick.

References:

• Am. J. Phys., Vol. 59, No. 4, April 1991 Pages 349 - 355
  The Feynman inverse sprinkler problem: A detailed kinematic study
  Michael R. Collier
  Richard E. Berg
  Richard A. Ferrell
  Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
  (Received 21 February 1990; accepted for publication 21 June 1990)
  
• Am. J. Phys., Vol. 57, No. 7, July 1989 Pages 654 - 657
  The Feynman inverse sprinkler problem: A demonstration and quantitative analysis
  Richard E. Berg
  Michael R. Collier
  Lecture-Demonstration Facility, Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
  (Received 1 June 1988; accepted for publication 29 August 1988)
  
• Am. J. Phys., Vol. 56, No. 4, April 1988 Pages 307 - 308
  Inverse sprinklers: Two simple experiments and the resolution of the Feynman-Forrester conflict
  Leonardo Hsu
  Dartmouth High School, North Dartmouth, Massachusetts 02747
  (Received 6 January 1987; accepted for publication 14 August 1987)
  

Quick Disclaimer: Most of this stuff is purely from memory; I remember the Gleick book but it's been several years since I read it. I also know I have the Berg paper here somewhere but I can't be sure exactly which pile it's in. Therefore, although I lack the imagination to make this stuff up, I might not have the timeline and other such details exactly right. Rest assured, however, I did manage to get the correct references (above) from the American Institute of Physics by doing a search for the Feynman Inverse Sprinkler.