An S-shaped lawn sprinkler spins one way when water is pumped out of it.

physics/feynman.sprinkler New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

An S-shaped lawn sprinkler spins one way when water is pumped out of
it.  If you put it underwater and suck water in, which way does it
turn?

There was a puzzle I remember reading in "Surely You're Joking, Mr.
Feynman!" about an S-shaped water sprinkler.  When it is turned on, it
spins counter-clockwise (assuming it looks like an S, not a backward
S).  But when you put it underwater and suck water in, which way does
it turn?  I remember Feynman giving two explanations, for two different
answers.

-- Jim Hsu <jimhsu@ATHENA.MIT.EDU>

[ Editor: the first paragraph is the editor's summary. ]

Show solution

According to Gleick, author of "Genius," the answer is that it does not
move.  The reason is that it sucks water in uniformly over all entrance
angles to the pipes, so no net momentum vector.  This differs from the
(obvious) spin imparted when pumping water out, which produces a jet of
definite vector momentum.

-- Carl Witthoft <carl@aoa.utc.com>

Mathew Hendry wrote:
> You have a rotary lawn sprinkler, looking very roughly like this from
> above:
>
>  __
>    \
>     \    hose    _    hose
>    ( )==========|_|========== <-- water in
>     \           pump
>      \__
>
>      ^
>      |
>   sprinkler
>
> In normal use, water is pumped through the hose into the centre of
> the sprinkler, and travels down the arms, spraying water out of the
> ends.  Consequently, the sprinkler rotates around a pivot at its
> centre, in a clockwise direction (again, looking from above).
>
> To form the puzzle, the sprinkler is instead placed underwater and
> water pumped through it in the opposite direction - i.e. water passes
> into the ends of the arms and up them into the centre, whence it
> travels along the hose, into the pump, and so on.
>
> The puzzle is this - in which direction will the sprinkler rotate in
> this situation? You must provide reasoning for your answer, of
> course.

In fact, the sprinkler head will not move at all.

This has been tested in real life many times.

The force of the water does not come from the pump, or the "suction"
into the hose, but from the external body of water.  The water coming
into the end of the sprinkler head comes fairly uniformly from all
directions around each of the ends of the sprinkler head, and imparts
no net momentum on the sprinkler head.

-- Stephen H. Landrum <slandrum@3do.com>

[ Editor: from Herb Weiner's web page "Marilyn's Sprinkler Answer
Incomplete" (http://www.wiskit.com/marilyn/sprinkler.html, last updated
October 20, 1996; copyright 1996 Herb Weiner), part of his "Marilyn is
Wrong" pages on the "Ask Marilyn" column by Marilyn vos Savant in
Parade Magazine. ]

Question (Parade Magazine, October 6, 1996):

If a lawn sprinkler with a rotating head were to suck water in instead
of spewing it out -- that is, if you were to put it under water and
apply suction to the other end of the hose -- in which direction would
the sprinkler head turn: in the same or the opposite direction?  And
why?

-- Joe Piskor, East Hartford, Conn.

Answer:

This very phenomenon was the subject of much discussion and argument
among nuclear physicists and quantum theorists until the American
physicist Richard Feynman (who had waffled back and forth between
educated guesses) decided to conduct an experiment and learn the
result through direct observation.  After getting everything set up
and operating (although he decided to use compressed air in a glass
bottle to force the sprinkler inside to send the water back out
through the hose), he opened the valve a little farther and then a
little farther yet, and the whole thing exploded, spraying glass and
water everywhere and making a big mess in the basement of Princeton's
new cyclotron lab, from which he was then exiled.  Supposedly, the
sprinkler didn't turn at all, and it's now accepted that, because the
water enters all the holes from all directions at the same time, it
applies no force.  Imagine how tough it's going to be for these guys to
learn whether the Big Bang theory is correct!

-- Marilyn vos Savant

Marilyn's account of Feynman's experiment is accurate, as far as I
know.  However, Feynman's work was by no means the end of the story.  A
number of people have taken a serious look at the issue, and several
papers have been published.  The most recent paper that I'm aware of
is by Collier, Berg & Ferrell, University of Maryland, and was
published in the American Journal of Physics, Vol. 59, No. 4, April
1991, pp. 349-355.  References to earlier work of theirs and others is
included therein.  Collier, et. al., concluded that the inverse
sprinkler does indeed rotate in the reverse direction.  A successful
demonstration requires careful attention to detail, especially the
elimination of friction.

I became interested in this topic last fall, when I supervised two of
our freshmen physics majors who set out to test this concept.  For
further details, see
http://www.luc.edu/depts/physics/projects.html

-- Dick Bukrey <rbukrey@luc.edu>