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Once when I was in college, a fellow physics major stormed into the
physics library all fired up about a question about a water sprinkler and
which way would it spin if you ran it backwards. Later I found that the
question was popularized in one of Feynman's books (I think it was _Surely
You're Joking_) in which Feynman makes a mess in someone's lab trying to
answer he question. At the time I remember it as a curious but not
particularly important puzzle. Now one of my students has put that puzzle
back on the front burner for me.
If you don't know the puzzle, here it is:
A popular kind of lawn sprinkler has a head which is free to rotate and
arms that are crooked in the horizontal plane. With the sprinkler
connected to a hose, water jets out the ends of the arms, and the head and
arms rotate. The tangential velocity of the arms is in the opposite
direction of the tangential velocity of the water.
Suppose, however, that the sprinkler were placed under water, say, at the
bottom of a swimming pool. Suppose further that a pump were connected to
the hose so that water was drawn into the arms instead of expelled from
them. Which way would the sprinkler rotate? Would it rotate at all? Why?
A student of mine got so interested in this question that he built an
elegant device to try it out. He figured water would make too much of a
mess so his apparatus runs on air and depends on a shopvac to blow or suck
air through it. (This student is fortunate enough to have a machine shop
in his basement and a father who showed him how to use the metal lathe --
believe me, I'm jealous!)
His device is built as follows: two copper right-angle joints are soldered
into the arms of a T connector which is braised onto the top of a heavy
brass tube. This tube fits tightly into a second brass tube. There is a
bearing separating the top (rotor) tube from the bottom (stator?) tube.
When air is blown into the lower tube it passes into the smaller tube, out
the arms, and the head rotates. The inner tube is machined to fit very
smoothly into the outer tube -- when the device is under pressure I don't
feel any breeze at all coming through the bearings.
Not a great description -- hope the following ASCII diagram helps:
(ASCII art caveat -- alignment may be off depending on your email reader)
SIDE VIEW:
air comes _ __ _
toward you -> (*)====|__ |====(X ) <-- air jets away from you
out of this tube B| |B
) | | (
) | | (
) | | (
) | | (
) | | (
___) (
to shopvac hose <-- ______ (
KEY:
) (
) ( outer tube - fixed to base
) (
| |
| | inner tube - free to rotate with head
| |
B - bearings
=======(x) horizontal arm , bends away from viewer
TOP VIEW:
__________---________| |
| ________ __________|
| | ---
Enough technicalities -- what happens?
Intuition and gardening experience are correct in predicting that if the
shopvac is set to "blow," the head pictured here rotates clockwise (viewed
from above). The tangential velocity of the tubing is the opposite
direction to the tangential velocity of the air.
My student was kind enough _not_ to tell me what happens when the
direction of the airflow is reversed. I thought about it for a while,
mostly in terms of momentum or Newton's 3rd law. From that perspective,
my conclusion was that the head would also rotate clockwise but this time
the tangential velocity of the tubing would be in the same direction as
the tangential velocity of the air. (I drew a little vector diagram of
the mutual forces between air particles and wall as they occur in the
elbow of the tubing.)
I was wrong. Set to suck, the armature rotates in the opposite direction.
Very decisively. Counter-clockwise as viewed from above in this diagram.
When air is drawn into the armature, the tangential velocity of the arm
is still opposite to the tangential velocity of the air.
When we did this in class some students said: "So what? the tubing is
just sucking itself forward in the air!" Maybe they have a point, but I
couldn't get a more rigorous explanation out of this camp. Interestingly,
all the kids who did more thoughtful analyses got wrong results.
I (and my students!) have a lot of questions, but first of all:
When I think about this from a newtons 3rd perspective I get one answer:
suck and blow both go clockwise. I'm not much on fluids, but my other
approach involved some Bernoulli-babble (which I'd be embarrassed to quote
here) and yielded: suck and blow both go counterclockwise. Each
explanation is clearly wrong!
Does anyone have a satisfactory answer? Surely I am missing something
obvious!
David Strasburger
Noble & Greenough School
Dedham MA
PS: in the wake of the tennis ball discussion, let me assure you that the
observations described herein have been recorded faithfully, carefully,
and repeatedly! If anyone is truly in doubt we can probably figure out
how to post a video clip to the web!