will turn in the direction of the long arrow
when blown into and in the direction of the
short arrow when sucked on. The air, here,
on entering the cylinder can continue its r o-
tation unimpeded, and this motion is accord-
ingly compe nsated for by a rotation in the
This observation is correct and interesting: it shows
that if the incoming water did not give up all its a ngu-
lar momentum upon hitting the inner wall of the reverse
sprinkler, then the device would turn toward the incom-
ing water, as we discus sed at the be ginning of Sec. III.
In his introduction to Mach’s Mechanik, mathemati-
cian Karl Menger describes it a s “one of the great sci-
entiﬁc achievements of the [nineteenth] century,”
it seems that the passage we have quoted was not well
known to the twentieth century scientists who com-
mented publicly on the reverse sprinkler. Feynman
no answer to the problem and wrote as if he expected and
observed rotation (though, as some have pointed out, the
fact that he cranked up the pressure until the bottle ex-
ploded suggests another explanatio n: he expected rota-
tion and didn’t see it). In Refs. 14 and 15 the authors dis-
cuss the problem and claim that no rotation is observed,
but they pursue the matter no further . In Ref. 16, it is
suggested that students demons trate as an exercis e that
“the direction of rotation is the same whether the ﬂow is
supplied through the hub [of a submerged sprinkler] or
withdrawn from the hub,” a result which is discounted
by almost all the re st of the literature.
Shortly after Feynman’s memoirs appeared, A. T. For-
rester published a paper in which he concluded that if
water is sucked out of a tank by a vacuum attached to a
sprinkler then the sprinkler will not rotate.
But he also
made the bizar re claim that Feynman’s original experi-
ment at the Princeton cyclotron, in which he had high
air pres sure in the bottle push the water out, would ac-
tually cause the sprinkler to rotate in the direction of
the incoming water.
An exchange on the issue of con-
servation of a ngular momentum between A. K. Shultz
and Forr e ster appeared shortly thereafter.
lowing year L. Hsu, a high school student, published an
exp erimental analysis which found no rotation of the re-
verse sprinkler and questioned (quite sensibly) Forre ster’s
claim that pushing the water out of the bottle was not
equivalent to sucking it out.
E. R. L indgren also pub-
lished an experimental result that supported the claim
that the reverse sprinkler did not turn.
After Feynman’s death, his graduate research advi-
sor, J. A. Wheeler, published some reminiscences of
Feynman’s Princeton days from which it would appear
that Feynman observed no motion in the sprinkler be-
fore the bottle exploded (“a little tremor as the pres-
sure was ﬁrst applied . . . but as the ﬂow c ontinued there
was no rea c tion”).
In 1992 the journalist James Gle-
ick published a biography of Feynman in which he states
that both Feynman and Wheeler “were scrupulous about
never revealing the answer to the orig inal question” and
then claims that Feynman’s answer all along was that
the sprinkler would not turn.
The physical justiﬁca-
tion that Gleick o ﬀers for this answer is unenlightening
and wrong. (Gleick e choes one of Mach’s comments
that the water entering the reverse sprinkler comes in
from many dire c tions, unlike the water le aving a regular
sprinkler, which forms a narrow jet. Although this ob-
servation is correct, it is not particularly relevant to the
question at hand.)
The most detailed and pertinent work on the sub-
ject, b oth theoretical and experimental, was published by
Berg, Collier, and Fe rrell, who claimed tha t the reverse
sprinkler turns toward the incoming wa ter.
by Schultz’s arguments about conservation of angular
the authors oﬀered a somewhat convoluted
statement of the correct observation that the sprinkler
picks up a bit of angular momentum before reaching
a steady state of zero torque once the water is ﬂowing
steadily into the sprinkler. When the water stops ﬂow-
ing, the sprinkler c omes to a halt.
The air-sucking reverse sprinkler at the Edgerton Cen-
ter at MIT shows no movement at all.
As in the setups
used by Feynman and others, this sprinkler arm is no t
mounted on a true pivot, but rather turns by twisting
or bending a ﬂexible tube. Any tra ns ie nt torque will
therefore cause, at most, a brief shaking of such a device.
The University of Maryland’s Physics Lecture Demon-
stration Facility oﬀer s video evidence of a reverse sprin-
kler, mounted on a true pivot of very low friction, turning
slowly toward the incoming water.
According to R. E.
Berg, in this particular setup “while the water is ﬂow-
ing the nozzle rotates at a constant angular sp e e d. This
would be consistent with conservation of angular momen-
tum exce pt for one thing: while the water is ﬂowing into
the nozzle, if you reach and stop the nozzle rotation it
should remain still after you release it. [But, in practice,]
after [the nozzle] is released it starts to r otate again.”
This behavior is consistent with non-zero dissipation of
kinetic energy in the ﬂuid ﬂow, as we have discussed. An-
gular momentum is conserved, but only after the motion
of the tank is taken into account.
We have oﬀered an ele mentary theoretical treatment of
the behavior of a reverse sprinkler, and concluded that,
under idealized conditions, it should e xperience no torque
while ﬂuid ﬂows steadily into it, but as the ﬂow com-
mences, it will pick up an angular momentum opposite
to that of the incoming ﬂuid, which it will give up as the
ﬂow e nds. However, in the pres e nce of viscosity or turbu-
lence, the reverse sprinkler will expe rience a small torque
even in steady state, which would cause it to accelerate
toward the incoming water. T his torque is balanced by
an opposite torque acting on the surrounding ﬂuid and
ﬁnally on the tank itself.
Throughout our discussion, our foremost concern was