The continuous rotation of the reverse sprinkler has been a puzzle for over two decades. This article presents a series of experiments that demonstrate that a properly designed reverse sprinkler experiences no steady-state torque and does not rotate. Ignoring transients when the flow starts and stops, if any sustained rotation of the reverse sprinkler occurs, it is because a force couple produces a torque accompanied by vortex flow inside the body of the sprinkler. No steady-state rotation occurs if the vortex is suppressed or prevented from forming in the first place. Demonstrative proof is given that an ideal reverse sprinkler does not rotate.

1.
R. P.
Feynman
,
Surely You're Joking Mr. Feynman
(
Norton
,
NY
,
1985
), pp.
63
65
.
2.
A. T.
Forrester
, “
Inverse sprinklers: A lesson in the use of a conservation principle
,”
Am. J. Phys.
54
(
9
),
798
799
(
1986
). Forrester invoked conservation of angular momentum to show that the inverse sprinkler will never rotate but also claims that Feynman's apparatus is governed by different physics because his sprinkler was in a pressurized containment vessel.
3.
A. K.
Schultz
, “
Comment on the inverse sprinkler problem
,”
Am. J. Phys.
55
(
6
),
488
(
1987
). Shultz arrived at the opposite conclusion as Forrester using conservation principles.
4.
A. T.
Forrester
, “
Comments on a letter by A. K. Schultz
,”
Am. J. Phys.
55
(
6
),
488
489
(
1987
). Forrester claims that the rotation Schultz predicts is only a transient effect.
5.
R. E.
Berg
and
M. R.
Collier
, “
The Feynman inverse sprinkler problem: A demonstration and quantitative analysis
,”
Am. J. Phys.
57
(
7
),
654
657
(
1989
).
6.
M. R.
Collier
,
R. E.
Berg
, and
R. A.
Ferrell
, “
The Feynman inverse sprinkler problem: A detailed kinematic study
,”
Am. J. Phys.
59
(
4
),
349
355
(
1991
).
7.
A.
Jenkins
, “
An elementary treatment of the reverse sprinkler
,”
Am. J. Phys.
72
(
10
),
1276
1282
(
2004
).
8.
Argon, Helium, and the Rare Gases
, edited by
G. A.
Cook
, p
196
(
Interscience Publishers
,
NY
,
1961
), vol. I, p. 196. Although the viscosity variation with temperature is similar for different gases, argon was chosen because its overall viscosity is about 27% greater than air (or N2). By varying the temperature of the argon between 268 and 313 K, the viscosity varied between 207 and 234 micropoise.
9.
E.
Mach
,
The Science of Mechanics: A Critical and Historical Account of Its Development
, translated by
T.
McCormack
, 6th ed. (
Open Court Publishing Co.
,
LaSalle Illinois
,
1960
), p
390
. The first German edition is copyright 1883 and the first English translation Open Court edition is 1893.
10.
C.
Mungan
, “
Inverse lawn sprinkler
,”
Phys. Teach.
43
,
L1
L2
(
2005
).
11.

The rotational inertia of the 1-quart yogurt container plus copper elbows and washer (for additional ballast) was approximately 1.71 × 10−4 kg•m2. The rotational inertia of ½ liter of water with a 5-cm radius was calculated to be 6.25 × 10−4 kg•m2. The rotational inertia of the deli container air sprinkler was approximately 4.15 × 10−5 kg•m2 (including the turntable doubles this). Treating the air inside as a rotating disk, its rotational inertia is approximately 4.71 × 10−10 kg•m2.

12.
It has been suggested that the viscous dissipation by flow around the intake nozzle can produce a significant effect resulting in the steady-state torque. For example,
S.
Dasgupta
,
P.
Mitra
, and
S.
Sengupta
report a steady torque by altering the flow pattern around the intake nozzle, in “
More on inverse sprinklers
,”
Eur. J. Phys.
11
,
311
(
1990
). They altered the flow by introducing a sheet of cardboard just in front of the nozzle. Although they did not specifically say so, we assume that the cardboard is not part of the sprinkler assembly, but is being held in place by an outside force and therefore they have created a force couple. They enhanced the effect with a sleeve over the nozzle, but that too is assumed to not be part of the sprinkler assembly. We posit that a combination of the Bernoulli and Coanda effects are responsible for the attraction between the nozzle and cardboard or sleeve. We have reproduced their experiments and replicated their results. We then repeated the experiment with the sleeve attached to the nozzle to make it part of the sprinkler assembly, thereby eliminating the force couple. Even though the flow alteration around the intake nozzle was identical, there was no steady torque with this geometry.
13.
The ultimate source of vorticity in the hub has to be from the interaction of the air with the walls through viscous forces. The loss of mechanical energy in the flow is proportional to the friction loss coefficient and is given for commercial pipe fittings in handbooks. For example, for a 90° elbow, 45° elbow, and sharp-edged entrance to circular pipe, the coefficient is equal to 0.90, 0.42, and 0.50, respectively. These values are from
W. F.
Hughes
and
J. A.
Brighton
,
Schaum's Fluid Dynamics
, 2nd ed. (
McGraw-Hill
, NY,
1991
), p.
121
. The assumption here is that friction with the wall produces additional turbulence and that, in turn, has an effect on vortex formation in the hub; there is no way of determining the losses for turbulent flow by purely analytical methods and the effect on vortex formation is entirely speculative.
14.

Jenkins (Ref. 7, p. 1278) points out that having the water acquire a net angular momentum around the sprinkler pivot in the absence of an external torque seems like a violation of Newton's laws only because we are neglecting the movement of the tank itself. Likewise, we argue that since the wall is rooted to the Earth, the Earth moves to conserve angular momentum.

15.

This information is the result of an informal poll taken on the tap-l listserve. The University of Utah and the U.S. Naval Academy have the soda-can-in-water versions.

16.
M. P.
Païdoussis
and
M.
Tétreault-Friend
, “
Aspirating cantilevers and reverse sprinklers
,”
Am. J. Phys.
77
(
4
),
349
353
(
2009
).
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