Feynman's Sprinkler: Explaining the Paradox Without Experiment

[Curl]

I can't believe I couldn't find a thread about this.

I'd like to see a few ways of explaining this, using pure thought, not experiment trash.

If you don't know what I'm talking about (shameonyou) it goes like this:

Take a regular S shaped garden sprinkler (the ones that spin when you run water through them) and submerge it in an inviscid liquid. Then suck fluid from the middle. Assuming no friction anywhere, what happens to the sprinkler? Which way does it spin, or does it?

Every way I think about it, it's messed up. Let's see what you can come up with. Diagrams encouraged.

 

[Andy Resnick]

THis was covered very will in Am. J. Physics:

http://ajp.aapt.org/resource/1/ajpias/v72/i10/p1276_s1?isAuthorized=no
http://ajp.aapt.org/resource/1/ajpias/v59/i4/p349_s1?isAuthorized=no
http://ajp.aapt.org/resource/1/ajpias/v73/i3/p198_s2?isAuthorized=no
http://ajp.aapt.org/resource/1/ajpias/v56/i4/p307_s1?isAuthorized=no
http://ajp.aapt.org/resource/1/ajpias/v57/i7/p654_s1?isAuthorized=no

The most straightforward explanation I know of is recognizing that the fluid leaving the forward sprinkler is a highly directional jet, while the water sucked into a reverse sprinkler is not- the flowfield is very broad in angle to the orifice.

 

[rcgldr]

Prior threads here:

https://www.physicsforums.com/showthread.php?t=329809

https://www.physicsforums.com/showthread.php?t=303350

 

[Curl]

Hehe, I figured it out, its very simple. Thanks guys.

 

[yuiop]

A video of the actual result of sucking water backwards through the reverse sprinkler can be seen here: http://www.physics.umd.edu/lecdem/outreach/QOTW/arch4/q061.htm

 

[skeptic2]

Thank you for the video yuiop, but the explanation may not be quite so simple. It seems to me there is another force involved, that of the centripetal force of the water or air rounding the bend in the tube. In the forward direction the centripetal force adds to the reactionary force of the water leaving the nozzle but in the reverse direction it subtracts. However since centripetal force varies as mv^2/r, the v^2 factor should cause the centripetal force to eventually become dominant. What we may see as the water's velocity is increased from zero is that the sprinkler head begins to turn in the direction counter to it's direction in forward mode and as the velocity of water is increased the rotation rate increases to a maximum. As the water's velocity is further increased, the rotational velocity of the sprinkler begins to slow down, stop and reverse as the centripetal force becomes dominant.

Perhaps the reason Feynman kept increasing the pressure was in order to see this effect.

 

[JaredJames]

I'd like to see a few ways of explaining this, using pure thought, not experiment trash.

I'm curious why don't want any "experiment trash" and what makes experiments "trash"?

It's the best way to answer your question so far as what happens goes.

 

[cjl]

I just did a quick analysis using a control volume, momentum flux, and some inviscid assumptions, and much to my surprise, I get that in a purely inviscid flow, it should rotate in the same direction as it did under normal operation, but with 1/3 the torque. I'll post the analysis here later, after I've had a chance to run it by a friend of mine first to see if there are any obvious errors (I also want to check a couple of things first).

 

[Curl]

Make sure you don't use inertial control volumes or it becomes a mess and can easily make errors.

I'd like to see what you did, since you should get no torque in steady state.

 

[cjl]

Make sure you don't use inertial control volumes or it becomes a mess and can easily make errors.

I'd like to see what you did, since you should get no torque in steady state.

That's what I expected as well, which is why I want to go over it a bit more before posting it.

 

[cragar]

Can we say that when the water speeds up going into the pipe that there is a decrease in pressure and the the pressure is greater on the other side with no inlet , Or is this wrong?

 

[Curl]

If it is an inviscid fluid then there is no pressure gradient in the pipe or else the fluid will accelerate endlessly. We're assuming steady state.