Feynman's Sprinkler: Explaining the Paradox Without Experiment

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Discussion Overview

The discussion revolves around the Feynman's Sprinkler paradox, specifically exploring the behavior of a submerged S-shaped garden sprinkler when fluid is sucked from its center in an inviscid liquid. Participants aim to explain the phenomenon through theoretical reasoning rather than experimental evidence.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the paradox and invites others to provide theoretical explanations, emphasizing the use of thought over experiments.
  • Another participant references multiple articles from the American Journal of Physics, suggesting that the fluid dynamics involved can be understood by considering the directional nature of the fluid jets from the sprinkler.
  • A participant mentions a video demonstrating the results of sucking water through the sprinkler, but another counters that the explanation may not be straightforward, introducing the concept of centripetal force affecting the sprinkler's motion.
  • One participant proposes that in an inviscid flow, the sprinkler should rotate in the same direction as in normal operation but with reduced torque, indicating a need for further analysis to confirm this claim.
  • Concerns are raised about the use of inertial control volumes in the analysis, with a suggestion that such an approach could lead to errors in understanding the torque dynamics.
  • Another participant questions the relationship between water speed and pressure within the pipe, leading to a discussion about pressure gradients in inviscid fluids and steady-state assumptions.

Areas of Agreement / Disagreement

Participants express differing views on the mechanics of the sprinkler's behavior, with some supporting the idea of reduced torque in inviscid flow while others challenge the assumptions and introduce additional forces. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight limitations in their analyses, such as assumptions about inviscid flow and the implications of using inertial control volumes. There is also a focus on the need for careful consideration of pressure dynamics in the system.

Curl
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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.
 
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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.
 
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Hehe, I figured it out, its very simple. Thanks guys.
 
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
 
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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.
 
Curl said:
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.
 
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).
 
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.
 
  • #10
Curl said:
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.
 
  • #11
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?
 
  • #12
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.
 

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