# The curve of the stream of water running from a faucet **URL:** \ **Category:** Factual Questions\ **Created:** [May 30, 2013, 10:07pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749 "2013-05-30T22:07:18Z")\ **Posts on this page:** 15\ **Page:** 1
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [May 30, 2013, 10:07pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/1 "2013-05-30T22:07:18Z")
In his memoir, Feynman described figuring out the equation that described the curve of water flowing from a tap with the valve slightly open. How would you check something like that? That curve looks like a lot of functions. Thanks, Rob ---
**Author:** ![standingwave](https://avatars.discourse-cdn.com/v4/letter/s/9de0a6/32.png) [@standingwave](https://boards.straightdope.com/u/standingwave)\ **Post date:** [May 30, 2013, 10:30pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/2 "2013-05-30T22:30:25Z")
> [@sweeteviljesus](#): > > In his memoir, Feynman described figuring out the equation that described the curve of water flowing from a tap with the valve slightly open. How would you check something like that? That curve looks like a lot of functions. Obviously there are a lot of variables involved but I did find this: > **[Faucets](https://blog.plover.com/physics/faucet.html)** > > From the highly eclectic blog of Mark Dominus ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [May 30, 2013, 10:34pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/3 "2013-05-30T22:34:42Z")
If the water is flowing straight down as it comes out of the faucet it will continue straight down. Suppose when it exits the faucet it has a horizontal component of h and a vertical component directed downward of v to its velocity. It will in the absence of air resistance keep the same horizontal component so its displacement from (0,0) at the faucet exit at time 0 will be x = ht horizontally and y = vt + 0.5gt[sup]2[/sup]. So the equation of the curve is y = (v/h)x + 0.5gh[sup]-2[/sup]x[sup]2[/sup]. This is a parabola. From your description I suspect that Feynman was not yet a practicing physicist when he figured this out since it would be hardly noteworthy if her were so I’d guess this is what Feynman determined using high-school physics. If he took air resistance into account, then he probably had more physics at this time. I seem to recall the restraining force of friction due to air resistance is proportional to the velocity squared, but am not sure. In any case, you’d use that force and F = ma to alter the acceleration. Note this does not require knowing the mass m because both directional component accelerations will be proportional to m so it will not affect the curve’s shape. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 30, 2013, 10:51pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/4 "2013-05-30T22:51:40Z")
I’d imagine that the working assumption was that the water was maintaining a continuous stream rather than breaking up. Since the amount of water per time is the same at any cross-section of the stream, and the water further down is moving faster due to the acceleration of gravity, the cross-sectional area must be smaller further down. ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [May 31, 2013, 12:18pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/5 "2013-05-31T12:18:14Z")
What I don’t understand is how to confirm that the observed behavior matches the theory. Thanks, Rob ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [May 31, 2013, 4:20pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/6 "2013-05-31T16:20:16Z")
> [@sweeteviljesus](#): > > What I don’t understand is how to confirm that the observed behavior matches the theory. Take a picture and check the shape? Maybe you are asking something different… ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [May 31, 2013, 7:29pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/7 "2013-05-31T19:29:35Z")
Yeah, but you’d need a really tall column of water to start to see errors, wouldn’t you? Thanks, Rob ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [May 31, 2013, 8:20pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/8 "2013-05-31T20:20:34Z")
> [@Pasta](#): > > Take a picture and check the shape? Maybe you are asking something different… Yeah, that seems pretty easy. hang a sheet of graph paper behind the water stream, and put the camera far away (with a zoom lens) to minimize [parallax error](http://en.wikipedia.org/wiki/Parallax_error#Parallax_error_in_measurement_instruments), and then you can measure the width of the water stream at various heights by seeing how its boundaries line up with the graph paper. The relationship starts to fall apart when the speed of the water gets high enough for aerodynamics to start affecting things, or when the water has been falling for enough time to allow tiny imperfections to result in droplet formation due to surface tension, but if you’ve ever watched a real faucet trickling out water, you know that smooth, continuous flow can survive for several inches below the faucet outlet. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [May 31, 2013, 8:33pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/9 "2013-05-31T20:33:07Z")
> [@sweeteviljesus](#): > > Yeah, but you’d need a really tall column of water to start to see errors, wouldn’t you? Depends how well you want to test it, as is the case for all scientific questions. However, I would suspect that the approximations taken in any simple derivation would start breaking down fairly visibly in a household faucet. ---
**Author:** ![tracer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tracer/32/20578_2.png) [@tracer](https://boards.straightdope.com/u/tracer)\ **Post date:** [May 31, 2013, 8:44pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/10 "2013-05-31T20:44:12Z")
Fun fact: If you run a comb through your hair (so that it picks up a substantial static electric charge), and then bring the comb close to a very very narrow stream of falling water from a faucet, the stream will be deflected away from the comb. Funner fact: This effect inspired Wilhelm Reich to build his [cloudbuster](http://www.rogermwilcox.com/Reich/cloudbusters.html). (Reich’s claim for how the cloudbuster worked: It drew deadly orgone radiation out of the atmosphere. The actual way a cloudbuster works: If you wait long enough, clouds will form and disperse on their own.) ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [May 31, 2013, 9:19pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/11 "2013-05-31T21:19:39Z")
> [@tracer](#): > > Fun fact: If you run a comb through your hair (so that it picks up a substantial static electric charge), and then bring the comb close to a very very narrow stream of falling water from a faucet, the stream will be deflected away from the comb. That should be deflected _towards_ the comb. The charge on the comb will attract the opposite charge to the water, and so will attract the water. ---
**Author:** ![tracer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tracer/32/20578_2.png) [@tracer](https://boards.straightdope.com/u/tracer)\ **Post date:** [May 31, 2013, 11:16pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/12 "2013-05-31T23:16:55Z")
> [@ZenBeam](#): > > That should be deflected _towards_ the comb. The charge on the comb will attract the opposite charge to the water, and so will attract the water. D’oh! Proof positive that human memory (mine, in this case) fills in the gaps with made-up nonsense. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 1, 2013, 12:07am UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/13 "2013-06-01T00:07:42Z")
On the other hand, though, a powerful magnet will deflect the water away, since water is diamagnetic. That one’s harder to see, though, since few people have a sufficiently-powerful magnet lying around. ---
**Author:** ![Jeff\_Lichtman](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jeff_lichtman/32/1531_2.png) [@Jeff\_Lichtman](https://boards.straightdope.com/u/Jeff_Lichtman)\ **Post date:** [June 1, 2013, 6:52am UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/14 "2013-06-01T06:52:32Z")
Feynman wasn’t considering the path of the stream of water - he was considering the shape of the stream as it comes out of a faucet. [Here is a description by Feynman himself](http://blog.plover.com/physics/faucet.html) of the problem and how he solved it. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [June 1, 2013, 12:11pm UTC](https://boards.straightdope.com/t/the-curve-of-the-stream-of-water-running-from-a-faucet/659749/15 "2013-06-01T12:11:57Z")
> [@Jeff\_Lichtman](#): > > Feynman wasn’t considering the path of the stream of water - he was considering the shape of the stream as it comes out of a faucet. Here is a description by Feynman himself of the problem and how he solved it. Yes. We all know that. And your link was already given, back in Post 2.