Faucet Physics Question

[Bork]

Why does a stream of water coming out of a faucet narrow as it falls?

Are there any equations which model the diameter of the stream as a function of the distance below the faucet?
The initial speed of the water and the diameter of the faucet are given constants.

[Voltron87]

Nice first post.

I think I understand what you're saying, but I doubt there is an equation for that as there are way too many variables.

[bholdr]

simple answer: the stream narrows because of the combination of acceleration of the falling water and surface tension holding the stream together.

complicated answer: how the hell should i know? i'm sure there is an equation, but i'm just as sure i wouldn't understand it.

daryn may know, wacki could find it...

[daryn]

hmm i did take fluid mechanics. i know we talked about this too. i think it has to do with conservation of mass laws.

picture it like this, the water falls faster near the bottom of the stream than near the top. the same amount of mass has to pass through certain areas of the stream in the same amount of time, so it has to narrow as it goes faster.

[MelchyBeau]

water is attracted to itself. amazing I know. water is also attracted to edges. so there is going to be water falling from the edge of the faucet. but as it falls, it becomes attracted to the other water, thus it meets.

Melch (wacki isn't the only scientist on these forums)

[edtost]

so velocity is proportional to cross-sectional area?

[wacki]

[ QUOTE ]
(wacki isn't the only scientist on these forums)


[/ QUOTE ]

Cool, what specialty are you in?

[Sweaburg]

Inversley proportional...in a pipe at least.

[Patrick del Poker Grande]

[ QUOTE ]
the same amount of mass has to pass through certain areas of the stream in the same amount of time

[/ QUOTE ]
It's been quite a while since fluid mechanics for me, but I really doubt this. Why do you have to have conservation of mass through any particular area of the stream? There's nothing about this system that requires this.

[Patrick del Poker Grande]

[ QUOTE ]
Inversley proportional...in a pipe at least.

[/ QUOTE ]
For the same mass flow rate and running at or near capacity, yes, but not in general.

[Patrick del Poker Grande]

[ QUOTE ]
water is attracted to itself. amazing I know. water is also attracted to edges. so there is going to be water falling from the edge of the faucet. but as it falls, it becomes attracted to the other water, thus it meets.

Melch (wacki isn't the only scientist on these forums)

[/ QUOTE ]
I'm going to go with this one as being closest to the actual answer.

[ThaSaltCracka]

http://img.photobucket.com/albums/v474/ThaSaltCracka/FarSide_Mar15x.jpg

[BeerMoney]

[ QUOTE ]
[ QUOTE ]
water is attracted to itself. amazing I know. water is also attracted to edges. so there is going to be water falling from the edge of the faucet. but as it falls, it becomes attracted to the other water, thus it meets.



Melch (wacki isn't the only scientist on these forums)

[/ QUOTE ]
I'm going to go with this one as being closest to the actual answer.

[/ QUOTE ]

I would agree with this too.. Also note that when water comes out of the faucet it passes through an aerator.. This is what i think makes it wider at the top to begin with. Notice that if you saw water coming out of an open pipe or a hose, i don't think this same phenomenon occurs.

[daryn]

</font><blockquote><font class="small">In risposta di:</font><hr />
Inversley proportional...in a pipe at least.

[/ QUOTE ]

yes, i believe this is correct for our faucet stream too. it's just like a pipe with no walls.

[Sweaburg]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
water is attracted to itself. amazing I know. water is also attracted to edges. so there is going to be water falling from the edge of the faucet. but as it falls, it becomes attracted to the other water, thus it meets.



Melch (wacki isn't the only scientist on these forums)

[/ QUOTE ]
I'm going to go with this one as being closest to the actual answer.

[/ QUOTE ]

I would agree with this too.. Also note that when water comes out of the faucet it passes through an aerator.. This is what i think makes it wider at the top to begin with. Notice that if you saw water coming out of an open pipe or a hose, i don't think this same phenomenon occurs.

[/ QUOTE ]

That aerator idea sounded good but I just took the aerator off my faucet and saw the same effect.(I know I know, turn down the nerd but this is more interesting than the research I am doing)

Also if the water is attracted (ie wants to stick) to the edges of the tap wouldn't that mean less water flowing from the edges?

Does it have anything to do with the velocity profile across the stream? The water in the middle of the faucet is travelling faster if I remember correctly.

[Redeye]

[ QUOTE ]
hmm i did take fluid mechanics. i know we talked about this too. i think it has to do with conservation of mass laws.

picture it like this, the water falls faster near the bottom of the stream than near the top. the same amount of mass has to pass through certain areas of the stream in the same amount of time, so it has to narrow as it goes faster.

[/ QUOTE ]

Assuming the fluid flow is laminar this is correct.

[daryn]

</font><blockquote><font class="small">In risposta di:</font><hr />
</font><blockquote><font class="small">In risposta di:</font><hr />
hmm i did take fluid mechanics. i know we talked about this too. i think it has to do with conservation of mass laws.

picture it like this, the water falls faster near the bottom of the stream than near the top. the same amount of mass has to pass through certain areas of the stream in the same amount of time, so it has to narrow as it goes faster.

[/ QUOTE ]

Assuming the fluid flow is laminar this is correct.

[/ QUOTE ]

yes, that's it. laminar flow baby.

[Patrick del Poker Grande]

It's not laminar if it's going through an aerator.

[daryn]

</font><blockquote><font class="small">In risposta di:</font><hr />
It's not laminar if it's going through an aerator.

[/ QUOTE ]

i thought the guy said he took it off.

[Patrick del Poker Grande]

[ QUOTE ]
[ QUOTE ]
It's not laminar if it's going through an aerator.

[/ QUOTE ]

i thought the guy said he took it off.

[/ QUOTE ]
Well to be honest, I'm not sure if we're talking about it with it on or off any more now, but I believe the narrowing effect of the stream was essentially the same with or without the aerator. I don't think the effect we're looking for here has anything to do with it being laminar.

I think it's all in water's tendency to attract to itself. I don't have the fluid dynamics knowledge anymore to say anything real intelligent about it other than I think this is roughly where the answer is.

[TimM]

[ QUOTE ]
Why do you have to have conservation of mass through any particular area of the stream? There's nothing about this system that requires this.

[/ QUOTE ]

Once you reach a steady laminar flow, the rate at which the water comes out of the faucet must match the rate at which it goes down the drain. You can say the same thing about the rate of water passing through any horizontal plane intercepting the stream.

[daryn]

</font><blockquote><font class="small">In risposta di:</font><hr />
</font><blockquote><font class="small">In risposta di:</font><hr />
Why do you have to have conservation of mass through any particular area of the stream? There's nothing about this system that requires this.

[/ QUOTE ]

Once you reach a steady laminar flow, the rate at which the water comes out of the faucet must match the rate at which it goes down the drain. You can say the same thing about the rate of water passing through any horizontal plane intercepting the stream.

[/ QUOTE ]

in other words i am correct right? it IS conservation of mass.

[slickpoppa]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Why do you have to have conservation of mass through any particular area of the stream? There's nothing about this system that requires this.

[/ QUOTE ]

Once you reach a steady laminar flow, the rate at which the water comes out of the faucet must match the rate at which it goes down the drain. You can say the same thing about the rate of water passing through any horizontal plane intercepting the stream.

[/ QUOTE ]

in other words i am correct right? it IS conservation of mass.

[/ QUOTE ]

I dont think it can be completely explained by conservation of mass. It must have something to do with the cohesive properties of water. Think about it, if it were just a conservation of mass thing, wouldn't sand have the same property of bunching together? I haven't done any lab experiments about sand coming out of a faucet, but I am pretty sure that a stream of sand does not get narrower.

Also think about it from a conservation of momentum standpoint. Picture a molecule of water that leaves the faucet from the edge of the faucet. If the stream gets narrower, that means that the molecule must have experienced an inward force. So at the very least the cohesive property of water must have something to do with it.

[Redeye]

[ QUOTE ]
Well to be honest, I'm not sure if we're talking about it with it on or off any more now, but I believe the narrowing effect of the stream was essentially the same with or without the aerator. I don't think the effect we're looking for here has anything to do with it being laminar.

I think it's all in water's tendency to attract to itself. I don't have the fluid dynamics knowledge anymore to say anything real intelligent about it other than I think this is roughly where the answer is.

[/ QUOTE ]

It won't matter if its on or off, you'll observe the effect both ways. The fluid flow is really more laminar than turbulent with or without the aerator on. As Daryn said before, its all basically about the conservation of mass through a given cross-sectional area. As long as there is no significant turbulence, the amount of fluid that passes through a given cross-seciton of the stream remains constnat. As the velocity of the fluid flow increases, the amount of water entering and exiting a cross-section must be the same therefore the diameter of the cross-section must decrease. As the fluid flow reaches terminal velocity, the diameter will eventually stop decreasing.

[daryn]

well i'm sure it has to do with cohesion, clearly, but is what we're talking about in the first place, laminar flow. i just remember the prof. telling us basically what tim said. the same amount of water (mass) has to be going down the drain as there is coming out the faucet. he called it an application of conservation of mass.

so since it's going faster at the bottom, you can't have too much mass exiting, therefore the stream narrows.

[MelchyBeau]

only in OOTia can you go from one thread about a shitty ass poem to another thread about whiskey to another about fluid dynamics.

p.s. I'm right, it has to do with the attraction of water molecules to each other.

Melch

[stinkypete]

[ QUOTE ]

in other words i am correct right? it IS conservation of mass.

[/ QUOTE ]

yeah, you're correct, and i'm surprised people on this forum aren't smart enough to understand the concept.

the amount of liquid/time falling through any part of the stream is constant. the water close to the floor/sink is falling faster than the water at the top of the tap. for the same amount of water to fall through some horizontal plane at the bottom, the cross section has to be smaller since the velocity is faster.

if the cross section stayed the same and the water still accelerated, you'd have water being created out of nowhere... so in that sense, referring to conservation of mass makes sense.

[TimM]

[ QUOTE ]
in other words i am correct right? it IS conservation of mass.

[/ QUOTE ]

Seems pretty obvious. This plus the fact that gravity is accelerating the water, plus the cohesion, makes the stream narrow.

With sand, say going through a tall hourglass, you probably get some spreading of the stream due to collisions and air resistance. but you also get a less dense stream as you get further down, for the same conservation of mass reasons. Consider just two grains falling one just after the other. Over time the distance between them must increase, as the first grain has always been accelerating just a little longer than the second grain.

[slickpoppa]

[ QUOTE ]
well i'm sure it has to do with cohesion, clearly, but is what we're talking about in the first place, laminar flow. i just remember the prof. telling us basically what tim said. the same amount of water (mass) has to be going down the drain as there is coming out the faucet. he called it an application of conservation of mass.

so since it's going faster at the bottom, you can't have too much mass exiting, therefore the stream narrows.

[/ QUOTE ]

Of course it must obey conservation of mass, but the most important part of the equation is the cohesion. Theoretically, if the water molecules were not attracted to each other at all, the stream would not narrow at all. And how much the stream narrows is a function of the viscosity of the liquid, which is a function of how much the molecules are attracted to each other. So to focus on the conservation of mass aspect of the equation is not particularly helpful.

[stinkypete]

[ QUOTE ]

p.s. I'm right, it has to do with the attraction of water molecules to each other.

[/ QUOTE ]

sorry buddy, you're not. what he described will happen even if the water molecules are packed as closely as possible at the top.

[wacki]

You guys are making this way more complicated then it needs to be.

[stinkypete]

[ QUOTE ]

And how much the stream narrows is a function of the viscosity of the liquid,

[/ QUOTE ]

no it isn't... not to any significant degree

[ QUOTE ]

So to focus on the conservation of mass aspect of the equation is not particularly helpful.

[/ QUOTE ]

sure it is, if you think of it in the right way. call it conservation of mass, conservation of matter, or whatever. the change in velocity is what is important.

[wacki]

All of your answers can be found here:

http://ist-socrates.berkeley.edu/~phyh7a/

Homework #10.

[slickpoppa]

[ QUOTE ]
[ QUOTE ]

And how much the stream narrows is a function of the viscosity of the liquid,

[/ QUOTE ]

no it isn't... not to any significant degree

[ QUOTE ]

So to focus on the conservation of mass aspect of the equation is not particularly helpful.

[/ QUOTE ]

sure it is, if you think of it in the right way. call it conservation of mass, conservation of matter, or whatever. the change in velocity is what is important.

[/ QUOTE ]

We might be talking about two ways of explaining the same thing. Nevertheless, I am not convinced of your explanation. Answer this question: If there were a liquid which had absolutely no attraction to istelf, what force would cause a molecule of that liquid which starts on the edge of the faucet to move inwards?

[Redeye]

[ QUOTE ]
Of course it must obey conservation of mass, but the most important part of the equation is the cohesion. Theoretically, if the water molecules were not attracted to each other at all, the stream would not narrow at all. And how much the stream narrows is a function of the viscosity of the liquid, which is a function of how much the molecules are attracted to each other. So to focus on the conservation of mass aspect of the equation is not particularly helpful.

[/ QUOTE ]

A stream of something non-polar like methanol would behave the exact same way as water, the cohesiveness of water is not why the stream becomes narrow. The narrowing of the water is basically Bernoulli's principle. I believe what is happening is that as the fluid velocity increases the pressure of the stream decreases and therefore the force exerted on the stream by air pressure increases narrowing the stream.

[slickpoppa]

[ QUOTE ]
The narrowing of the water is basically Bernoulli's principle. I believe what is happening is that as the fluid velocity increases the pressure of the stream decreases and therefore the force exerted on the stream by air pressure increases narrowing the stream.

[/ QUOTE ]

That is what I am looking for. So if this happened in a vaccuum, the stream would not narrow?

[Redeye]

[ QUOTE ]
That is what I am looking for. So if this happened in a vaccuum, the stream would not narrow?

[/ QUOTE ]

Crap...good question, I'll have to think about this for awhile.

[styleish]

the pressure terms in bernoulli's equation cancel so it doesn't matter if it's in a vacuum or not. bernoulli's equation just shows that the velocity increases as the water moves down. then mass conservation shows that because the water is moving faster the diameter must decrease.

[InchoateHand]

straight.

[The Goober]

This has essentially already been said, but I'll take a shot at explaining this...

Everyone agrees that for a steady stream of water or sand or anything else, the mass / unit time passing through any plane of the stream (the flux) has to be equal - this is the conservation of mass part, and is essential. The flux for any cross-section of the stream is equal to Area x Velocity x Density. Since the velocity increases further down the stream, the area and/or the density must decrease to compensate. Since the stream is a unbroken column of water, the density cannot decrease (because its a liquid) and so the cross-sectional area must decrease. In the sand case, the individual grains of sand act sort of like a gas, so the density of sand grains will go down and the stream will not narrow.

So the part about water molecules being attracted to each other is just saying that the bonds are strong enough to make it a liquid, not a gas.

[MrOnizuka]

Just wanted to say that 7A at Berkeley sucks.

Between that class and CS61A I'm thinking of switching to something useless like geography.

bleh, thanks for reminding me I didnt do any homework this weekend. /images/graemlins/smirk.gif

[Piz0wn0reD!!!!!!]

[ QUOTE ]
hmm i did take fluid mechanics. i know we talked about this too. i think it has to do with conservation of mass laws.

picture it like this, the water falls faster near the bottom of the stream than near the top. the same amount of mass has to pass through certain areas of the stream in the same amount of time, so it has to narrow as it goes faster.

[/ QUOTE ]

if you poured balls out of a big tube, the stream of balls would not narrow as it picked up speed. Its because the water is attracted to itself.

[styleish]

balls are not fluid.

[Lazymeatball]

[ QUOTE ]
balls are not fluid.

[/ QUOTE ]
and that is the reason why they were a useful example.

[Matt Flynn]

Did someone give the equation? Assuming no air enters the water after leaving the faucet (which is close enough), it is velocity x area through which water flows. In other words, mass is conserved.

v1 x A1 = v2 x A2.

A = pi x (r x r) so drop out pi:

v1 x r1 x r1 = v2 x r2 x r2 (can't get it to read r sqaured correctly)

Or: v2/v1 = r1 x r1 / r2 x r2

Chapter 1 in any intro physics book. Can't believe one of the MIT boys didn't get here first.

Matt

[theBruiser500]

Matt Flynn RULEZ!!

[TimM]

This does not tell us anything about the diameter from the stream at a given distance from the faucet.

http://ist-socrates.berkeley.edu/~phyh7a/hw10.pdf

Top of page 7.

But I'm not sure this is correct. Shouldn't the viscosity resist the acceleration due to gravity somewhat? Maybe this is negligible for water.

http://xtronics.com/reference/viscosity.htm

[daryn]

</font><blockquote><font class="small">In risposta di:</font><hr />
the pressure terms in bernoulli's equation cancel so it doesn't matter if it's in a vacuum or not. bernoulli's equation just shows that the velocity increases as the water moves down. then mass conservation shows that because the water is moving faster the diameter must decrease.

[/ QUOTE ]

</font><blockquote><font class="small">In risposta di:</font><hr />
Everyone agrees that for a steady stream of water or sand or anything else, the mass / unit time passing through any plane of the stream (the flux) has to be equal - this is the conservation of mass part, and is essential. The flux for any cross-section of the stream is equal to Area x Velocity x Density. Since the velocity increases further down the stream, the area and/or the density must decrease to compensate. Since the stream is a unbroken column of water, the density cannot decrease (because its a liquid) and so the cross-sectional area must decrease. In the sand case, the individual grains of sand act sort of like a gas, so the density of sand grains will go down and the stream will not narrow.

So the part about water molecules being attracted to each other is just saying that the bonds are strong enough to make it a liquid, not a gas.


[/ QUOTE ]

i just want to take this opportunity to say damn i'm good. patrick, don't let your employer see this!

[Philuva]

[ QUOTE ]
This does not tell us anything about the diameter from the stream at a given distance from the faucet.


[/ QUOTE ]

Matt's equation tells us that since the water must be moving faster further away from the faucet because of gravity (v2 &gt; v1) then in order for the ration to work r1&gt; r2.

[The Goober]

So after posting this, I looked at an actual smooth stream of water from my faucet and noticed something - at the very bottom of the stream, the stream stopped narowing, and instead it broke up and started mixing with air. Clearly, there is some point (before reaching terminal velocity) where the surface tension is not enough to keep the stream as a solid column of water and instead the density does go down as the water breaks into smaller droplets. So, the viscosity / surface tension does play a pretty big part here. I imagine that if one poured out a nice big stream of syrup from a very high distance, you would see the stream get pretty damn narrow before it starts to break up (and it may not break up at all if its still a stream when it reaches terminal velocity). I think this is the only reason that it would change things if you did this in a vacuum - without air, there is no terminal velocity and even the most viscous liquid stream would eventually break up into smaller droplets.

[Matt Flynn]

oh bother.

a = acceleration of 1G

yes viscosity affects a but it is negligible. if you want to get that accurate you should just measure it empirically or get somebody who took physics to help you.

so v2 = v1 + (a x t)

...conveniently allowing you to adjust a for gravities on other worlds.

(v1 + (at)) / v1 = (r1 squared)/(r2 squared)

r2 squared = (r1^2) x v1 / (v1 +at)

So diameter at time t =

2r1 x the square root of ( v1 / (v1 + at) )


hope that's what you were looking for. on to superatoms...

matt

[daryn]

yes, once it ceases to be laminar flow, all bets are off so to speak.

[Patrick del Poker Grande]

[ QUOTE ]
[ QUOTE ]
the pressure terms in bernoulli's equation cancel so it doesn't matter if it's in a vacuum or not. bernoulli's equation just shows that the velocity increases as the water moves down. then mass conservation shows that because the water is moving faster the diameter must decrease.

[/ QUOTE ]

[ QUOTE ]
Everyone agrees that for a steady stream of water or sand or anything else, the mass / unit time passing through any plane of the stream (the flux) has to be equal - this is the conservation of mass part, and is essential. The flux for any cross-section of the stream is equal to Area x Velocity x Density. Since the velocity increases further down the stream, the area and/or the density must decrease to compensate. Since the stream is a unbroken column of water, the density cannot decrease (because its a liquid) and so the cross-sectional area must decrease. In the sand case, the individual grains of sand act sort of like a gas, so the density of sand grains will go down and the stream will not narrow.

So the part about water molecules being attracted to each other is just saying that the bonds are strong enough to make it a liquid, not a gas.


[/ QUOTE ]

i just want to take this opportunity to say damn i'm good. patrick, don't let your employer see this!

[/ QUOTE ]
Well I'm glad this makes you feel good about yourself having apparently stuck it to me or something. I'm not worried about my job over a silly fluid dynamics question, as I'm sure they're more concerned with my structural analysis on things like weapon systems, satellites, and my analysis on the space shuttle starting next week.

Not only that, but I'm still not going along with the mass-conservation as the reason the stream narrows. Yes, you may have mass conservation, but it's not the reason it happens. First, there's nothing saying that the water/air mixture must keep the same density. There's nothing saying that air doesn't enter or exit the stream. In fact, my position is that it does exit the stream and that's what allows it to narrow. You could probably say that if you make it a closed system inside some set cylinder of diameter greater than or equal to the original faucet diameter. Then you could say that at each cross-section of this cylinder, the air has just moved towards the outside of the cylinder and then you have the same average density or flux through any given section. Fine, that matches conservation of mass. That doesn't explain why the air moves to the ouside of the column or the water moves towards the inside. The water could keep increasing speed and have less composite density through any given section and the stream would still have the same outer diameter and it'd still be within the constraints of mass conservation.

In short, mass conservation is most likely preserved, but it's not the cause of the phenomenon we're looking at here. There's nothing about mass conservation that says the water stream has to narrow instead of spraying out wider. The cause we're looking for is the effect of the air leaving the stream, thus narrowing it, instead of entering it and diffusing it into a spray.

I'm sorry this all wasn't very well worded, but I'm a bit busy writing reports and proposals for work right now, so I can't exactly give it a ton of attention.

[Patrick del Poker Grande]

I guess the problem is that most people here are already just assuming that the water attracts to itself, thus it's easy to just apply conservation of mass and then say that the diameter of the stream is getting smaller because the velocity is increasing. You never say why it must be getting smaller instead of the water just being more diffuse. I'm saying that the hydrophilic effect you've already assumed... is the answer, or at least the beginning of it, that you've jumped past half the answer and applied it to get the other half. In the end, it's this effect in combination with conservation of mass that leads to the narrowing stream phenomenon. The disagreement here all stems from differing assumptions. I didn't assume as much as others did here.

[daryn]

i hear what you are saying, but some things just aren't necessary to answer a question. for instance, if i ask you what is 2+2, do you answer 4, or do you start in with elementary number theory, to define the terms first?

[Patrick del Poker Grande]

Yeah, that's fine, but the problem here is that you can't necessarily assume these things. It's not 2+2. In fact, there was a post some time earlier where one guy observed the stream breaking up again after a longer fall. Your assumption doesn't allow for this, yet it does happen and mass is still being conserved. There definitely is a significant other part to this phenomenon that you're skipping completely over. There are two parts to the solution here - one is mass conservation, but the other is whatever is making the water attract to itself. You just assumed the latter of these two when I don't think it can just be assumed. It clearly cannot, as it falls apart when the stream reaches higher speeds. The question that needs to be answered is what makes the water attract itself? Is it just something about surface tension and water's natural affinity toward itself? Is it aerodynamics? This is the interesting part of the question if you ask me. The equations that were listed before are the part that I thought was elementary and didn't need to be talked about.

[wacki]

[ QUOTE ]
The question that needs to be answered is what makes the water attract itself? Is it just something about surface tension and water's natural affinity toward itself? Is it aerodynamics? This is the interesting part of the question if you ask me.

[/ QUOTE ]

It's called hydrogen bonds which can get to about 10% of the the strength of covalent bonds. I must say that Patrick is the first person to view this problem in the proper manner IMO.

[mostsmooth]

[ QUOTE ]
Why does a stream of water coming out of a faucet narrow as it falls?

Are there any equations which model the diameter of the stream as a function of the distance below the faucet?
The initial speed of the water and the diameter of the faucet are given constants.

[/ QUOTE ]
i know not much about physics, but im gonna take a stab at this before i read any replies.
the water coming out of the faucet is spread out at the tap by the screen or whatever. as it falls it contracts to form the smallest package. i imagine the air pressure is what forces the water together. (possibly something to do with surface tension as well??)
i wonder how close i am?

[mostsmooth]

[ QUOTE ]
[ QUOTE ]

p.s. I'm right, it has to do with the attraction of water molecules to each other.

[/ QUOTE ]

sorry buddy, you're not. what he described will happen even if the water molecules are packed as closely as possible at the top.

[/ QUOTE ]
not if there was no attraction to each other though, no?
if the attraction wasnt there, the water would fall like the previously mentioned sand, straight down and no diameter tightening, correct?

[styleish]

for this faucet problem, by using bernoulli's equation we are assuming that the viscosity is 0. the viscosity, i believe, along with surface phenomena are what cause the instabilities in the flow at higher speeds among other things. however, for the flow prior to this i believe the solution posted by wacki is a good enough approximation of the actual phenomena for our purposes. i completely agree with you, however, in that we are taking an extremely elementary look at this problem. but doesn't every solution to a physical problem include certain simplifying assumptions?

[Patrick del Poker Grande]

[ QUOTE ]
doesn't every solution to a physical problem include certain simplifying assumptions?

[/ QUOTE ]
Yes, but you can't assume the very answer to the problem, which is what I contend many here did.

[mostsmooth]

ok more from me the idiot
after reading the posts, i think i may have been pretty close.
i didnt think of the velocity stuff.
but it reminds me of concept of getting sucked toward the center of a black hole ( feet first, is there any other way?). youre feet would start stretching (getting thinner in the process) and then your legs and so on, just like the water stream gets thinner as it gets faster. eventually after a long enough fall (increase in speed), the water will overcome its attraction to itself and break off into droplets. without the waters attraction to itself, i dont think we see this phenomenon(the stream getting thinner as it falls, it would just break apart right away rather than thinning), no?
i obviously have no formal physics training(though i love thinking about this crap), but i think what im saying is accurate? can somebody give me an amen?
/images/graemlins/cool.gif

[wacki]

I find it very ironic that a man that typed this:

i know not much about physics

had one of the better posts in this thread.

[felson]

[ QUOTE ]
Can't believe one of the MIT boys didn't get here first.

[/ QUOTE ]

Sorry I'm late to the party. I was out shopping for pocket protectors.

[felson]

When I read the first post, my instant answer was the same as Daryn's: conservation of mass.

Water streams are not continuous tubes of water all the way down (sorry if this is obvious). As the water accelerates downward, the stream breaks apart into separate balls. Matt asked for an MIT opinion, so here's the work of an MIT professor in which you can see this begin to happen.

http://web.mit.edu/museum/exhibits/flashes3.html

I didn't study fluids, so I'm not going to embarrass myself by speculating further.

EDIT: Here is a better picture of what I meant, something I have seen in person. When the strobe lights are off, the streams look normal (because they are normal). When on, you see their composition.

http://web.mit.edu/Edgerton/www/WaterPiddler.html

[Matt Flynn]

no worries. you are right on time. i took it to the point of assumption failure when the stream breaks apart. you get to write the equations for the splatter.

matt

[Ray Zee]

to add a little humor to this i asked a girl who was a plumber for the pyramids. she was a pharoahs faucet major.

i bet it is because at the start of the fall there is resistance from the faucet so the water speeds up quickly at first elongating the stream.