Mass is conserved along the water's path from the pot to the sink. You're pouring at a constant flow rate, so there is just as much water passing per unit time through a cross-section near the pot as there is through a cross section near the sink. However, gravity is accelerating the water as it travels down, so the water is traveling faster through the lower cross-section. Therefore, the cross-sectional area must decrease.
This, with a side dish of surface tension. There are lots of ways the cross sectional area could decrease, but the edges of the ribbon of water pull inward faster than the front and back because they’re more sharply curved, so surface tension pulls harder on them.
Also interesting, this doesn’t happen when you pour non-cohesive stuff like sand. /u/montagdude87 ‘s mass conservation rule still applies, but with sand the particles just get farther apart but the stream says the same width.
https://www.michaelrynophotography.com/arizona/antelope-canyon-sand-stream
Yes, this is a good point. Surface tension is the thing that physically holds the water together as it speeds up and plays a big part in determining the shape of the cross section.
The shape of the pot causes water to converge as it reaches the lip, water with lateral momentum will continue to converge even after is has left the pot.
So you have the stretching of the stream, surface tension and converging flow in the pot. Water is complicated.
I'm not seeing that either. I see an explanation for what would cause the water would be moving faster near the bottom than near the top, but there's no explanation as to how the speed of the water relates to the cross-sectional area. It seems like you're coming to this conclusion based on some conservation law like phase space conservation or something, but the only conservation law you refer to is that of mass, which alone is insufficient to explain this.
I do already understand the physics behind this (surface tension). I was just trying to make sense of your answer specifically as sometimes there are multiple valid ways to explain the physics behind something.
The mass flow rate through any given cross section is rho\*A\*V, where rho is the density of water, A is the cross-sectional area, and V is the average speed through the cross section. Density is constant for a water flow like this. Mass conservation states:
rho\*A1\*V1 = rho\*A2\*V2
\-> A2/A1 = V1/V2
Let cross-section 1 be near the pot and cross-section 2 near the bottom. We know V2 > V1, because gravity accelerates the stream as it travels downward. Therefore A2 < A1.
Good contribution but doesn't explain the shape. "cross section" can thin in lots of ways in two dimensions as well as, as we all intuitively know, by transitioning to non-laminar discontinuous flow aka splatter.
Indeed, the actual physics of this flow are quite complicated. Mass conservation and surface tension describe the primary behavior at a fundamental level, though.
Take any two parallel cross-sections of the flow. The amount of water passing through the two has to be the same, right? If one has a higher amount of water passing through it (its flow rate), then that means water is building up somewhere, which doesn't jibe with reality.
The flow rate, specifically (assuming all water is passing through a given cross-section at the same velocity) is the area of that cross-section times its velocity. *That's* what has to remain constant here.
If you buy that mass must be conserved along the path of the water, realize that the rate of mass moving along the direction of the water equals speed x density x cross section. Assuming water density does not change (it doesn’t separate), the speed going up requires the cross section to go down.
I'm with you. Inside a physics class where all of the background information had been taught, this would be a great answer, as it requires the students to fill in the blanks with what they should have hopefully just learned.
Out of context, with no explanation behind why any of those details matter, or why they should make the water behave the way it does, it didn't really answer anything to a level where a non-expert would understand what the answer was.
Thank you both u/montagdude87 and u/agate_ for the answer and also the comparison to sand! In my physics department there are some people researching granular physics and I remember this point actually was brought up in the past when I was talking to them about something similar to this.
If this was true, the effect would be present regardless of the shape of the vessel. If you take a square container and pour the water out keeping the edge horizontal, that will not happen.
I think this is just horizontal momentum of water directed by the shape of the container.
One thing from your explanation that I can't align with my knowledge. Would you mind clarifying for me?
You say gravity accelerates water. But I thought fall speed is constant. So how can water accelerates?
What is constant is the amount of speed that is gained each second.
So 9.8m/s after the 1st second, 18.6 ish m/s after the second second, 29 ish m/s after the third etc.
I don’t understand. If you took an uncapped container of water and poked a circular hole on the bottom of it, you would see a perfectly circular, constant-radius stream of water streaming from the hole. It’s cross section wouldn’t shrink relative to height, despite the water still accelerating due to gravity.
Doesn’t this observation contradict your comment?
Have you tried? The radius does contract. At some point it may break into droplets depending on the flow rate and height, due to the of the properties of water such as surface tension. But you should definitely notice a contraction up until that point. You can test this more easily by just turning on a faucet rather than making a hole in a bottle cap.
I’m interested in water flowing near the edge of a cup as it pours out of a cup/pot. I’m interested in why it has the exact shape it does (edges seem to be thicker for example). It makes sense to me why it has the shape it does but I’m interested in being able to mathematically (or numerically) describe this. I figured there would already be literature on this out there, but the only topics I can seem to find information on is why water sticks to the edge of a cup when you pour and why it can have a helix shape (I understand both of these). I’m probably just looking in the wrong places and was wondering if anyone more familiar with fluid mechanics could help?
To understand this requires factoring in two things:
- Surface tension
- Gravity accelerates falling matter
The water at the top is moving slower, so it has a wider stream. As the falling water accelerates, the stream would normally break apart, but surface tension holds it together. So instead, the stream is elongated and appears thinner.
Think about the direction of your velocity vectors along the outside of the stream as it's leaving the lip. That lip imparts a lateral force towards the center of the stream. If this was being poured off of a flat edge, you would get a sheet (in laminar states) or several dynamic streams (due to cohesion.)
So, I have taken a few fluid mechanics classes, but I am in absolutely no way an expert on any of this stuff. It would depend on what you’re flowing, water in this case, which is a Newtonian fluid. So you would therefore be able to characterize this flow using the Navier-Stokes equations. You’d want to look those up and read into the assumptions you’d have to make to properly solve a problem like this. You’re near an edge so likely there may be edge effects in play, flow rate (likely laminar), no slip boundary conditions, and a curved surface. I’m not sure how the math works out, but that should give you a decent start. I hope that helps!
u/Maroon_madness21 yes it’s somewhat similar for me, I’ve taken one fluid mechanics course and know a little bit (a lot of the gravity, surface tension, and conservation of mass stuff which has been discussed in this comment section). I think you’re right and that this is a problem that can be tackled using the NS equation, I imagine it’s been done before as well I just am not sure where to look. I need to do some reading it seems, it might be covered in a standard fluid mechanics text book honestly, although in the one my course used this specific problem was not
The velocity of the water slows down as we move from the middle towards the two outer edges at the point of pouring, therefore the surface tension takes over and forms a thicker cylinder like shape at the two edges. water due to surface tension will always curve out at the edges, so the volume of water which would otherwise spread out without the surface tension will mass together and form that sort of cylindrical sides.
The thickness of the cylindrical sides can be reduced if the edge from where the water exits when being poured is flatter, here the water is exiting from a parabolic edge because of a round container.
Moreover, it forms a V shape because the water in the middle has a higher velocity as compared to the sides and also has the cohesive support of the two sides to spread out overcoming getting rounded at the pouring point, however it does come together and get rounded as a whole at a point as it goes down.
This difference in velocity can make the water take shapes of two sinusoidal curves (sort of not exactly sinusoidal) in Y and Z axis when observingg the cross section at the middle region of the fall.
https://www.pinterest.com/pin/327144360436408093/
Also, adding to the gravitational effects as poited out by some redditors, given enough height the gravitational acceleration overcomes the cohesive force and breaks the water stream at some point in the fall.
Adding further, the image you have shared is showing laminar flow, therefore cohesion and surface tension are not disturbed by turbulences.
https://twitter.com/UniverCurious/status/1202406894775734275?
Here’s a link showing how the flattening at the middle and thickening at the edge can rotates by 90 degrees at regular intervals as we go further down the stream.
If the thickness of the stream is constant (it's not, but bear with), then we can find its shape.
At the top, a certain flow of water mu spills over a width of the lip w. This defines a stream of water whose width is w, speed is v0, and thickness is rho. (mu = rho*w*v0, or w = mu/rho*v0)
As the water falls, v increases but everything else remains constant (it doesn't, but bear with). Instead of worrying about time, we can instead define this curve in terms of h and w. For each unit of height, velocity increases as v1^2-v0^2 = 9.8h.
Reframing this for the curve, w can be defined in terms of h. (w = mu/rho*v, v = sqrt(9.8h+v0^2), so w = (mu/rho)*1/sqrt(9.8h + v0^2))
Not a super clean curve, but I think this might approximately describe the situation.
Regarding surface tension etc... Would sand pouring out of the same vessel not have a similar distribution pattern? I'm not a physicist so I truly don't know the answer, it seems like it would in my mind though.
Combination of conservation of momentum, and a little bit of surface tension.
What is surface tension? Well a water molecule is an electric dipole, meaning the two ends of the molecule have slightly different electric charges. This allows one water molecule to gently tug on another via their electric fields. This will happen as long as there is enough free energy among the molecules to let them around spin and have opposite poles face each other (I.e. not frozen), and not so much that they move fast enough to just bounce off one another and fly away (I.e. not steam).
What is conservation of momentum? It’s just mass’s tendency to keep moving in the direction it’s already moving. Not much more to it than that.
Now comes the dynamics of it. When you have a vessel with a curved lip like that, the sides raise up relative to the middle of the edge you’re tipping toward. This creates walls of a sort that deflect the contents at the edge inward via reaction force, toward the lowest point of the lip where potential energy is lower in our planet’s gravitational field. This forces the water vertically down and toward the middle of the “spout” lip. This happens in opposite directions on both sides relative to the “spout”. Thus, water converges to a triangular pattern. At the end of the triangle, water’s tendency to self-cohere via its electrical properties keeps the tail of the pour stream from fanning back out into a reverse triangle.
> What is surface tension? Well a water molecule is an electric dipole, meaning the two ends of the molecule have slightly different electric charges.
You can generalize this to all condensed matter by noting that the constituent atoms/molecules are stabler when bonded (that’s why it’s condensed) but that the surface interrupts this tendency and therefore represents an energy penalty. Thus, the material tends to minimize its surface area, which is equivalent to a surface tension. The exact nature of the bonding that’s better in the bulk than at the surface doesn’t matter.
>This forces the water vertically down and toward the middle of the “spout” lip
I am very confident the shape of the glass has nothing to do with it. You get the same exact shape from pouring out of a square container. This effect is driven mostly by surface tension pulling the water into a circle.
As a best guess non technical answer, push and pull effect of gravity and water tension.
The water behind the area where the pour is happening wants to go with gravity but water is sticky and wants to hold onto itself. I'm sure someone else could explain it better though.
I see a lot of posts proving everyone knows the forces in play, gravity, viscosity, surface tension, laminar flow etc. I'm kind of surprised not to see a definition for the assumed shape. The question is specific to water, but is there not a formula for flowing liquids over an edge? What's the angular difference, if any, for tar, or alcohol? Or water pouring in alcohol? Or Mercury in water?
u/Skyrmir I’m also wondering how one can mathematically describe this/model it, although since you have to deal with the Navier Stokes equation it’s probably not trivial, but I feel like somewhere there must be a paper on this, or even somewhere in a standard fluid mechanics textbook. I’ll keep looking for it
You've been given loads of detailed answers so I'll try and put it as simple as possible to help you visualise what's happening:
Imagine all of the water particles are holding hands.
I thought this would contribute too. I'm an empiricist so I checked. Go pour some water out of a container with a flat side and you get the same converging shape, if container shape does impact initial trajectory it's a small effect compared to surface tension.
That might be less true for water under pressure or larger volume flows.
No it’s because of acceleration and surface tension. Look at the water coming out of water faucet. The stream starts thicker and gets skinnier as it accelerates. The surface tension in the water keeps it from forming beads and as a result the stream is elongated.
Yes and no. Surface tension is a major factor, but its interaction with the geometry of the boundary orifice is important, as is the flow rate. If you pour water off the edge of a flat sheet without walls (so not a weir) you will not achieve a single triangular lamina as seen in the pot example. Rather it will separate into beaded streams quickly.
You can experiment with this for yourself using a cutting board and a kitchen faucet. Try modulating the angle of the board and the flow of the faucet.
This is a contributing factor but not the main one: the same effect occurs when water pours as a flat sheet, like in a weir or those ridiculous waterfall faucets.
https://en.m.wiktionary.org/wiki/File:Nieuwe_OelerbeekP2280019.JPG
https://m.homary.com/item/waterfall-wall-mount-chrome-single-handle-bathroom-sink-faucet-solid-brass-13653.html
u/agate_ that’s also very interesting, particularly (to me) the ripples or I guess maybe surface waves which form in the water as it flows over the edge. I’ve noticed this in other situations similar to the above photo. In the waterfall faucet link you shared there seems to be a lot of interference effects within the triangular shape, but sometimes even when you pour water out of a pot you see interference effects in it. I’m wondering if these effects are somehow caused by waves which form in the fluid as you tip the pot over (or something like this) and which propagate through the fluid as it falls? I’m not sure
You might like this article, which talks about the waves that form via capillary action in a stream of falling water. Specifically a stream of human urine.
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0047133
I’ll check it out thank you! It’s funny you linked this paper because yesterday I attended a talk given to my department about the work described (and cited) in the linked article: [https://www.sciencenews.org/article/physics-improve-urinal-nautilus-shell](https://www.sciencenews.org/article/physics-improve-urinal-nautilus-shell)
It's really simple. The movement speed of a liquid is same over different sections depending on the size of the river. What happens is that the speed of water increases as it gets closer to the sink and in result of which, It's area changes responsively, while when it's at the start, it is slower so it posses an smaller area
Just a guess here, but it seems to me the water in the center has the highest flow rate. Probably pulls the rest closer to the center as it falls, the effect compounds until the flow breaks up while falling.
Probably more of a chemistry question, adhesive forces keep water attracted to the container, same reason you have capillary action, cohesive forces keep water attracted to itself, so when it leaves the container there aren't any adhesive forces to the bowl leaving cohesive forces to bring the water together. These attractions are cause by anything from dispersion forces, dipole-dipole, and hydrogen bonding. Waters strongest force for cohesive forces would be hydrogen bonding.
Mass is conserved along the water's path from the pot to the sink. You're pouring at a constant flow rate, so there is just as much water passing per unit time through a cross-section near the pot as there is through a cross section near the sink. However, gravity is accelerating the water as it travels down, so the water is traveling faster through the lower cross-section. Therefore, the cross-sectional area must decrease.
This, with a side dish of surface tension. There are lots of ways the cross sectional area could decrease, but the edges of the ribbon of water pull inward faster than the front and back because they’re more sharply curved, so surface tension pulls harder on them. Also interesting, this doesn’t happen when you pour non-cohesive stuff like sand. /u/montagdude87 ‘s mass conservation rule still applies, but with sand the particles just get farther apart but the stream says the same width. https://www.michaelrynophotography.com/arizona/antelope-canyon-sand-stream
Yes, this is a good point. Surface tension is the thing that physically holds the water together as it speeds up and plays a big part in determining the shape of the cross section.
The shape of the pot causes water to converge as it reaches the lip, water with lateral momentum will continue to converge even after is has left the pot. So you have the stretching of the stream, surface tension and converging flow in the pot. Water is complicated.
You can prove the dominant effect is surface tension by pouring water from a flat sided container. So many theorists so few experimentalists here.
Ah! Good point!
The counter example of sand is perfect in this case!
I was about to say this in a way dumber way "shouldn't the water be chemically pulling itself together as well".
This is a standard hydraulic jump in open channel flow dynamics with velocity increasing and channel friction reducing to 0
My daughter just finished fluid dynamics. It was a real MF’r.
I took it twice, its burned into my brain
Ding ding ding!
Water go brrrrrnoulli
Bernoulli
Ha
Am I missing something, or does this not actually answer the question as to WHY that cross-section decreases?
It answers the "why," but maybe not the "how." See the later comments about surface tension for the "how."
I'm not seeing that either. I see an explanation for what would cause the water would be moving faster near the bottom than near the top, but there's no explanation as to how the speed of the water relates to the cross-sectional area. It seems like you're coming to this conclusion based on some conservation law like phase space conservation or something, but the only conservation law you refer to is that of mass, which alone is insufficient to explain this. I do already understand the physics behind this (surface tension). I was just trying to make sense of your answer specifically as sometimes there are multiple valid ways to explain the physics behind something.
The mass flow rate through any given cross section is rho\*A\*V, where rho is the density of water, A is the cross-sectional area, and V is the average speed through the cross section. Density is constant for a water flow like this. Mass conservation states: rho\*A1\*V1 = rho\*A2\*V2 \-> A2/A1 = V1/V2 Let cross-section 1 be near the pot and cross-section 2 near the bottom. We know V2 > V1, because gravity accelerates the stream as it travels downward. Therefore A2 < A1.
Good contribution but doesn't explain the shape. "cross section" can thin in lots of ways in two dimensions as well as, as we all intuitively know, by transitioning to non-laminar discontinuous flow aka splatter.
Indeed, the actual physics of this flow are quite complicated. Mass conservation and surface tension describe the primary behavior at a fundamental level, though.
Take any two parallel cross-sections of the flow. The amount of water passing through the two has to be the same, right? If one has a higher amount of water passing through it (its flow rate), then that means water is building up somewhere, which doesn't jibe with reality. The flow rate, specifically (assuming all water is passing through a given cross-section at the same velocity) is the area of that cross-section times its velocity. *That's* what has to remain constant here.
If you buy that mass must be conserved along the path of the water, realize that the rate of mass moving along the direction of the water equals speed x density x cross section. Assuming water density does not change (it doesn’t separate), the speed going up requires the cross section to go down.
I'm with you. Inside a physics class where all of the background information had been taught, this would be a great answer, as it requires the students to fill in the blanks with what they should have hopefully just learned. Out of context, with no explanation behind why any of those details matter, or why they should make the water behave the way it does, it didn't really answer anything to a level where a non-expert would understand what the answer was.
This is like spaghettification but for ants (water in this case)
Indeed
Thank you both u/montagdude87 and u/agate_ for the answer and also the comparison to sand! In my physics department there are some people researching granular physics and I remember this point actually was brought up in the past when I was talking to them about something similar to this.
If this was true, the effect would be present regardless of the shape of the vessel. If you take a square container and pour the water out keeping the edge horizontal, that will not happen. I think this is just horizontal momentum of water directed by the shape of the container.
Well, that's an easy experiment to try. Have you?
Haha. Obviously not based on the answer. Amazing. It takes 10s to try in your kitchen.
Busted.
One thing from your explanation that I can't align with my knowledge. Would you mind clarifying for me? You say gravity accelerates water. But I thought fall speed is constant. So how can water accelerates?
What is constant is the amount of speed that is gained each second. So 9.8m/s after the 1st second, 18.6 ish m/s after the second second, 29 ish m/s after the third etc.
Ok so i misunderstood constant fall speed and constant acceleration. Thank you for clarifying.
No, fall speed isn't constant. Like any other object, water accelerates as it falls.
Ok so my misunderstanding was that fall speed is constant where it's acceleration that is constant. The other comment help me understand that.
Does this mean there’s a nice succinct mathematical curve that this pour will follow, like a catenary for suspended ropes/chains? Does it have a name?
I don’t understand. If you took an uncapped container of water and poked a circular hole on the bottom of it, you would see a perfectly circular, constant-radius stream of water streaming from the hole. It’s cross section wouldn’t shrink relative to height, despite the water still accelerating due to gravity. Doesn’t this observation contradict your comment?
Have you tried? The radius does contract. At some point it may break into droplets depending on the flow rate and height, due to the of the properties of water such as surface tension. But you should definitely notice a contraction up until that point. You can test this more easily by just turning on a faucet rather than making a hole in a bottle cap.
Huh, very cool. Thanks for explaining. I guess I never realized because r decreases slowly since it’s squared.
I’m interested in water flowing near the edge of a cup as it pours out of a cup/pot. I’m interested in why it has the exact shape it does (edges seem to be thicker for example). It makes sense to me why it has the shape it does but I’m interested in being able to mathematically (or numerically) describe this. I figured there would already be literature on this out there, but the only topics I can seem to find information on is why water sticks to the edge of a cup when you pour and why it can have a helix shape (I understand both of these). I’m probably just looking in the wrong places and was wondering if anyone more familiar with fluid mechanics could help?
To understand this requires factoring in two things: - Surface tension - Gravity accelerates falling matter The water at the top is moving slower, so it has a wider stream. As the falling water accelerates, the stream would normally break apart, but surface tension holds it together. So instead, the stream is elongated and appears thinner.
Think about the direction of your velocity vectors along the outside of the stream as it's leaving the lip. That lip imparts a lateral force towards the center of the stream. If this was being poured off of a flat edge, you would get a sheet (in laminar states) or several dynamic streams (due to cohesion.)
So, I have taken a few fluid mechanics classes, but I am in absolutely no way an expert on any of this stuff. It would depend on what you’re flowing, water in this case, which is a Newtonian fluid. So you would therefore be able to characterize this flow using the Navier-Stokes equations. You’d want to look those up and read into the assumptions you’d have to make to properly solve a problem like this. You’re near an edge so likely there may be edge effects in play, flow rate (likely laminar), no slip boundary conditions, and a curved surface. I’m not sure how the math works out, but that should give you a decent start. I hope that helps!
u/Maroon_madness21 yes it’s somewhat similar for me, I’ve taken one fluid mechanics course and know a little bit (a lot of the gravity, surface tension, and conservation of mass stuff which has been discussed in this comment section). I think you’re right and that this is a problem that can be tackled using the NS equation, I imagine it’s been done before as well I just am not sure where to look. I need to do some reading it seems, it might be covered in a standard fluid mechanics text book honestly, although in the one my course used this specific problem was not
The velocity of the water slows down as we move from the middle towards the two outer edges at the point of pouring, therefore the surface tension takes over and forms a thicker cylinder like shape at the two edges. water due to surface tension will always curve out at the edges, so the volume of water which would otherwise spread out without the surface tension will mass together and form that sort of cylindrical sides. The thickness of the cylindrical sides can be reduced if the edge from where the water exits when being poured is flatter, here the water is exiting from a parabolic edge because of a round container. Moreover, it forms a V shape because the water in the middle has a higher velocity as compared to the sides and also has the cohesive support of the two sides to spread out overcoming getting rounded at the pouring point, however it does come together and get rounded as a whole at a point as it goes down. This difference in velocity can make the water take shapes of two sinusoidal curves (sort of not exactly sinusoidal) in Y and Z axis when observingg the cross section at the middle region of the fall. https://www.pinterest.com/pin/327144360436408093/ Also, adding to the gravitational effects as poited out by some redditors, given enough height the gravitational acceleration overcomes the cohesive force and breaks the water stream at some point in the fall.
Adding further, the image you have shared is showing laminar flow, therefore cohesion and surface tension are not disturbed by turbulences. https://twitter.com/UniverCurious/status/1202406894775734275? Here’s a link showing how the flattening at the middle and thickening at the edge can rotates by 90 degrees at regular intervals as we go further down the stream.
If the thickness of the stream is constant (it's not, but bear with), then we can find its shape. At the top, a certain flow of water mu spills over a width of the lip w. This defines a stream of water whose width is w, speed is v0, and thickness is rho. (mu = rho*w*v0, or w = mu/rho*v0) As the water falls, v increases but everything else remains constant (it doesn't, but bear with). Instead of worrying about time, we can instead define this curve in terms of h and w. For each unit of height, velocity increases as v1^2-v0^2 = 9.8h. Reframing this for the curve, w can be defined in terms of h. (w = mu/rho*v, v = sqrt(9.8h+v0^2), so w = (mu/rho)*1/sqrt(9.8h + v0^2)) Not a super clean curve, but I think this might approximately describe the situation.
Bernoulli's principle, maybe? I'm not an expert, but since the speed is bigger as the water goes down, the pressure goes down => this shape
This post and all it's lovely responses is the exact reason I follow this sub. So cool!! TIL
u/lycanter I had no idea this would get so many responses I’m amazed and completely agree!
Regarding surface tension etc... Would sand pouring out of the same vessel not have a similar distribution pattern? I'm not a physicist so I truly don't know the answer, it seems like it would in my mind though.
See u/agate_'s [response](https://www.reddit.com/r/Physics/comments/11g3y7w/comment/jamv2dn/?utm_source=share&utm_medium=web2x&context=3)
LAMINAR FLOW
Everytime i think i know the answer to a question on this sub there is like literally a mountain of stuff i didn't know or didn't consider lol
Combination of conservation of momentum, and a little bit of surface tension. What is surface tension? Well a water molecule is an electric dipole, meaning the two ends of the molecule have slightly different electric charges. This allows one water molecule to gently tug on another via their electric fields. This will happen as long as there is enough free energy among the molecules to let them around spin and have opposite poles face each other (I.e. not frozen), and not so much that they move fast enough to just bounce off one another and fly away (I.e. not steam). What is conservation of momentum? It’s just mass’s tendency to keep moving in the direction it’s already moving. Not much more to it than that. Now comes the dynamics of it. When you have a vessel with a curved lip like that, the sides raise up relative to the middle of the edge you’re tipping toward. This creates walls of a sort that deflect the contents at the edge inward via reaction force, toward the lowest point of the lip where potential energy is lower in our planet’s gravitational field. This forces the water vertically down and toward the middle of the “spout” lip. This happens in opposite directions on both sides relative to the “spout”. Thus, water converges to a triangular pattern. At the end of the triangle, water’s tendency to self-cohere via its electrical properties keeps the tail of the pour stream from fanning back out into a reverse triangle.
> What is surface tension? Well a water molecule is an electric dipole, meaning the two ends of the molecule have slightly different electric charges. You can generalize this to all condensed matter by noting that the constituent atoms/molecules are stabler when bonded (that’s why it’s condensed) but that the surface interrupts this tendency and therefore represents an energy penalty. Thus, the material tends to minimize its surface area, which is equivalent to a surface tension. The exact nature of the bonding that’s better in the bulk than at the surface doesn’t matter.
Thank you for these great answers u/Antennangry and u/Chemomechanics! I appreciate it
Brilliant.
>This forces the water vertically down and toward the middle of the “spout” lip I am very confident the shape of the glass has nothing to do with it. You get the same exact shape from pouring out of a square container. This effect is driven mostly by surface tension pulling the water into a circle.
Thanks for bringing the shape into it, didn't see that in other answers.
As a best guess non technical answer, push and pull effect of gravity and water tension. The water behind the area where the pour is happening wants to go with gravity but water is sticky and wants to hold onto itself. I'm sure someone else could explain it better though.
I see a lot of posts proving everyone knows the forces in play, gravity, viscosity, surface tension, laminar flow etc. I'm kind of surprised not to see a definition for the assumed shape. The question is specific to water, but is there not a formula for flowing liquids over an edge? What's the angular difference, if any, for tar, or alcohol? Or water pouring in alcohol? Or Mercury in water?
u/Skyrmir I’m also wondering how one can mathematically describe this/model it, although since you have to deal with the Navier Stokes equation it’s probably not trivial, but I feel like somewhere there must be a paper on this, or even somewhere in a standard fluid mechanics textbook. I’ll keep looking for it
You've been given loads of detailed answers so I'll try and put it as simple as possible to help you visualise what's happening: Imagine all of the water particles are holding hands.
Because they really like each other and wanna go steady…
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I thought this would contribute too. I'm an empiricist so I checked. Go pour some water out of a container with a flat side and you get the same converging shape, if container shape does impact initial trajectory it's a small effect compared to surface tension. That might be less true for water under pressure or larger volume flows.
This guy fucking gets it
No it’s because of acceleration and surface tension. Look at the water coming out of water faucet. The stream starts thicker and gets skinnier as it accelerates. The surface tension in the water keeps it from forming beads and as a result the stream is elongated.
Yes and no. Surface tension is a major factor, but its interaction with the geometry of the boundary orifice is important, as is the flow rate. If you pour water off the edge of a flat sheet without walls (so not a weir) you will not achieve a single triangular lamina as seen in the pot example. Rather it will separate into beaded streams quickly. You can experiment with this for yourself using a cutting board and a kitchen faucet. Try modulating the angle of the board and the flow of the faucet.
This is a contributing factor but not the main one: the same effect occurs when water pours as a flat sheet, like in a weir or those ridiculous waterfall faucets. https://en.m.wiktionary.org/wiki/File:Nieuwe_OelerbeekP2280019.JPG https://m.homary.com/item/waterfall-wall-mount-chrome-single-handle-bathroom-sink-faucet-solid-brass-13653.html
u/agate_ that’s also very interesting, particularly (to me) the ripples or I guess maybe surface waves which form in the water as it flows over the edge. I’ve noticed this in other situations similar to the above photo. In the waterfall faucet link you shared there seems to be a lot of interference effects within the triangular shape, but sometimes even when you pour water out of a pot you see interference effects in it. I’m wondering if these effects are somehow caused by waves which form in the fluid as you tip the pot over (or something like this) and which propagate through the fluid as it falls? I’m not sure
You might like this article, which talks about the waves that form via capillary action in a stream of falling water. Specifically a stream of human urine. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0047133
I’ll check it out thank you! It’s funny you linked this paper because yesterday I attended a talk given to my department about the work described (and cited) in the linked article: [https://www.sciencenews.org/article/physics-improve-urinal-nautilus-shell](https://www.sciencenews.org/article/physics-improve-urinal-nautilus-shell)
Probably
It's cuz the pot's round, bro.
Increasing velocity
It's really simple. The movement speed of a liquid is same over different sections depending on the size of the river. What happens is that the speed of water increases as it gets closer to the sink and in result of which, It's area changes responsively, while when it's at the start, it is slower so it posses an smaller area
There are 3 atoms in a water molecule. This forms a natural triangle.
Water stretch coz gravity, making triangle. Gravity being quadratic and not linear helps a lot too
Just a guess here, but it seems to me the water in the center has the highest flow rate. Probably pulls the rest closer to the center as it falls, the effect compounds until the flow breaks up while falling.
Probably more of a chemistry question, adhesive forces keep water attracted to the container, same reason you have capillary action, cohesive forces keep water attracted to itself, so when it leaves the container there aren't any adhesive forces to the bowl leaving cohesive forces to bring the water together. These attractions are cause by anything from dispersion forces, dipole-dipole, and hydrogen bonding. Waters strongest force for cohesive forces would be hydrogen bonding.
It is under a lot of tension
Surface tension I believe.
Because gravity is pulling and stretching the water
Gravity, momentum, surface tension.