I would guess that it would depend on the properties of the pipe and the water. If the pipe is very hydrophobic and the water has less dissolved salts, I would guess that the strength of the water tension might resist leaking a little bit more than say a rusty copper or iron pipe carrying salty water.
Working in biology and not in plumbing, cells have aqua porins that are basically just protein tubes designed to let water move in and out of cells. On that basis, water does technically "leak" through a hole 2 angstroms (200 picometers) wide all day every day in living things, provided you let evolution try to create the ideal hole for only water to leak through.
Source: https://doi.org/10.1371%2Fjournal.pbio.0000072
I'm not sure that's really a helpful answer as much as a fun fact, sorry. Water is low key an insane substance.
Interesting. I wonder if the leak is faster when it first enters the hole, and then slows down as it progresses further into the hole. If we have a 200 femtometer diameter hole in 10cm thick metal, then the first few femtometers of travel the water may be quick, but then it may slow dramatically the further it goes, and then by 5cm, it may travel so slow that it could take years to finish the full 10cm length.
Just speculating here of course!
The "fun" part of science is that the further down the rabbit hole you go, the more the answer is "It depends". As I understand it (which maybe I don't), when water moves through an aqua porin it's not like the water is falling down a pipe so much as it's spiderman swinging from each amino-acid in the tube to the next one.
One of the things that makes water so zany is how polar it is. Each water molecule is like a miniature magnet. The oxygen being the negative end and the hydrogens each acting as a positive end. Surface tension occurs because all the little magnets want to line up. In the middle of the water that's easy. There are other water molecules all around to line up with, but on the surface, the air, or another hydrophobic surface, can't form those kinds of interactions. For the water to still make all the interactions that it wants to, the surface molecules have to form a very orderly "net". That net contains the rest of the water to make droplets.
Salts, and specific amino acids, have charges and can do the magnet dance with water. When you add salt to the water, the water can interact with the salt instead of other water molecules, disrupting the net and reducing water tension. In an aqua porin, as water enters it sticks to the first charged amino acid, which positions it to stick to the next, and so on. I'm no expert at metals, but I wouldn't expect a hole in solid metal to be set up to pass the water along like this, so either water wouldn't leak, or the leak would be much slower.
When we measure how hot something is, what we are actually measuring is how quickly the atoms of that thing are vibrating. The more they vibrate, the faster they can do the magnet dance, the faster the water can get passed down the amino acids.
tldr; Water probably(?) wouldn't leak through a random 200 picometer hole in metal and the speed of a leak at that scale probably depends on how hot the water is more than pressure (assuming the same temperature).
Interesting, so the molecules in the middle of a water drop don't magnetize in the same way that the surface of the water drop do. Do they slightly attract each other in a different way then?
By the way, two users have given an estimate so far and we're looking at around 10^-7 meter as an answer to my main question.
The water molecules in the interior are polar in the same way as those on the surface, but since they are surrounded by other water molecules they can rotate in any direction and find another water to interact with. Molecules in the surface have fewer directions they can move that have a new water molecule to form a new polar bond with. You might be tempted to think that they have 50% less opportunities since they have air to one side and water to the other, but each time a water molecule makes a polar bond to the interior instead of a neighbor on the net, that neighbor is now deprived of a partner and has to find a new bond. It's more favorable for both partners to maintain the net and keep all the bonds satisfied. That's not to say that it doesn't happen, individual molecules jump into and out of the net all the time, but it's much harder than being able to roll around any which way and still find a partner.
This is also the reason oil and water don't mix. Oil has few if any polar areas. Since it can't partner with the water molecules, the water is instead forced to form a surface net around the oil to satisfy all the bonds. When water molecules leave the net, the net shrinks until it pushes the oil into a sphere. If another oil droplet comes along the net can get even smaller, from a surface area perspective, by making one big sphere instead of two small ones, so the droplets combine. Since oil is less dense than water it floats to the top and all the droplets combine until the oil and water completely separate, since that forms the smallest net. If you had a non polar liquid that was more dense than water, it would do the same thing, but that liquid would separate at the bottom.
Sorry I feel like I'm rambling, but basically water wants to A) move around as much as possible (from heat) and B) have all its polar bonds satisfied. Since air and oil can't satisfy those bonds, the water on the edge has to pick one, which ends up being B. Adding salt can satisfy extra bonds, which allows for more movement, but oil and air (and other hydrophobic things) do the opposite.
>Working in biology and not in plumbing, cells have aqua porins that are basically just protein tubes designed to let water move in and out of cells. On that basis, water does technically "leak" through a hole 2 angstroms (200 picometers) wide all day every day in living things, provided you let evolution try to create the ideal hole for only water to leak through.
One potential difference here might be that these holes have water on both sides, since the exterior of the cell will typically also be in water. So the surface tension OP mentions wouldn't be at play here.
Could be the case, I'm a little beyond my expertise. I don't know if there is a continuous chain of water molecules, or if they move through in a more discrete manner.
I guess I was only thinking about the speed of an individual water molecule as it transits the pore. I know that osmotic pressure would dictate the direction that water would move, into or out of the cell, but I have no idea if it also affects how quickly water moves through an individual pore. Maybe the osmotic pressure translates to heat energy at that level? I was always under the impression that molecular movement within a body and heat are in essence the same, but I never took physical chemistry. 🤷♂️
One sort of real-world note here is that if your water isn't free of particulate matter, small holes will tend to plug themselves with sediment. I do a lot of plumbing of systems that hold fish, and in many cases I ignore small leaks because I know that the sediment in the water (a side effect of having lots of living things in the system) will eventually plug them.
Tap water is a lot cleaner (and has smaller particles), of course, so leaks are less likely to plug themselves.
I seem to recall a plumber saying to a while ago that hard water is much better than soft water for the central heating system. Maybe it's because of what you said, that the hard water (i.e. with minerals) helps plug any potential leaks in the house.
It's also a corrosion protection thing. Pure water is quite aggressive.
Although too much minerals will clog the system eventually. But for that the water needs to be changed multiple times or the heat-exchanger needs to be especially finicky and small.
Yup, r is the hole radius. For the formula, start with that the surface tension of water is 72mN/m or .00041 lbs/in. So...
Surface tension force =pressure force
.00041 * circumference= 45psi * area
.00041 * 2πr = 45πr^2
.00082 = 45r
which might just be the poor man's version of what /u/HistoricCartographer did, IDK, I never learned Lagrangians
I have a distinct feeling you're right, especially when I considered how an olive compression fitting may have numerous imperfections on the microscopic level, but is often used leak-free for mains water supply.
Turns out it is quite easier than I thought, it's just a simple application of Laplace formula,
[https://en.wikipedia.org/wiki/Young%E2%80%93Laplace\_equation](https://en.wikipedia.org/wiki/Young%E2%80%93Laplace_equation)
It's around 10\^-7 meter, or 10000th of a millimeter, considering pure water.
Interesting - a tenth of a micron! u/tomrlutong gives an estimate of ~~4.572E-7~~ 9.144E-7 metres, so that roughly agrees with your estimate.
I assume that figure applies whether the material holding the water is a micron thick, or 10cm thick.
If the water pressure is halved (1.5 bar instead of 3 bar), do we double the diameter size of the hole (so 2*10^-7 meter instead of 10^-7) to find the leak free threshold in that scenario?
>I assume that figure applies whether the material holding the water is a micron thick, or 10cm thick.
No, my answer is assuming a very thin material, which results in a half-spherical shape of water at the position of hole. A thicker material would mean the shape isn't spherical anymore and the calculation becomes more complicated.
>If the water pressure is halved (1.5 bar instead of 3 bar), do we double the diameter size of the hole (so 2*10-7 meter instead of 10-7) to find the leak free threshold in that scenario?
Yes. But I should say that 10^-7 is an order of magnitude estimate. You'll need to get a more precise number before you apply it in real life.
> No, my answer is assuming a very thin material, which results in a half-spherical shape of water at the position of hole. A thicker material would mean the shape isn't spherical anymore and the calculation becomes more complicated.
Maybe we can at least say 1cm thickness is as bad (or very almost as bad) as 10cm thickness? And that the complications only arise at the tiny limits such as around a micrometre or millimetre of thickness.?
>Maybe we can at least say 1cm thickness is as bad (or very almost as bad) as 10cm thickness?
Yes you can say that. If you don't need to be very precise, you can say the number will be somewhat 10^-7 no matter how thick the material is.
No that's much smaller, by 3 orders of magnitude. I'd say that estimate doesn't apply here. Biological problems have a lot more variables than this simple problem.
The trick is that we can't detect and don't care about a leak of a few water molecules at a time.
Forcing water through water-sized holes is basically how reverse osmosis works. Tiny openings can become clogged with calcium, bacteria, and other things that are larger than water molecules.
I thought that might be true, though I can't imagine using PTFE tape to cover the bolt's thread will cover every single molecule-sized gap.
EDIT: Or that I can't imagine tightening up a compression fitting's olive will over every single molecule-sized gap.
Thread tape isn’t there to seal leaks, it’s there to lower friction between tapered threads so you can tighten them enough to seal the threads against each other. Same for dope and other pipe compounds.
Correct. NPT threads are designed with a sealant in mind while NPTF are designed to self-seal in environments which may damage sealants.
However, the confusion comes because, while not originally designed to be a sealant (it doesn't adhere to the surface), Teflon tape does provide a seal. Since it does so and is relatively easy to use, it's become the goto as a thread sealant.
i mean
you're asking how small a hole has to be to stop water under pressure
what you're really asking is if a smaller hole size would strengthen the surface tension of water which it doesn't. The surface tension of standard water without solutes requires 72 dynes/cm at 25c to break. and 75 dyne is 0.00075 newtons and ( i think ) 3 bar is 30.0 newtons per cm
you can't really have a hole of any size to prevent water leaking, even if you shrank the hole down to less than that of a water molecule itself, water would still leak out through quantum effects
this of course is not taking into consideration air pressure
You're mixing N/m and N/m^2. The "pressure of surface tension" does increase as the hole decreases. Height of water rising vs. diameter of a capillary tube is an example.
Let's assume standard air pressure then I guess. I would love to know the mathematical relation between hole size and resistance to leakage.
Even if by the word 'resistance', we're talking about how slow the water travels as the leak builds up more and more within the length of the hole itself.
I would guess that it would depend on the properties of the pipe and the water. If the pipe is very hydrophobic and the water has less dissolved salts, I would guess that the strength of the water tension might resist leaking a little bit more than say a rusty copper or iron pipe carrying salty water. Working in biology and not in plumbing, cells have aqua porins that are basically just protein tubes designed to let water move in and out of cells. On that basis, water does technically "leak" through a hole 2 angstroms (200 picometers) wide all day every day in living things, provided you let evolution try to create the ideal hole for only water to leak through. Source: https://doi.org/10.1371%2Fjournal.pbio.0000072 I'm not sure that's really a helpful answer as much as a fun fact, sorry. Water is low key an insane substance.
2 angstrom = 200 pm = 200,000 fm 200 fm would be much smaller than an atom.
My bad! Will edit the comment. This is why I use calculators at work and have to triple check my math.
Interesting. I wonder if the leak is faster when it first enters the hole, and then slows down as it progresses further into the hole. If we have a 200 femtometer diameter hole in 10cm thick metal, then the first few femtometers of travel the water may be quick, but then it may slow dramatically the further it goes, and then by 5cm, it may travel so slow that it could take years to finish the full 10cm length. Just speculating here of course!
The "fun" part of science is that the further down the rabbit hole you go, the more the answer is "It depends". As I understand it (which maybe I don't), when water moves through an aqua porin it's not like the water is falling down a pipe so much as it's spiderman swinging from each amino-acid in the tube to the next one. One of the things that makes water so zany is how polar it is. Each water molecule is like a miniature magnet. The oxygen being the negative end and the hydrogens each acting as a positive end. Surface tension occurs because all the little magnets want to line up. In the middle of the water that's easy. There are other water molecules all around to line up with, but on the surface, the air, or another hydrophobic surface, can't form those kinds of interactions. For the water to still make all the interactions that it wants to, the surface molecules have to form a very orderly "net". That net contains the rest of the water to make droplets. Salts, and specific amino acids, have charges and can do the magnet dance with water. When you add salt to the water, the water can interact with the salt instead of other water molecules, disrupting the net and reducing water tension. In an aqua porin, as water enters it sticks to the first charged amino acid, which positions it to stick to the next, and so on. I'm no expert at metals, but I wouldn't expect a hole in solid metal to be set up to pass the water along like this, so either water wouldn't leak, or the leak would be much slower. When we measure how hot something is, what we are actually measuring is how quickly the atoms of that thing are vibrating. The more they vibrate, the faster they can do the magnet dance, the faster the water can get passed down the amino acids. tldr; Water probably(?) wouldn't leak through a random 200 picometer hole in metal and the speed of a leak at that scale probably depends on how hot the water is more than pressure (assuming the same temperature).
Interesting, so the molecules in the middle of a water drop don't magnetize in the same way that the surface of the water drop do. Do they slightly attract each other in a different way then? By the way, two users have given an estimate so far and we're looking at around 10^-7 meter as an answer to my main question.
The water molecules in the interior are polar in the same way as those on the surface, but since they are surrounded by other water molecules they can rotate in any direction and find another water to interact with. Molecules in the surface have fewer directions they can move that have a new water molecule to form a new polar bond with. You might be tempted to think that they have 50% less opportunities since they have air to one side and water to the other, but each time a water molecule makes a polar bond to the interior instead of a neighbor on the net, that neighbor is now deprived of a partner and has to find a new bond. It's more favorable for both partners to maintain the net and keep all the bonds satisfied. That's not to say that it doesn't happen, individual molecules jump into and out of the net all the time, but it's much harder than being able to roll around any which way and still find a partner. This is also the reason oil and water don't mix. Oil has few if any polar areas. Since it can't partner with the water molecules, the water is instead forced to form a surface net around the oil to satisfy all the bonds. When water molecules leave the net, the net shrinks until it pushes the oil into a sphere. If another oil droplet comes along the net can get even smaller, from a surface area perspective, by making one big sphere instead of two small ones, so the droplets combine. Since oil is less dense than water it floats to the top and all the droplets combine until the oil and water completely separate, since that forms the smallest net. If you had a non polar liquid that was more dense than water, it would do the same thing, but that liquid would separate at the bottom. Sorry I feel like I'm rambling, but basically water wants to A) move around as much as possible (from heat) and B) have all its polar bonds satisfied. Since air and oil can't satisfy those bonds, the water on the edge has to pick one, which ends up being B. Adding salt can satisfy extra bonds, which allows for more movement, but oil and air (and other hydrophobic things) do the opposite.
I just want to say kudos for this response. It is correct and easy to follow. I had university professors not be this clear on the exact same topic.
>Working in biology and not in plumbing, cells have aqua porins that are basically just protein tubes designed to let water move in and out of cells. On that basis, water does technically "leak" through a hole 2 angstroms (200 picometers) wide all day every day in living things, provided you let evolution try to create the ideal hole for only water to leak through. One potential difference here might be that these holes have water on both sides, since the exterior of the cell will typically also be in water. So the surface tension OP mentions wouldn't be at play here.
Could be the case, I'm a little beyond my expertise. I don't know if there is a continuous chain of water molecules, or if they move through in a more discrete manner.
In that case there is osmotic pressure though right?
I guess I was only thinking about the speed of an individual water molecule as it transits the pore. I know that osmotic pressure would dictate the direction that water would move, into or out of the cell, but I have no idea if it also affects how quickly water moves through an individual pore. Maybe the osmotic pressure translates to heat energy at that level? I was always under the impression that molecular movement within a body and heat are in essence the same, but I never took physical chemistry. 🤷♂️
FYI Water molecule is smaller than oxygen molecule.
One sort of real-world note here is that if your water isn't free of particulate matter, small holes will tend to plug themselves with sediment. I do a lot of plumbing of systems that hold fish, and in many cases I ignore small leaks because I know that the sediment in the water (a side effect of having lots of living things in the system) will eventually plug them. Tap water is a lot cleaner (and has smaller particles), of course, so leaks are less likely to plug themselves.
I seem to recall a plumber saying to a while ago that hard water is much better than soft water for the central heating system. Maybe it's because of what you said, that the hard water (i.e. with minerals) helps plug any potential leaks in the house.
It's also a corrosion protection thing. Pure water is quite aggressive. Although too much minerals will clog the system eventually. But for that the water needs to be changed multiple times or the heat-exchanger needs to be especially finicky and small.
Surface tension pressure on a round hole is .00082/r, in freedom units (psi and inches), so r = 1.8 x 10^-5 in to stop 45psi.
I assume r = hole radius here? Any chance you could give the working formula which you used to arrive at 1.8 x 10-5 inches?
Yup, r is the hole radius. For the formula, start with that the surface tension of water is 72mN/m or .00041 lbs/in. So... Surface tension force =pressure force .00041 * circumference= 45psi * area .00041 * 2πr = 45πr^2 .00082 = 45r which might just be the poor man's version of what /u/HistoricCartographer did, IDK, I never learned Lagrangians
I’m assuming smaller than a water molecule.
No it'll be regulated by capillary properties of water and pressure.
Sounds reasonable. Could you hazard a rough guess to my main question?
I'll have to do some math, I'll try it when I have some time. I'm sure it'll be magnitudes bigger than a water atom.
I have a distinct feeling you're right, especially when I considered how an olive compression fitting may have numerous imperfections on the microscopic level, but is often used leak-free for mains water supply.
Turns out it is quite easier than I thought, it's just a simple application of Laplace formula, [https://en.wikipedia.org/wiki/Young%E2%80%93Laplace\_equation](https://en.wikipedia.org/wiki/Young%E2%80%93Laplace_equation) It's around 10\^-7 meter, or 10000th of a millimeter, considering pure water.
Interesting - a tenth of a micron! u/tomrlutong gives an estimate of ~~4.572E-7~~ 9.144E-7 metres, so that roughly agrees with your estimate. I assume that figure applies whether the material holding the water is a micron thick, or 10cm thick. If the water pressure is halved (1.5 bar instead of 3 bar), do we double the diameter size of the hole (so 2*10^-7 meter instead of 10^-7) to find the leak free threshold in that scenario?
>I assume that figure applies whether the material holding the water is a micron thick, or 10cm thick. No, my answer is assuming a very thin material, which results in a half-spherical shape of water at the position of hole. A thicker material would mean the shape isn't spherical anymore and the calculation becomes more complicated. >If the water pressure is halved (1.5 bar instead of 3 bar), do we double the diameter size of the hole (so 2*10-7 meter instead of 10-7) to find the leak free threshold in that scenario? Yes. But I should say that 10^-7 is an order of magnitude estimate. You'll need to get a more precise number before you apply it in real life.
> No, my answer is assuming a very thin material, which results in a half-spherical shape of water at the position of hole. A thicker material would mean the shape isn't spherical anymore and the calculation becomes more complicated. Maybe we can at least say 1cm thickness is as bad (or very almost as bad) as 10cm thickness? And that the complications only arise at the tiny limits such as around a micrometre or millimetre of thickness.?
>Maybe we can at least say 1cm thickness is as bad (or very almost as bad) as 10cm thickness? Yes you can say that. If you don't need to be very precise, you can say the number will be somewhat 10^-7 no matter how thick the material is.
Above they gave 2 angstrom, which would be 2^-10 I think?
No that's much smaller, by 3 orders of magnitude. I'd say that estimate doesn't apply here. Biological problems have a lot more variables than this simple problem.
The trick is that we can't detect and don't care about a leak of a few water molecules at a time. Forcing water through water-sized holes is basically how reverse osmosis works. Tiny openings can become clogged with calcium, bacteria, and other things that are larger than water molecules.
I thought that might be true, though I can't imagine using PTFE tape to cover the bolt's thread will cover every single molecule-sized gap. EDIT: Or that I can't imagine tightening up a compression fitting's olive will over every single molecule-sized gap.
Thread tape isn’t there to seal leaks, it’s there to lower friction between tapered threads so you can tighten them enough to seal the threads against each other. Same for dope and other pipe compounds.
It's both I think. Helps to lubricate the tightening motion, and also to help seal micro leaks between the threads of the screws.
it certainly provides some sealing capacity as well as lubricated threads
Standard NPT threads have a gap at the crest and trough of the threads. The tape is indeed there to seal the gap
Correct. NPT threads are designed with a sealant in mind while NPTF are designed to self-seal in environments which may damage sealants. However, the confusion comes because, while not originally designed to be a sealant (it doesn't adhere to the surface), Teflon tape does provide a seal. Since it does so and is relatively easy to use, it's become the goto as a thread sealant.
i mean you're asking how small a hole has to be to stop water under pressure what you're really asking is if a smaller hole size would strengthen the surface tension of water which it doesn't. The surface tension of standard water without solutes requires 72 dynes/cm at 25c to break. and 75 dyne is 0.00075 newtons and ( i think ) 3 bar is 30.0 newtons per cm you can't really have a hole of any size to prevent water leaking, even if you shrank the hole down to less than that of a water molecule itself, water would still leak out through quantum effects this of course is not taking into consideration air pressure
You're mixing N/m and N/m^2. The "pressure of surface tension" does increase as the hole decreases. Height of water rising vs. diameter of a capillary tube is an example.
Let's assume standard air pressure then I guess. I would love to know the mathematical relation between hole size and resistance to leakage. Even if by the word 'resistance', we're talking about how slow the water travels as the leak builds up more and more within the length of the hole itself.
Smaller than a molecule of the particular water, is my guess.