Calculating water pressure and the required mass of water

[Reiten]

Basically what I'm trying to do is calculate the amount of water it would take to generate a given pressure at the water tap. Or to put it more simply I'm trying to figure out where the water line is damaged, well more for fun then actually being practical.

The water system is simply a well on top of the hill so no pumps are involved.
The only problem is that the only thing I can really measure is the amount of water coming out of the tap in a given time. Given only this much info is there some way to calculate the approximate amount of water that has to be in the pipes?

Been trying to figure this out for the last 2 evening, so I'd appreciate any help on the subject.

 

[sophiecentaur]

So you want to locate a leak. Firstly, it's not the amount of water in the pipes that governs the static pressure - it's the head of water. If the water from the source is flowing, the head of water will be more than just the height of the leak above you so you need to measure with no water flowing.
1. Fit a long hose to the tap in your house and take the hose end up to the top of the slope.
2. Turn off the inlet valve at the top of the hill or block the outlet from the well / spring.
3. Wait till water stops flowing out of the hose end; the water level will disappear down inside the hose as water drains through the leak. The flow will stop once the water level is the same as the height of the leak. (You will have a U tube with the same level each side) You may need to let a bit more water in when you are nearly there then repeat 3)
4. Slowly move down the hill with the hose till water appears in the top of the hose.
5. The level in the end of the hose will be exactly at the level of the hidden leak. Start digging at that height and you should find the leak at that level

If you have a pressure gauge then you can connect it, knock off the supply at the top and watch the pressure drop as the level gets down to the level of the leak. Pressure will then stay constant. The height of the leak will be equal to the head that the meter shows. BUT this method actually requires an accurate pressure gauge or you could end up digging at the wrong height. The U tube method requires no measurement and it doesn't matter what route the hose or down pipe take. The levels will be the same, whatever, once water stops flowing. It's such an accurate method that they use it for tiling in large buildings, two guys working towards each other with the water level and getting the level 'spot on'. (a mm or two)

Have fun

 

[anorlunda]

1. Fit a long hose to the tap in your house and take the hose end up to the top of the slope.
2. Turn off the inlet valve at the top of the hill or block the outlet from the well / spring.
3. Wait till water stops flowing out of the hose end; the water level will disappear down inside the hose as water drains through the leak. The flow will stop once the water level is the same as the height of the leak.

I love that @sophiecentaur . Very clever.

 

[Reiten]

Thanks, that's a really interesting approach @sophiecentaur . I'll definitely try this out if I can get my hands on a long enough hose.

Though there are 3 things I'm unclear on:
1)As I infer from your answer, the diameter of the hoes doesn't matter?
2) At what point do I open the water tap and fill the hose? After step 1 or step 2.
3)Does it matter if I simply start slowly dragging the hoes end down the hill and wait till water flows out, or should I face the end skywards and wait till water appears there?

Honestly I still don't fully understand how the hoes method works. Will have to look into it some more when I get the time.
Thanks once more for the idea.

 

[sophiecentaur]

1. Correct.
2. Fill the hose whenever you like but it would be less work to fill it (turn on the tap at the house after you have carried the end up the hill.
3. If the leak is a small one, you may need to take some time to wait for levels to settle. moving downhill slowly, you could 'chase' the water level to keep it near the mouth of the hose. Once the visible level stops changing, the level will be the same as the leak.

I still don't fully understand how the hoes method works.

it may not be instinctively obvious but remember that the levels in a U tube with any various diameters or routes taken ( not necessarily a pure 'U' shape) will always settle down as equal, the level at your end of the hose must be the same as the level of the leak. IF you happen to spill any water from your end of the hose, you can always top it up and a bit of trial and error would give you a good level.
I have one question for you, though. What is the symptom of your problem? What is the actual evidence that your pipe has a leak? IS the level in your well dropping or does the supply stop? It's just possible that your fault is not actually a leak but some sort of constriction instead.

 

[Reiten]

The first thing I noticed was that the pressure(or flow rate not sure of the correct term) at the tap had dropped significantly. After noticing this I went up to the well and noticed that the water level is basically around the bottom of the outlet pipe. Plugged the outlet and after 2 hours the level in the well had gone up by 10 cm. Not sure if that's normal since no one who would know is still around. Since the well is producing and keeping water the only logical conclusion is a leak in the pipe.

 

[Reiten]

I've been thinking a bit more about this and have realized where I was making wrong assumptions, so good for me :)

I've also been thinking of ways to calculate the position of the leak in a way that I completely understand. Since I've come to understand that my understanding of the underlying physics is somewhat flawed, I'd like to hear your input on this idea @sophiecentaur .

First Iļl give a short description of how the pipe layout should be. There is a well at the top of the hill, next there is a tap at the bottom of the hill, and then the pipes split in 2, one goes to my house while the other goes to the neighbor. My idea is to find out how much water is in the pipe. Basically I plug the well and make sure that no more water flows into the system. Next I drain the water from the pipe using the tap at the base of the hill, and see how much water comes out. Next I use the diameter of the pipe and calculate how many meters would be needed to hold the amount of water that came out of the pipe. Would this work or am I missing something?

Thanks for the input.

 

[sophiecentaur]

Since the well is producing and keeping water the only logical conclusion is a leak in the pipe.

That sounds reasonable to me. Good thinking.

I've been thinking a bit more about this and have realized where I was making wrong assumptions, so good for me :)
First Iļl give a short description of how the pipe layout should be. There is a well at the top of the hill, next there is a tap at the bottom of the hill, and then the pipes split in 2, one goes to my house while the other goes to the neighbor. My idea is to find out how much water is in the pipe. Basically I plug the well and make sure that no more water flows into the system. Next I drain the water from the pipe using the tap at the base of the hill, and see how much water comes out. Next I use the diameter of the pipe and calculate how many meters would be needed to hold the amount of water that came out of the pipe. Would this work or am I missing something?

That's another way to do it - well done. (You would need to wait a reasonable time for the water level to fall as far as the actual leak) It could give you the right answer as long as the pipe is the same bore all the way and takes a straight path. If there is a wiggle in the pipe then it could tell you that the leak is higher up than it is. If the pipe is not too far underground then it would be worth while giving it a go. The ground could well be pretty soggy around the leak which would give you a clue;.
BTW what sort of height / pipe length are we talking here? You obvs wouldn't want to have to buy a massive long hose just to do it my way if your way works.
PS Are you sure that your neighbour doesn't have a leaking tap in his house? Could that explain the loss?

 

[Reiten]

what sort of height / pipe length are we talking here?

Using the tap at the base of the hill as the starting point, the height difference would be 30ish meters and the pipe length would be 100ish meters.

Are you sure that your neighbour doesn't have a leaking tap in his house? Could that explain the loss?

We are on good terms with the neighbor and fairly certain that the problem is not there. To give it some more context. The wells water level rose by 10 cm in ~2h. The diameter of the well is 1 m. So in terms of volume of water that is produced in 1 hour:

(3,14x0,5²*0,1)/2 = 0,0785/2 = 0,03925 m³ = ~40l​

In my opinion that's just to much for a leaking tap. Any problems within the houses would have been noticed, since this situation has been going on for 3 weeks.

Soggy ground was the default method I was planing to use to find the leak, once the weather allows for it. As I said in the first post this is more for fun, though it has been a lot more useful then I thought .

There is one thing I want to confirm. Assuming I use my method: Once I calculate the amount of water in the pipe, I should start measuring from the height of the tap and not from the tap itself(since there is some flat ground from the start of the slope to the tap), or am I missing something?

 

[256bits]

Basically I plug the well and make sure that no more water flows into the system

Air has to enter the pipe to replace the water that exits the tap.
How do you plan on doing that?

 

[russ_watters]

The first thing I noticed was that the pressure(or flow rate not sure of the correct term)

Flow rate. the pressure at the tap is zero (atmospheric). But you can use flow rate and details of the piping system to calculate upstream system pressure.

 

[sophiecentaur]

The volume method should use the length of down pipe from a point level with the tap in the House where you do the draining. The water in the U below that will stay there.
100m of hose could be too expensive but could you borrow? Odd lengths won’t matter.

 

[sophiecentaur]

Flow rate. the pressure at the tap is zero (atmospheric). But you can use flow rate and details of the piping system to calculate upstream system pressure.

Trouble is that the pipes, route and joints are hidden and the pressure is dropping whilst the pipe is emptying. Some hard sums to do.

 

[russ_watters]

Trouble is that the pipes, route and joints are hidden and the pressure is dropping whilst the pipe is emptying. Some hard sums to do.

Well, taking it further I was thinking that you could estimate the pressure loss inside the house and once you get outside the velocity is so low the pressure loss is negligible. But in terms of finding a leak, i don't think this helps - i was just answering that little piece.

 

[256bits]

100m of hose could be too expensive but could you borrow? Odd lengths won’t matter.

Just use a vertical pipe and measure the height the water reaches.
Only problem is the height of the pipe - with a 20 degree slope the pipe would have to be up to 30 meters.

 

[256bits]

A basic problem here is that a lot is that a lot is unknown. - the history of the well water production,, new users of water in the vicinity, any changes to the landscape in the vicinity which actually could be up many miles away which lends itself to the geology of the area, precipitation, its age which lends itself to silt accumulation and depth of the well.

Wells depend upon the water table.
Stated,

Since the well is producing and keeping water the only logical conclusion is a leak in the pipe.

That's not the only conclusion.
You don't say what happened when you closed the tap at the bottom of the hill for 2 hours.
Did the well begin filling up in this case? At the same rate then no leak.
I am assuming when you say you plugged the "outlet", you are calling the end of the pipe in the well as the "outlet" of the well.

Some other considerations you might want to think about.
It also could be that the well itself could not be itself anymore and is starting to dry up for a number of the reasons.
New users will drop the water table and that means less head for this well.
Changes to the landscape may mean the water underground is not being replenished.
Lower precipitation would also mean less replenishment of the underground water.
Silt accumulation is preventing the well to be adequately filled after use - the well may need a cleaning out.

The wells water level rose by 10 cm in ~2h

Is that as high as the water level in the well will ever get if you wait longer?
What's the level after 4 hours? a day?
The flow is not all that bad if you had several meters of head in the well and you are not filling swimming pools, but sharing with a neighbor then a couple of sessions of washing dishes and the well is done for the time being.

You have checked the flow rate into the well already - that's good, no money spent, just gathering information.
The next to do is to check the maximum height the water reaches within the well and gather that information and again no money spent. Converse with your neighbour on a good time to shut down flow for a good whole day, so both of you get a chance to plan ahead. After a day, take a reading, or take intermittent readings every 4 hours or so to make a graph. ( On the sides of the well there may be seen faint water marks of past history of well water height.) That should give an idea of the draw that is available per day for both you and your neighbor before the well is done. Does the available draw fall short, match or exceed what you estimate each household would use per day?

As an addition, another way to check for a leak is to minimally ( say 10 psi ) pressurize the pipe and see if the pressure stays or drops after a length of time. Turn off the tap at the bottom of the hill, just add a length of vertical pipe to the "outlet" of the well with a no leak connection, fill the pipe up with water, and watch what happens may be enough. No drop in the pipe = no leak.

 

[sophiecentaur]

A basic problem here is that a lot is that a lot is unknown

I basically have to agree with that. It's the sort of problem for which you really have to be there and assess the actual situation. Trying to analyse and cure a problem by remote control is risky.
I am trying to picture the situation. There is a 'well' that's 30m higher up a hill than the house ("at the top"). which is unusual because where does the water come from to fill the well? A very wide flat top or some artesian mechanism is the only solution that I can think of.
I can't help thinking that, if I were there, I would look and say "Ahhh. I see it all now" etc.
There are many possible solutions but I still can't think of a solution, other than that hose method that would give a pretty conclusive answer. It's also the method that involves least digging. That's one reason it still gets my vote.

 

[256bits]

That's one reason it still gets my vote.

Absolutely. My vote too for checking the location of a leak in supply line.
I was just stating a few preliminary tests and evaluations to see the state of the well and if it is adequate for present needs. One sometimes doesn't notice something slowly failing, until well ( pun? ), it fails, and then looks for a catastrophic cause. So check the well, check the supply line and check present consumption.
The 'source' of the artesian could be miles and miles away. This well seems to have broken through an impermeable layer down to the underground water. I do not see any mention of flooding, or mini lakes down the hill where the houses are located.

 

[Reiten]

I am trying to picture the situation. There is a 'well' that's 30m higher up a hill than the house ("at the top"). which is unusual because where does the water come from to fill the well?

I'll try to give a better description of the whole situation. The town, where the houses are, is located in a valley. The houses are located at the bottom of the valley, while the well is located almost at the top of on of the side walls. Hope this give you a better idea, if not I can draw a simple picture.

where does the water come from to fill the well?

For this part I'm not sure I'm using the correct English terms so bear with me. The water comes from an underground spring. The side of the mountain is full of theses, though only a few ever come above ground, but if you know where to look you can easily find water in a fairly shallow well. The well I'm talking about is only ~2 m deep. As to where the water from all the springs on the sides of the mountain goes, there is a river going through the valley.

You don't say what happened when you closed the tap at the bottom of the hill for 2 hours.

Oh but I know, the level of the well does not rise. I didn't think I need to write out something so simple. I also think that most of your other questions are obsolete after this point, but if there is something you want to know, please ask.

It also could be that the well itself could not be itself anymore and is starting to dry up for a number of the reasons.

While I can't deny that the well could not be producing as much as before it still manages to produce 40l an hour. That's quite a big amount for 2 houses, consisting of a total of 3 people, to waste each hour. I'm also certain that the underground spring is still around. This might sound somewhat unscientific, but my mothers side of the family has always been sensitive to underground water lines and I've inherited this trait. While working around the well I was getting a headache, which means that the water line is still there.

 

[sophiecentaur]

There's another issue here and that's how the pipe got damaged in the first place. Also I wonder what it's made of. Galvanised was popular at one time but when it 'goes' it's thin and leaking over most of its length. UPVC pipe is not too pricy to replace though and it lasts very well. It could have been partially sheared by subsidence. Has any work been carried output there? A bit of detective work could avoid too much digging.

 

[sophiecentaur]

@Reiten If you have any problem understanding my description of the 'hose' method, you can always do a small scale model with a few metres of the hose you already have and see what I mean about finding levels, independent of the route and shape of the pipes. It would be a shame if you were avoiding the method because you are not confident in its basics. I'd bet the Romans used that sort of method when they were engineering their decorative fountains.

 

[256bits]

a

@Reiten If you have any problem understanding my description of the 'hose' method, you can always do a small scale model with a few metres of the hose you already have and see what I mean about finding levels, independent of the route and shape of the pipes. It would be a shame if you were avoiding the method because you are not confident in its basics. I'd bet the Romans used that sort of method when they were engineering their decorative fountains.

I've never had the opportunity of using that method but it will work.

Back home the servicing of the wells was varied depending upon the type.
The stock well was of an iron pipe down the middle of a 3 x 3 foot square hole with wooden casing, about 40 foot deep and 10 feet of water, with the regular rod and piston type pump, and foot valve. Pulling the pump was a good couple days work with building a tripod, and front end loader, lifting up and unscrewing sections, I think 8 feet each. One time for a pull was The iron pipe sprung a leak so that need a fix. The upper part of the casing began loosing its strength so that needed a fix. Guess who was elected to go down the slimy pit to do that. Just journeying down memory lane about wells. Sorry.

 

[sophiecentaur]

a

I've never had the opportunity of using that method but it will work.

Back home the servicing of the wells was varied depending upon the type.
The stock well was of an iron pipe down the middle of a 3 x 3 foot square hole with wooden casing, about 40 foot deep and 10 feet of water, with the regular rod and piston type pump, and foot valve. Pulling the pump was a good couple days work with building a tripod, and front end loader, lifting up and unscrewing sections, I think 8 feet each. One time for a pull was The iron pipe sprung a leak so that need a fix. The upper part of the casing began loosing its strength so that needed a fix. Guess who was elected to go down the slimy pit to do that. Just journeying down memory lane about wells. Sorry.

Wells don't figure in everyday life for many people in the UK there are very few people who live that far from a mains water supply. In the '50s I used to stay with my grandparents in Devon. Their water was from a well across the yard from them. Fond memories for me. The well is still there (visible but maybe not working). They used it up till the time the mains water and drainage arrived and then the well was 'condemned' as being unfit for human consumption and it had a notice pinned on it. (Coincidence??)
Too much information here, perhaps but they had a chemical toilet and Grandad used to go to the bottom of the garden and empty it into the brook every now and again. Sterile stuff perhaps but still not a nice idea.

 

[Reiten]

It would be a shame if you were avoiding the method because you are not confident in its basics.

The 100 meters of hoes is more of a stopping point then me not fully understanding the method. I already did a small scale model with a plastic bottle as a well and some transparent plastic pipes(or whatever those small things are called).

I should probably also say that the well is located at my grandmothers house and I can only go there on the weekends, when I'm off work. So I have yet to try it on a larger scale to see how it goes with actual hoses. Didn't want to mess with larger amount of water in my apartment XD

 

[sophiecentaur]

The 100 meters of hoes is more of a stopping point then me not fully understanding the method. I already did a small scale model with a plastic bottle as a well and some transparent plastic pipes(or whatever those small things are called).

I should probably also say that the well is located at my grandmothers house and I can only go there on the weekends, when I'm off work. So I have yet to try it on a larger scale to see how it goes with actual hoses. Didn't want to mess with larger amount of water in my apartment XD

It's another of those tiresome practical difficulties. I sympathise.

 

[Reiten]

@sophiecentaur and @256bits thanks for the ideas and explanations. I'll put this thread on hold until the weather allows me to actually get some work done. I'll try my best to remember to post the results from the leak search.

 

[Reiten]

Managed to find the leak, it was extremely unspectacular. Turns out the leak was at the place where the tap, that is at the base of the hill, connects to the water pipe. After the ground finally wasn't frozen or wet anymore and we unpacked the tap from its bulky frost protection, we noticed that the ground was unusually wet. So started digging and found the leak. The metal pipe used for the tap had rusted through. After repairs the water level is back to usual.

@sophiecentaur Since the leak was at such a low place I could test the hose method from the house tap with a transparent hose. The water level stopped around the level of the leak. It was really educational to actually use it on a large scale. Thanks once more for the suggestion.

Now I only need to figure out how to do some maintenance on the well. Over all these years the hill has managed to dislocate the upper concrete ring of the well, so I'll need to figure out a good way to push it back. I'd really like to lift it up, but getting any form of machinery up there seems to be hard, so I'll have to look for a more medieval approach.

On a side note: Anyone know if it's a good idea to put small rocks(smaller the a fist) at the bottom of the well? It doesn't sit well with me that the bottom of the well is plain earth.

 

[sophiecentaur]

@sophiecentaur Since the leak was at such a low place I could test the hose method from the house tap with a transparent hose. The water level stopped around the level of the leak. It was really educational to actually use it on a large scale. Thanks once more for the suggestion.

It's been a win win. Great!
The experiment worked and you didn't need to excavate the hill.

I'll have to look for a more medieval approach.

How about rollers pushed in underneath whilst the ring is lifted with a lever? The only snag would be if the ring cracks. You have to hope it is strong enough for its size.
A tetrahedral (three legs) frame over the hole would let you use a pulley system or hoist. You could estimate the weight involved first. Scaffold poles are pretty strong in compression (with wide enough feet in place).