Flow rate in a gravity fed water pipeline 1

[gilesm89]

Hi everyone,

Was hoping for some help from a pipeline guru.

I am looking into the maximum flow for a pipeline from a reservoir to an outlet about 40m lower.

The way I have been looking at it is what is elevation head of the reservoir surface and that is effectively the driving head for the flow. I am then looking at a pipe friction handbook and taking note of the head loss m/100m and then matching the total headloss to the elevation difference from reservoir surface to outlet. The book then gives me the flow rate in L/s for that value.

Am I on the right track? I did note that the longitudinal profile is a bit up and down (but never higher than the reservoir. Will this affect the flow rate? Must the hydraulic grade line be above the pipe elevation at all times?

Also the PN rating of pipe. As far as I understand PN8 could accommodate 80m of pressure. Does this vary with temperature?

Hope this makes sense!

 

[LittleInch]

Makes fairly good sense, but would be good to see this in a profile and have some details attached - length, flowrate, pipe size etc

Your head available is the top of the lowest liquid level in the reservoir minus your elevation of the end point. As long as any undulations in the pipe do not exceed the lowest liquid level in reservoir (probably best to make that 5m below the lowest liquid level) you don't need to think about it. you might want or need to put air vents at the high points if your flow velocity isn't high enough to blow the bubbles along - 2-3m/sec is probably enough, but much less than 1 you might run into trouble. There are formulas to calculate that - just search on this website for more details.

Friction loss form any handbook or guide is only valid when the pipe is full of water. Depending on your distance, flowrate / flow velocity , size of pipe and slope at your end point this might not apply. I think it is the Froude number you need to calculate if your pipe ends in an open end to see if the pipe will be full or not. If you have some sort of regulating valve at the end or your velocity is high you shouldn't need to bother.

PN rating - your critical distance is the highest level of the water minus the lowest point in your pipeline if this is below the end point. If this is less than 80m then PN8 will suffice. Yes it varies with temperature for PE - past 20C it starts to de-rate up to 0.4 at 50C. Any suppliers website or PE handbook will give you these details.

Designing something like this may not be as simple as you think so I would advise you get come official assistance rather than relying on free advice from a website.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[katmar]

The potential problem you are facing is known as "slack flow". The best reference I have found in this regard is "Air in Water Pipes" by Gilles Corcos. I am unsure of the commercial status of this document. It is listed by Amazon, but is also available for free download from some prestigious university sites. It is about 60 pages and definitely worth investing a few hours in reading.

LittleInch's advice is probably sufficient is you just want an overview, but read Corcos if you must actually design a real system. I have just one comment on what LittleInch has written - the undulations must not result in the local high points penetrating the Hydraulic Grade Line rather than being above some fixed height. Corcos explains this in detail, and also how to determine the velocity to flush the air out of the system.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[LittleInch]

katmar - good spot - silly me. If I'd had a profile in front of me it would have been easier...

Giles - what katmar means is that when you get your profile, draw a line from the minimum level of the reservoir to your end point in a straight line. If your end point is a free exit to air then draw it to this point. If your ground profile goes above that line at any point then you have a slack flow system and your hydraulic gradient is limited by that high point leading to lower flow and slack flow which will not be a smooth flow

To avoid slack flow, which is not a good thing, you will need to introduce some sort of back pressure control on the end of the pipe to keep it full of water.

if you post the profile it will be a lot clearer.

see very simple sketch attached.

anything more starts to get a bit complex for a forum post

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[racookpe1978]

But a siphon (high intermediate point above the reservoir level) could be built in, could it not, if the drain is sufficiently low enough and the length long enough to pull a vacuum inside the inlet to the siphon to suck up water from the reservoir?

Clearly, not more than the local barometric limit on the vacuum height though. (760 mm Hg minus altitude)

 

[bimr]

This is Hydraulics 101.

See the sample problem:

http://courses.washington.edu/cee345/345s02p1.pdf

Am I on the right track? Yes

I did note that the longitudinal profile is a bit up and down (but never higher than the reservoir. Will this affect the flow rate? Yes, as the length of the pipe changes, there is increased resistance to flow,

Must the hydraulic grade line be above the pipe elevation at all times? As long as the pipe remains full, it will not have an affect.

Also the PN rating of pipe. As far as I understand PN8 could accommodate 80m of pressure. Does this vary with temperature? Temperature will have little affect. Note that you also have to be concerned about negative pressure on the pipe if you have a significant elevation drop.

Hope this makes sense!

 

[katmar]

As racookpe1978 and bimr have pointed out the pipe level can be above the HGL if the pipe is full (i.e. we have a siphon). But the functioning of a siphon is dependent on the actual flow rate and the pipeline may not work well at all flow rates and may have start-up issues. The safe option is to avoid having the pipe above the HGL at any point.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[LittleInch]

Yes it might work, but I've never understood why anyone would operate this way, when the increase in flow from a system where at the high point the pressure is 1 bara at a certain flowrate, the highest pressure difference you can get to is around 0.3bara and consequential vapour break out etc etc. for this theoretical system that might be a bit more significant than for many others, there are still a lot of issues unknown here.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[gilesm89]

Thanks for the responses everyone.

With regards to whether it will be full or not: it might be sometimes but we are going to expect quite a varied flow in all likelihood so probably not always.

I have attached the longitudinal profile of the ground and I have drawn some hydraulic grade lines.

As you can see the HGL would intersect the ground elevation at numerous points.

So to keep the HGL above the pipe (as the red line shows) you would need some sort of pressure sustaining valve.

And if I decided that the resultant flow was not enough, I could add a pump (orange line) and still use a pressure sustaining valve - to the point that the pipes presuure rating is not exceeded.

That's just me thinking out loud! Not sure if anyone has any views on this? Thanks again!

 

[LittleInch]

I'm glad you posted real data as I was getting worried this was as student question...

Your green line is not physically possible unless you build a long tunnel.

The red and orange lines get a little close to the high point (normally allow 5m min above grade).

Also FYI the terminology is Back Pressure Control Valve , sometime shortened to Back Pressure valve (BPV), thought pressure sustaining was a good try. To do the yellow and orange lines you start to need a variable set point on your back pressure valve either varying it by flowrate (the higher the flow rate the lower pressure it can be), or via a pressure transmitter on the high point. This implies control equipment and electrical power.

The rather more basic alternative is to fix the back pressure equal to your high point - my dashed lines - which then keep the pipe full of water at all times. This type of valve can be self actuated (spring loaded control relays). It has the effect though of limiting the max flow due to gravity by quite bit in your case as your high point is really quite high. Is there an alternative route which reduces that second peak? Even if its a bit longer you'll get much more flow than the current profile (my dash dot line).

you probably still need a pipeline engineer to do some work for you, but not a bad try. Getting a pump to raise only a few metres is actually quite hard. You might want to investigate the range of pumps commonly available to give you some idea of what is practical or not versus different line sizes.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[katmar]

As is so often the case in engineering, the devil is in the details. Having now seen the actual profile I do not believe this pipeline can work with gravity flow alone. We can lift the HGL to the high point at 6.2 km by adding a back pressure valve or by using a smaller diameter pipe for the section after the high point, but this introduces another consideration.

If we do this, there will be about 10 m of available head between the start of the line and the high point at 6.2 km. Knowing the head and pipe length, we can calculate the flow rate for any particular pipe diameter and determine the velocity that would be achieved. This velocity can be compared with the velocity required to flush the air out of the many local high points. By my calculations this would never be achieved. (I would use a requirement of Froude No > 0.64 which is equivalent to Eq 1b in Corcos.)

This is no longer an Hydraulics 101 problem - or at least it wasn't in the class I took in the previous millenium. I recommend that you engage an experienced local consultant before you spend any money on equipment or construction works.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[LittleInch]

I tend to agree - 10m over 10km isn't very much so means a biiiig pipe doing a very low velocity.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[bimr]

You have approximately 45 m elevation drop over 9.5 km. You would need approximately 8 m elevation drop per km to enable the water to flow with a reasonable velocity.

You would have to install a pump somewhere around the 3-4 km mark.

Is this a water supply pipe? If so, what is the desired capacity?

 

[BigInch]

For any flow rate and diameter, calculate the head loss Hf over some distance X. Set the slope of the pipe = Hf/X and you can get have gravity flow.

You will probably need at the very least a slope of 0.005, 5 ft drop in 1000 ft (1/2 a foot in 100 feet, or a 5 m drop in 1000 m to get anywhere a useful flow rate.

If you were designing a gravity sewer system, you would need a number of "lift stations", something like I have drawn on top of your diagram.

you must get smarter than the software you're using.

 

[Xalii]

In deed the more flow you have, smaller can be the difference of head to have a requested minimum velocity. Attached you can find those values for a min velocity of 0.5 m/s. With this velocity you will still need to tackle the problem with air blockage.

Would be good also to clarify which type of outlets you have downstream. Is it a (or many) tap or a tank ? And why you expect to have a varied flow ?
1) If it is taps(or valves), the outlet pressure will be higher (when it is closed the all pipeline will be under pressure) and if the maximum required flow is smaller than the available water in your tank, the pipeline should never be partially full. Then if your peak flow match the above table it might be feasible playing with some pipe diameters.
2) If it is a tank the outlet pressure would be nil and the flow should be constant. If the flow is limited from the upper tank, part of your pipe might be not full.

But in any case excavation and/or changes in the path is highly recommended

 

[gilesm89]

Thanks so much everyone. This is very useful. Just for the record I will be engaging a consultant (who is on leave at the moment). I am just trying to assess various options that we have (I am an engineer come project engineer - basically a project manager!).

The majority of the line in this is an existing 450 PE100 PN8.

I have found that there is a shorter route if we teed off that line earlier. It also has a lower high point. See attached.

We are aiming for a absolute max of 230 L/s. If I know that this isn't feasible atleast I can cut my losses and start to consider duplicating the line!

 

[bimr]

With the proposed flow and pipe diameter, your project is feasible. It will be important to minimize the entrance of air into the pipe so that the pipeline can not become air bound.

 

[Xalii]

If I am not mistaking, a 450 OD, PE100 PN8 is a 407 internal diameter. With this diameter if you want to avoid negative pressure in your pipe, the maximum flow you can pass is about 180 l/s. The maximum flow for this pipe would be about 230 l/s but only if you have a flat (or concave) profile.
Find attached an Excel file showing the calculation. You can find a tutorial on how to use it on :

http://designwss.weebly.com/2-concept-design.html

 

[bimr]

One should evaluate this pipeline as a pressure pipe fed by gravity, not a gravity pipeline. A gravity pipeline will never work without the addition of lift stations. In the title, the OP states "gravity fed", not gravity pipeline.

The critical aspect in this application is to minimize air entrance as it will be difficult to clear air bubbles when the flow is moving downhill, especially at low velocities. Clearing the air will only be possible with adequate velocity to flush the air out. The required flushing velocity varies with the slope of the pipe.

Refer to the attachment for a chart that shows air clearing velocities.

Various articles describing trapped air in pipelines.

http://www.arivalves.com/index.php?option=com_zoo&task=category&category_id=46&;Itemid=29

http://www.netafimusa.com/files/literature/wastewater/Dangers-Trapped-Air.pdf

http://www.valmatic.com/pdfs/AirinPipelines.pdf

 

[BigInch]

See my diagram with lift stations.

you must get smarter than the software you're using.