Using 2" HDPE pipe to bring water down a 350 m vertical distance 1

[PEng222]

I need to bring water from a creek at about 2400 metres elevation for 1000 metres down a steep slope to a drill sump located at about 2050 metres elevation.

I'm planning to use a 2 inch HDPE open pipe for this and am trying to determine how much water this will provide, and if I need to worry about the pipe bursting.

My understanding is that as long as I have an open pipe at the bottom, water pressures and bursting won't be a problem.

Answers or references to an on-line resource would be appreciated.

 

[BigInch]

That's not entirely true. In fact, its not a good operating strategy either. If sand, leaves, a few pieces of wood, or whatever manage to block flow inside your pipe ... an explosion could be possible.

In general you must at least check the pressure at all low points along the pipeline. Beginning with any given inlet pressure, as the pipe descends, it gains static head. At any point along the pipe, static head in units of psig, and for water = 62.4 * elevation_drop_feet/144. The elevation drop is measured from the water surface above the pipe intake to the elevation of the point in question. That will give your maximum pressure possible at that point. At the lowest point of your pipeline, assuming that the 350 meter drop is to the lowest point, that should be right around 500 psig, around 3500 kPag.

Now, ONLY when the pipe is flowing, you could reduce the above static pressure by the friction loss of the flow at any given time. If your maximum possible flow is, say 5 liters per second, you might have some frictional pressure drop of 1 psi (7 +/- kPag) per 100 meters of pipe length (I imagined that number, so don't use it. And that's 100 meters of pipe length, not elevation). So, you can see that total pressure, static - friction, depends on where the point is. If the low point is close to the inlet, you won't have much friction loss to subtract. If the low point is at the end of a 1000 meter long pipeline, maybe you will have 10 psig, 70 kPag to subtract. Then your pressure at that point would be 490 psig, but ONLY when flowing at 5 l/s. If your flow stopped at the outlet, then pressure would quickly return to 500 psig.

If your pipe is open, it matters how much its open. If someone that wants more velocity comes along and puts a reducer on the outlet and flowrate goes down, pressures can go up.
If your pipe is not a constant slope, local low points can have a lot to say about maximum pressures.
If your pipe can become clogged, full pressure.
If your pipe breaks for some reason and you have to turn off the water, you will have full static pressure upstream of the point you stopped flow.
Open pipe end theory is generally NOT a safe design practice.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/

 

[zdas04]

For all BigInch's reasons, the "open pipe theory" is never a safe design practice. Are you trying to redirect the path of the stream with a 2-inch pipe? That is the only reason I can see that you would want full flow all day, every day. If you are going into a head tank, don't you think it will eventually get full? If it gets full is someone going to climb the 1,000 m hill to shut the valve with water overflowing onto the ground? No, you are going to shut a valve.

Another way of stating the pressure head is water will give you 9.727 kPa/m of elevation change. Your design develops around 9700 kPa of static head. SDR-13.5 HDPE is rated around 770 kPa at around 15C, it gets worse when it gets cold and at 2050 m elevation it will get cold. I've never seen terrain where you could bury pipe on a slope like that so I'm guessing you'll have at least part of the line above ground or buried in a shallow ditch, even running fast a 2-inch pipe full of water will freeze.

David

 

[cvg]

you can get around the very high static pressures by providing an intermediate tank every 100 vertical meters or so.

 

[BigInch]

Isn't there anybody out there that needs electricity. Leave out the tanks, make it a design for pressure and as much flow as you can and after you're finished with your drill sump, attach a mini hydroelectric plant to the end of that pipe and you'll have something to sell on.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/

 

[katmar]

This must be a sufficiently common application that a solution to the problem exists. We are all process and pipeline people here and see the difficulties, but I'm sure a farmer would know how to do it. A tank every 100 metres would solve the problem technically, but not economically. Perhaps a simple pressure relief valve exists for exactly this situation, and they could be installed in place of the open tanks. Even a short vertical open standpipe every X metres would serve this function.

Go speak to your local farmers supply co-operative and they will tell you how it is done.

Perhaps a short piece of smaller bore pipe at the start of the run would ensure that the pipe never runs full.

But take heed of the comments above - no valves except at the top, put a strainer at the top to prevent blockages, avoid low points, beware of freezing, etc.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BigInch]

Tanks would surely need valves. Even if you had a tank exactly at every 100m elev, if the water level in one tank changed by a small amount, it might create enough of a flow difference in one pipe segment such that the flows in all other segment would change, eventually resulting in overflowing one tank while draining the others... or v/v. You'd have to get the lengths exactly right, friction factors right, everything to get the same flow in each section. I think you'd need some valves just to start up flows correctly. It might turn into something more complicated than a hydraulic clock. I'll have to hand it to the farmers if they can do that with no valves anywhere.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/

 

[MikeHalloran]

Romans might do it with cascaded 'dropshafts'.

See e.g. " Hydraulics of Roman Aqueducts:
Steep Chutes, Cascades, and Dropshafts" by H. CHANSON




Mike Halloran
Pembroke Pines, FL, USA

 

[BigInch]

Man. What they coulda' done with HDPE pipe.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/

 

[PEng222]

Thanks a lot everyone; very informative!

I'm not worried about any debris in the pipe that might clog it- we are tapping into the stream at the outlet of a mountain tarn, so it is crystal clear water with no chance or debris (unless some little marmot-like critter gets too close out of curiosity and gets sucked in, I suppose). And, of course, we'll have a screen at the intake.

The pipeline will feed into an open sump at the bottom in a place where the overflow can be harmlessly directed into a big talus/scree slope and disappear into the ground. The sump will be used to provide water to a big core drilling rig.

Finally, the pipe goes downhill in its entirety- no low points are present.

So right now, my take is that an open pipe would work- but don't let it clog!

 

[BigInch]

Yes that's correct, but please remember ... that you've been warned. Good luck.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/

 

[cvg]

what hasn't been discussed is transients. normally we don't worry about them much in such a small line, but...

this line is very steep, pipe material is very smooth and there is a chance you may not have full pipe flow. at the bottom, assuming the pipe discharges under water you will have full flow. Farther up the slope you may not have full flow. Capacity will be limited by the orifice at the inlet. The result is you will likely have air in (part of) the line, could have transient surges and assuming the pipe is laying on the ground, it will need to be firmly staked. you will also have thermal expansion. All can produce high stresses on the pipe that you should be aware of.

 

[PEng222]

Thanks for the reminder about firmly anchoring the pipe. The slope is generally smooth, but has some big rocks, so we should be able to anchor it fairly well.

But the big question that no one has tried to answer yet is: how much flow can I expect to get? My little iPhone Pipe Sizer app tells me that at 10 feet per second velocity, I should be able to get 100 gal/min using a 2" pipe. So is 10 fps a reasonable velocity to use- seems low to me for such a big head.

So there must be better ways to calculate pipe flow that take into account the big change in elevation. Is there a good on-line reference that would explain how to do this?

Thanks

 

[katmar]

Assuming a full pipe, plus L = 1000m, ID = 50mm and head = 350m I get a velocity of 15 fps and a flow of 145 gpm

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[cvg]

see my last post, I believe flow is controlled by the inlet. The inlet is an orifice and amount of flow going through the orifice is related to the head, size of inlet and inlet conditions, temperature, viscosity etc.

Q = Ca [2gh]^0.5

I will let you estimate the value for the orifice coefficient (Ca)

 

[BigInch]

It isn't a trivial answer. Especially since we don't know the profile of the pipe, we can't figure out the slope. In fact, if you have multiple slopes, it can become quite complicated. Flowrate? And is it our job, or yours?

With no outlet valve controlling backpressure, flow at any point will conform to whatever the energy grade line says it is. You may have open channel flow at the subcritical, or at the supercritical level in some sections and pressure flow in another section, etc. Flow exactly at the critical level, usually doesn't remain critical for long.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/

 

[katmar]

BigInch, I think you are making it more complicated than it needs to be. If the inlet to the pipe is sufficiently flooded so that there is no vortexing and sucking in of air, and the pipe is full, and we know (stated above) there are no low points, all that counts is the overall equivalent length and the drop in height. The one potential problem that I do see is that if the head above the pipe inlet is not enough to drive 145 gpm through the inlet strainer the pipe will never fill. Then all of BigInch's concerns come into play.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[ione]

Katmar,

Have you applied the Manning formula for open channel to get the flow rate (145 gpm)? and if so which value have you entered for slope S?


V = K/n *[R^(2/3)* S^(1/2)]

Where

V = water velocity [ft/s]
K = 1.486
R = hydraulic radius = Cross sectional area/wetted perimeter [ft]
n =manning factor for roughness
S = slope[ft/ft]

If you have used another formula could you tell us which one?

 

[ione]

Katmar,

I try to expand my previous post.

Using the Manning formula reported above I’ve found v = 14.67 ft/s (comparable to your value) only if I enter S = 1 for the slope, that is considering a vertical pipe (which anyway corresponds to approx 119 gpm in a 2” pipe). But with a vertical difference of 350 m over a 1000 m pipe length I think I have to enter S = 0.35, which leads to v = 8.68 ft/s (which corresponds to approx 68.6 gpm).

Am I missing something?

 

[BigInch]

Now I see you're starting to see my point.

The value for s will control the flow in each segment of pipe. Flow may be higher in one segment than in another. One segment may flow full, another partially full. The final flowrate will be the minimum of any one of them, maybe even what can enter at the inlet, using inlet head and Cd for the inlet condition.

Once the minimum flow is determined, that's not to say the flowrate might not change, as that minimum flow could affect the flow previous segments, which changes the inlet conditions to the segment with the previous minimum flow.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch

http://virtualpipeline.spaces.live.com/