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

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

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

(OP)
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.

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

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/

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

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

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

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

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

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/

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

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

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

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/

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

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

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

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/

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

(OP)
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!

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

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/

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

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.  

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

(OP)
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
 

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

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

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

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)
 

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

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/

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

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

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

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?
 

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

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?
 

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

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/

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

@ione - No I have not used Mannings formula for open channel.  This is not open channel flow, although I guess you have not taken it as such either.  The OP has asked what flow would be achieved given the conditions of the pipe running full, and that is what I calculated.  By open flow the OP meant that the end of the pipe was open (no valve), the entire cross section of pipe was filled with water, and the pipe discharged freely.

I therefore used the Darcy-Weisbach equation with the conditions I gave above (March 8, 15:53) plus I assumed a roughness of 0.005mm.  The 145gpm I calculated was USgpm.  I agree 15 ft/s gives 119 Imperial gpm.

The slope I have used is a net drop of 350m over a length of 1000m.  How this actually occurs could be important - see below.

I suspect that the difference between your calculation and mine is the smoothness we have attributed to the pipe.  What value of n did you use for Manning?

@BigInch - The flowrate on a mass basis cannot be different in different sections of the pipe if there is no provision for accumulation.  The pipe is assumed to be running full and the "flexible steel bar analogy" we spoke of recently applies. ( thread378-266224: Velocity and Pressure Drop )

Concern over actual slope of pipe

Although I did not make a specific assumption over the actual slope of the pipe, it would have to be fairly even over the length of the pipe to achieve the flowrate I calculated and I do concede that any large deviation from the average would have to be considered carefully.  The two extremes to consider are
  1.   650m of horizontal pipe followed by a 350m vertical drop
  2.   a 350m vertical drop followed by 650m of horizontal pipe

In case 1. the slack flow would cause very low pressures at the end of the horizontal section, the water would vaporise increasing the friction and decreasing the flowrate (but the mass flow would still be constant over the length of the pipe).  The pipe may even collapse in on itself.  In case 2. the pressure at the junction of the vertical and horizontal legs would be high and bursting would have to be considered.  At the calculated flowrate the frictional pressure drop is 0.35 metre of water column per running metre, making the pressure at the junction 650 x 0.35 = 227.5 metre WC or 323 psig.

If the actual slope does not vary too much from the average the small variations in static pressure increase per running metre of length will be absorbed and the flowrate would be as calculated above.  If the actual slope were constant over the entire length the pressure gradient along the pipe would be zero because the frictional head loss would exactly match the static head increase.  If the pipe dropped below this imaginary constant slope line the pressure in the pipe would rise, but even if it were 50m below the constant slope line the pressure in the pipe would be only 5 bar.  A deviation above the average slope would be more problematic because it may cause vaporisation. So the strategy should be to remain slightly below the average line all the way.
 

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

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

Katmar, if there are different slopes, the flowrate can be different when starting up.  It is also different when you are analyzing the situation looking for the steady state flow, if you don't assume 1 constant slope, iterating flowrates between sections to eventually find the flowrate you're talking about, the system's steady state flowrate.

If its one uniform slope, pipe flowing full, Manning works and its a somewhat trivial problem.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch
http://virtualpipeline.spaces.live.com/

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

I would still submit that flow in the pipe has practically nothing to do with the slope. The pipe inlet will control the amount of water that can enter unless the capacity of the pipe due to the friction loss limits the flow to something less. Assumption of full pipe flow is not supported by any facts that have been presented. Given the steep slope, smooth pipe and limiting capacity due to the inlet, the pipe may not flow full over the full 1000 meters. Maximum flow in the pipe is about 140 gpm assuming that the entrance losses do not limit this to something less. However, unless the head over the inlet is more than just a few feet, the flow will be significantly less than 140.

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

cvg, I'm very "inclined" to agree.

I wouldn't expect to see much available head at the inlet in that kind of terrain where you get 350 meters to play with, unless there just happens to be a very conveniently placed and unusually deep reservoir up there, but he said its a "creek".  Probably 2 meters would be an unusually deep inlet head.

I think it will be limited by intake flow and it won't flow full, as the slope surely must be greater than supercritical, well at least not full flow until the pipe gets stopped up.  Then it will be full of pressure, but with little flow.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch
http://virtualpipeline.spaces.live.com/

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

This is good - we have found something we agree on. The entrance losses are very important in establishing the flow in the pipe.  Once the pipe is full, the entrance losses are just part of the overall resistance that is matched against the total available head but at start up the pipe is not full and there is no syphon effect to pull the water into the entrance.  A similar discussion way back in 2003 ( thread378-81608: Diesel fuel flow through a vertical pipe ) referred to gurgling and bubbling at start up in a diesel line down a mine and there I pointed out how important it was to get the diesel into the vertical pipe, before starting to calculate what is happening in the downleg itself.

In fact the entrance effect is (at worst) only 1/3rd of the start up problem.  The other loss that has to be overcome by the available head at the entrance is the acceleration of the water into the pipe.  For a square entrance the loss would be 0.5 velocity heads and the acceleration is of course 1 velocity head.  In order to establish a flow velocity of 15 ft/s a head of 5.5 ft would be required to overcome these two losses.  This situation could be improved somewhat by using a radiused inlet, and with a wide mouthed radiused entrance we could reduce the losses to 0.04 velocity heads (Crane TP410 pg A-29).  The acceleration losses cannot be improved upon, and there may be losses in an inlet strainer or grid as well.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

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

Katmar, we always agree.  Sometimes it just takes a little longer.

Direct the inlet into the creek flow and keeping it off the bottom of the creek will both help that as well.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch
http://virtualpipeline.spaces.live.com/

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

Continuity equation works here and so the most binding conditions determine the flow rate. In this sense entrance losses can govern the flow.

@Katmar,

Thanks for your explanation. Anyway I still can't get a grip on the use of Darcy-Weisbach equation.

Below the Darcy-Weisbach equation rearranged for velocity V

V = SQRT (hf *2g*D)/(L*f)

Where:

V = velocity
hf = head loss
g = gravity acceleration
D= pipe internal diameter
L = pipe length
f = friction factor.

In this case it is possible to assume elevation head is fully converted into friction loss so hf = 350 m

But friction factor depends both on epsilon/D (being epsilon the pipe absolute roughness) and on Re. But Re depends on fluid velocity V. How could we sort this out?


By the way I have entered 0.012 (no units) for manning's n value (for PE pipe with smooth inner wall).

 

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

ione, you are correct that no direct solution is possible because the velocity is a function of the friction factor, which in turn is a function of the velocity via the Reynolds number.  There are approximation methods for calculating the friction factor which make it possible to do a direct calculation, but an iterative solution converges so fast that I prefer to do it that way.  Just guess a velocity to start with and you quickly get to a stable answer.

My attitude towards the Manning equation seems to be the same as yours towards Darcy-Weisbach, so I have no feel for what n=0.012 means in prctice.  But a Google search suggests that you could use a value down to n=0.009 which would bring our results closer together.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

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

Katmar,

Thanks for swift reply. Meanwhile I have given a shot to Hazen Williams (which doesn't ask for iteration) and results seem to match.
 

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

The mass continuity equation works, but you don't know the area of flow, unless you assume its flowing full (which you must do to use those equations), otherwise the area of flow and the velocity will vary to make the steady state mass flow constant.

**********************
"The problem isn't working out the equation,
its finding the answer to the real question." BigInch
http://virtualpipeline.spaces.live.com/

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

BigInch,

Absolutely agree the "full pipe" assumption is mandatory for the equations above to be applicable. With this assumption the condition of subcritical flow is safe and the problem requires a simplified approach.
 

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

Hope the upstream "creek" doesn't get plugged with a fallen tree, rockslide, etc.  Or a drought and loses level.

Or freezes down to the suction level.   

Would the loss of the pipe (its water or its physical failure ) be life threatening?   Be ready with a backup until the thing can get rebuilt.

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

Definitely need sopme sort of a shutoff valve at the headworks, and perhaps some intermediate energy dissipators depending on the EGL and the pipe bursting strength.

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

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

(OP)
Again, thanks.  Just finished excavating the sump for storing water- so now we just need to install the waterline!

Thanks for the ballpark estimates of flow rate using a numerical approach- always important.

Getting the top of the pipe nicely under water shouldn't be a problem- there is about a one metre deep pond available that covers an area of about 30 square metres- I'll just anchor the pipe in that.

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

(OP)
Bottom Line here everyone:  the pipeline WILL be built and so there WILL be an answer to my two specific original questions.  For those of you kind enough to have provided some computational basis for answering the question regarding flow- thanks; it will be interesting to see what the flow will actually be and whether my pipe will immediately burst or not when I fill it with water.

Stay tuned.

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

I guess 85 gpm

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

PEng222 - Looking forward to the feedback.  It is always interesting to see how the practice matches the theory.  One metre of submergence may not be enough to achieve full pipe flow, but it seems that your actual flow rate is not too critical.  Make the first 10m or so as steep as possible - certainly not horizontal - because it is only the head over the inlet that is driving it here.

When you have bought and laid all that pipe let us know the actual length and ID as well please.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

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

(OP)
So just an update.  Due to a number of very useful comments here, we've decided not to take a chance with just using an open pipe to ensure that the waterline doesn't burst.

We also decided to use a lower intake point- which increases the waterline needed to 1500 metres, but reduces the elevation difference (head) to about 250 metres.  The extra length is needed because of how the creek flows relative to where the drill sump is located.

But the big change is to install three pressure relief sumps along the way- which will ensure that any one length of pipe never drops more than a hundred vertical metres, and therefore will never have more than about 143 psi pressure.  The HDPE is rated at 150 psi- so should work.

On the subject of professionalism: if I was totally calling the shots on this installation, I would insist on a proper hydraulic assessment by a qualified engineer- who would be expected to issue plans and a signed and sealed report that fully shows the calculations and assumptions he/she used to derive any outcomes, such as flow, etc.  Normally, this is not done in situations like this because there is much less head involved and so a waterline is just installed as part of the drilling routine.  But this is an unusual situation- if the waterline fails, the drilling would have to be suspended- and so it's important to get it right- something that only a professional and a formal analysis and report can do.

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

Hey it's been a few weeks.  Any updates PEng222?

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

(OP)
The pipes ( two- 2" HDPE) are now in place.  The pipeline has been broken into three sections, with a small pressure relief open sump at the end of each section.

But they won't be running water through the pipe until next week, so I can't yet report on how much water the system is producing.

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