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.

 

[katmar]

@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 )

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

 

[BigInch]

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/

 

[cvg]

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.

 

[BigInch]

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/

 

[katmar]

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 ) 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

 

[BigInch]

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/

 

[ione]

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).

 

[katmar]

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

 

[ione]

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.

 

[BigInch]

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/

 

[ione]

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.

 

[racookpe1978]

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.

 

[msquared48]

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

 

[PEng222]

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.

 

[PEng222]

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.

 

[cvg]

I guess 85 gpm

 

[katmar]

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

 

[PEng222]

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.

 

[ports394]

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

 

[PEng222]

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.