Open to Closed Channel Flow Equations 5

[PaulJankel]

Hello,
I am trying to establish the equations required to calculate the potential flow of water through an almost straight cement lined ductile iron pipe (diameter 0.5m / length 750m / head drop 350m) if i feed it from an open channel flow (i.e. a river) with flow 'x' cubic m / s.
My objective is to ascertain the effect of different river flow inputs on the flow into the pipe. The effect of friction and head loss within the pipe is important, but my main consideration is the effect on the open channel flow into the top of my closed channel pipe.
Can anyone help?
Thank you

 

[JStephen]

If you get enough vertical drop on a pipe, the head gain from the elevation will be more than pipe friction. In that case, the pipe won't necessarily be full of water, and flow will be limited just by entry conditions.

If the pipe opening is submerged, you can calculate the flow into the pipe as though the pipe were simply an orifice at the point. If the actual flow conditions develop some partial vacuum at that point, then you may underestimate the flow substantially, but there's no good way of know if that's the case.

If the pipe opening is not submerged, you'll be looking at some sort of weir-type flow into the pipe, and looking for a geometry that matches yours.

 

[PaulJankel]

Thank you JStephen.
The pipe will be submerged and will be full.
However I will be limiting the flow as it will be used to power a turbine.
I would be satisfied with a 2 cubic m / s flow.
I am trying to work out the minimum river flows necessary, and whether I can carry more water volume and hence use more turbines, if the input river flow is increased.
(I still have input flexibility as we have not allocated a specific site).

 

[katmar]

If the 0.5m diameter you give is the inside diameter, than I calculate the flowrate to be between 2.2 and 2.8 m3/s depending on the roughness of the lining.

As long as the inlet is flooded, it does not matter too much about the upstream flow conditions. Just be careful of vortexes and excessive air entrainment as that would decrease the flowrate significantly (and damage your turbine). Where you switch from open channel to closed pipe flow you will need a fairly deep calming (stilling) pool to ensure the pipe entrance stays flooded.

I cannot see that you can run more than one turbine off this pipeline - whoever did the original sizing seems to have done the same calculation that I just did!

regards
Katmar

 

[PaulJankel]

Wow Katmar
Thank you.
That is close to what I was gestimating. No one has designed the pipe yet. I am formulating 'what if' scenarios before I pay for a formal design. There is a wide range of turbines available, and it is really that decision which relied on the flow rate.
Please please can you advise me which are the correct equations to use for your calculation?

 

[katmar]

Paul,

It the standard old Darcy Weisbach formula, which you will find described in almost any fluid mechanics handbook. A Google search on "Darcy Weisbach" gives nearly 10,000 hits. The very first one is probably as much as you will ever need.

See

http://www.lmnoeng.com/DarcyWeisbach.htm

This site even has an online calculator to do the number crunching for you. This is useful because it requires iteration to calculate the flowrate from the pressure drop and pipe dimensions.

HTH
Katmar

 

[PaulJankel]

Katmar,

Thank you. That's the 'hf=f(L/D)V*V/2g' one right ?
(sorry cant write V squared) - what friction factor did you use ?

I am now drawn to use stainless steel with welded joints for the pipe (as opposed to concrete lined).

By the way. I was trying to work out the Reynolds number for this flow rate. Am I correct that under 2 cubic m / s I might get a Laminar flow ?

Thank you for your kind help.

 

[cvg]

you state that the pipe will be submerged AND will be full. That indicates that you have a sufficient tailwater / back pressure to allow the pipe to fill. In that case, the flow is not under inlet control. Calculation of the capacity will then be a function of the tailwater depth / back pressure - not the orifice equation.

 

[PaulJankel]

CVG,
Thank you for the clarification. Can you tell me which equation would be used?
Paul

 

[katmar]

Paul,

Yes, you have the right equation. You seem to be working in SI units - keep it that way. In your equation

hf = head in meter = 350m
f = Darcy Weisbach friction factor
This is often called the Moody friction factor
= 0.032 assuming a roughness of 3.0 mm and a flow of 2.2 m3/s
L = pipe length in meters
D = pipe ID in meters
V = average flow velocity in m/s
g' = acceleration due to gravity = 9.8 m/s^2

If you use stainless pipe the roughness will be about 0.05 mm and the flowrate will be about 3.6 m3/s.

Your flow will definitely NOT be laminar. The Reynolds number will be between 10^6 and 10^7 i.e. safely turbulent.

As CVG has stated, if you throttle the system the controlling equation will be something else (probably the valve characteristic) but Darcy Weisbach gives you the limiting (best) case.

The existance of different friction factors is confusing because not all texts make it clear which one they are using, and even fewer explain that there are several in common use. I have included a friction factor category in my Uconeer units conversion program to do this conversion. Uconeer is a freeware download from

http://www.katmarsoftware.com

regards
Katmar

 

[stanier]

Why not download the Epanet software. Its free and you can play around with the surface roughness and entrance conditions. if memeroy serves me right the equations are in the manual that you can also download.

http://www.epa.gov/ORD/NRMRL/wswrd/epanet.html

Open channel software that is also free is Flowpro2.

 

[PaulJankel]

Guyz,
What Can I say ? Thank you all very much for this detailed information. I am now trying to digest it.
Katmar, most significant is the increased flow which could generate an additional 50% energy output, above and beyond my initial minimum requirement. I will certainly check out your site.
Also Stanier I will have a look at that software.

 

[stanier]

Paul,

Then you will come to the hard bit. The transient analysis of a system. The turbine will have to be protected from the situation where the electrical load comes off. The water will not stop and the turbine will try and run away. A gate will need to close to reduce the flow. You will want this to happen as soon as possible to prevent overspeed. Problem, fast closing gates when the velocity is 3.66 m/s causes waterhammer.

No freeware for this analysis that I have come across.

Hytran by Professor Laughan in New Zealand can handle turbines on a single line. Contact Accutech in Perth Australia as they distribute Hytran. They will also do the analysis for you if you need it. Graeme Ashford is the guy to contact.info@accutech2000.com.au

 

[chicopee]

Elevation of river and of pipe is more important to flow in the pipe than the river flow itself. Use Bernouilli's equation.

 

[PaulJankel]

Stanier,
Thank you for your thoughts.
I am aware of water hammer issues, which I believe can be solved by the control system closing valves slowly. I have found an equation to determine 'critical' time for this operation.
The system will use a Pelton (impulse) turbine, which provides a physical separation between the water and the induction mechanism. Also the system will feed the UK national grid and will therefore be strictly controlled in terms of load (in and out). I am hoping this will avoid the feedback you suggest with a 'dropped' load.
I don't want to scare you guys...I am the developer. All works will be carried out by fully qualified designers and engineers. I just need to be fluent in the calculations required for concept design and to set out the broad parameters of the project features.
This thread has helped me correct my 'speed-learning' of
some basic fluid theory and has been extremely useful.

Chicopee,
Isn't the Bernouilli equation for determining head (or energy) loss through the pipe ? And does it apply to turbulent flow (which my system will experience)?

Thank you once again

 

[katmar]

The Darcy Weisbach formula is simply a special case of the general case described by Bernoulli. If you integrate Bernoulli for an incompressible liquid, you will get to the DW formula. I don't know the history, but I would suspect that the DW formula was developed empirically and the agreement with Bernoulli came later??

Sometimes it is worthwhile going back to Bernoulli to consider whether you have taken all aspects of the energy balance into account. For example, in your case it would show that the potential energy due to the liquid head is converted to losses (friction), generated power (turbine) and velocity head (speed of discharged water).

 

[katmar]

Sometimes I should listen to my own advice!

When your system is considered from the Bernoulli perspective then it immediately becomes obvious that my previous calcs were wrong. I had assumed that all the static head was consumed in overcoming the pipe frictional losses. But of course your turbine supplier will be requiring a certain head to drive the water through the nozzles and onto the wheel.

Say, for example, that your turbine needs 2 m3/s at a head of 200m. This means that only 150m of the original 350m is available to overcome the pipe friction in getting the water to the turbine. The pipe diameter required depends very much on the roughness of the pipe. Stainless pipe would require an ID of only 470mm, but a medium roughness concrete pipe would require 560mm (and a smooth concrete pipe somewhere between). All engineering problems are eventually decided on economic grounds! But as a developer you know that ;-)

 

[PaulJankel]

I can summarise my specs. as:

head = 350m (net head required for turbine)
length of pipe = 750m (although this might be +/- 200 m depending on topography)
diameter of pipe = 0.5m (internal)
flow = 2 cubic m/s (required for turbine)
material = welded stainless steel (to maximise the life span of the pipe), an effective 'straight run'. No lateral turns. Maximum turn of 40 degrees over 200m.

Based on the conservation of mass I know that whatever water I put through the system has to come from the reservoir or water source at the top of the system.

The pelton uses water jets, and as such the water flow through the pipe will be controlled and reduced from its full potential flow. The required flow of 2 cubic m/s is lower than the potential flow within my spec of pipe.

So can I presume that the reduction of the flow to 2 cubic m/s from its full potential flow will 'absorb' or negate any head loss due to friction. This is where the Bernoulli equation is deployed is it not ?

 

[PaulJankel]

Stanier,
I downloaded EPANET software as you suggested. It might take me a while to figure out how to use it but it looks simple and intuitive. Thank you.
Paul

 

[stanier]

Paul,

You are welcome.

Software from Haested Methods and BOSS uses the same engine to drive their software but you do get support and asnazzier front end for your thousands of dollars.

i found it relatively easy to get the hang of once I had run the tutprial in the help section a couple of times.

I modelled the water system in Ampara East Sri Lanka using it. The extended period simulation enabled me to review tower reservoir capcities, pump selection and pipeline sizing. I then demonstrated to the engineers there what was happening in the system over a 48 hour period. You can also use it to determine the effectiveness of chlorine dosing in a long pipeline using a kinetic reaction mode.

Its very powerful software. I believe that you can model turbines as reverse type pumps but I have never had that need. The web address I gave you did have a link to an Epanet Users Forum. I am not sure if that is active but if not a posting to this Forum may give you some help.

Geoff