Head loss in partially-full pipe?

[KernOily]

Dumb question time here guys. Yes I checked the archives.

I am trying to estimate head loss in a partially full pipe. Pipe pipe pipe, NOT a trapezoidal or rectangular channel or wood flume or etc. I have looked in all my references (Crane, Cameron, Marks, Lindeberg, Streeter & Wylie, etc.) but none _definitively_ say whether the Darcy equation, modified for hydraulic radius, is correctly applied to circular cross-sections, i.e. a pipe.

I assume the procedure is to calculate the velocity using Manning, and then use that in the Darcy equation with the hydraulic radius - yes? I got all kinds of examples in partially-full noncircular conduits. I am a round steel pipe guy though.

By the way, this is for design work for a new combined oily water/storm water/fire water sewer in a process plant. I am dropping 60' in elevation from my source (tank diked area) to my collection point (below-grade sump tank, 1200' away) so I am working on line sizes, head loss, estimating the potential for hammer events, etc. Thanks!


Thanks!
Pete

 

[MikeHalloran]

You may find this useful:

http://www.atkinsopht.com/eng/strmlins.htm

I have no affiliation; just a satisfied customer.



Mike Halloran
Pembroke Pines, FL, USA

 

[zdas04]

74Elsinore,
This is a pretty normal question (think of wellsite production without wellsite separators) and the normal approach to it is to calculate the superficial gas velocity and the superficial water velocity. The superficial velocities are simply the volume flow rate of each product divided by the flow area.

If both superficial velocities result in Laminar flow then the friction drop is really straight forward.

If they are both turbulent then I've found the Duckler correlation (see GPSA) to do a really good job of predicting actual pressure drops.

The real difficulty comes in when the gas is turbulent and the liquid is laminar. In that case the amount of work that is done by the gas dragging the liquid along is a really big source of dP that I've not yet found an equation that matches observed pressure drops.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[lilliput1]

Do you have at least 1/4" per ft slope in your elevation drop? If so, whymnot design for a full pipe?

 

[katmar]

If you are calling this line a sewer, then I imagine that there is only liquid that you want to send down the pipe. I suppose you could call it "two-phase flow" because there may be an air layer above the liquid in the pipe, and the air will be dragged along to some extent by the flowing liquid, but this is not really a situation that lends itself to a Duckler type analysis.

Sewer or drain design is more easily handled using Manning analysis, as you said yourself. I do not understand why you would then want to switch to a Darcy calculation? You should be thinking of your driving force in terms of slope rather than pressure drop. In a drain it is usual to have both ends open to the atmosphere and there isn't really any pressure drop in the usual Darcy sense. Although of course there is a drop in height and this could be expressed as a static head.

There was a discussion of this type of problem in thread378-98364 There you will find a reference I gave to a source which gives a full Manning analysis for circular pipes.

 

[KernOily]

Guys thanks for your reply.

katmar - I am calling this line a 'sewer' because that is what this service is usually called in the process plant business.

Your questions is well-posed as to whether I need to consider head loss or not. Yes both ends are open to atmosphere, well, the source end is and the sink end is an atmospheric tank.

In my problem, I used Manning to calc the full-pipe velocity based on my slope, which is 0.01 ft/ft (1/8" per ft), and then I used the area ratios to determine that the pipe is not running full at my design rate. I thought it would be wise to estimate the head loss due to friction and make sure that friction loss does not reduce the rate relative to the driving force made available via my static head drop, thereby reducing the flow capacity. That is why I am trying to calc the head loss.



Thanks!
Pete

 

[katmar]

Pete,

I agree totally with your aim of getting a second method to confirm your design. Perhaps the way to look at it via Darcy is to calculate the required diameter if the pipe were running full.

For example you have a slope of 0.05 ft/ft. Using Manning with N=0.012, this would give you a flow of 500 gpm of water in a 6" pipe running 3/4 full. If you now use Darcy to work out what diameter pipe you would need (running full) to get a flow of 500 gpm over a distance of 1200 ft with a head of 60 ft you get to a diameter of 5.2 inches. This should give you confidence that the 6" pipe will cope well.

katmar

 

[KernOily]

Thanks katmar. That's what I'll do and I'll post the result. Thanks!

Thanks!
Pete

 

[stanier]

Try and find the freeware Flowpro2. It allows you to model gravity flows.

In addition you might try and get Epanet. I am not sure that this allows for partially full pipe. It is freeware and very good. The engine is used by many professional packages. the tutorial makes it easy to learn.

If you go to

http://www.haestad.com

and enter their Civilquiz you can win prizes. One of the prizes is a ten node Sewercad package. It comes with a smart book on sewer design. if you dont have many junctions you could use this to model your pipeline.