Calculating GPM for Water Main Break: 8" Cast Iron Pipe, 84psi, 1/4" Gap & More

[Dan Sponaugle]

I'm looking to find the gallons per minute lost during a water main break. The information I have is this. 8 inch lined cast iron pipe. System pressure is 84psi. c-factor for the pipe is 100. The pipe was broken with a gap completely around the pipe of 1/4 of an inch. Gound cover is 4.5 feet deep with asphalt on top of 3 inches. Water was escaping into the shell rock ground with no water visiable at the surface. This was a real water main break recently. If there is any other information that would someone would need I'm sure I can get it. What formula or considerations should be thought about when trying to find the GPM's for a water main break? Thank you for any help you can give.

 

[tyroman]

Dan Sponaugle,

Welcome to PF!

The water would flow at a rate governed by the system's dynamics. This means for example, that if the pressure source is a centrifugal pump, the flow rate will be determined by the pump's "head-capacity" curve. A centrifugal pump will deliver a rate of flow which is determined by the system's flowing pressure drop (expressed in feet of head) as well as the net positive suction head availible to the pump. So, in your case (if the pressure source is a centrifugal pump), the flow rate would depend upon the head loss in the length (X) of 8 inch pipe, the equivalent head loss through the annular 1/4 inch "orifice" created by the break and the head loss for any flow which proceeds downstream of the break through the remaining piping system.

Pressure from a reservoir (static head) is similar to a centrifugal pump.

On the other hand, if the pressure source is a positive displacement pump, which delivers a constant flow rate regardless of the dynamic pressure drop (at least until the piping yields or a pressure relief system engages), then the flow through the break will be calculated differently.

Knowing more about the system, you may still have a problem determining a theoretical flow rate since the hydraulic characteristics of the Earth covering the broken pipe will be difficult to determine and will have a significant bearing on the "effective" flow resistance at the site of the break.

 

[Dan Sponaugle]

Additional information, Break area is fed by ground storage tanks and the zone is maintained by centrifugal pumps. Max HGL is 520ft and break site elevation is 325ft. Is there a speadsheet or some web tool that I can enter this data and gain the GPM's?

 

[tyroman]

Google "head capacity curve", "pump performance curve" and "system curve" for more information.

One of the links which Google returns is;

http://www.engineeringtoolbox.com/pump-system-curves-d_635.html

which will help you understand the factors involved.

Note that a significant leak will change the "system curve" which will in turn change the pump's operating point on its "head capacity curve" or "pump performance curve". You will need to determine the change in the "system curve" caused by the leak (difficult) and know the specific "head capacity curve" or "pump performance curve" of the pump(s) in operation at the time of the leak. If more the one pump was in operation, you will need to know if the pumps were in series or parallel (among other things).

 

[FredGarvin]

That is all assuming that it is a centrifugal pump, which, is 99% probable. However, if it were a positive displacement pump then this would be a pretty easy question to answer.

 

[stewartcs]

Assuming you can't infer the flow rate as previously pointed out from a pump curve, it seems to me determining the flow into the Shell rock is the difficult part as that would vary widely depending on the geology of the rock.

Just my 2 cents...

CS

 

[tyroman]

Fred,

My post #4 was assuming a centrifugal pump based upon Dan's post #3;

"Additional information, Break area is fed by ground storage tanks and the zone is maintained by centrifugal pumps."

And, with a PD pump (assuming there was flow beyond the break within the unaffected piping), wouldn't we still need to know more about that downstream piping system in order to determine the gallons per minute lost during the water main break? For example, the leak rate could be relatively small if the 8" line dumps into a reservoir 200' beyond the break.

Dan,

As stewartcs and I have mentioned, your main problem is going to be determining the hydraulic characteristics of the Earth covering the broken pipe, which will be difficult and will have a significant bearing on flow.

 

[FredGarvin]

My post #4 was assuming a centrifugal pump based upon Dan's post #3;

"Additional information, Break area is fed by ground storage tanks and the zone is maintained by centrifugal pumps."

Ha. He did say that, didn't he? Whoops.

And, with a PD pump (assuming there was flow beyond the break within the unaffected piping), wouldn't we still need to know more about that downstream piping system in order to determine the gallons per minute lost during the water main break? For example, the leak rate could be relatively small if the 8" line dumps into a reservoir 200' beyond the break.

True. I was thinking in terms of a very basic pump...pipe...leak scenario. If there is any kind of networking that could distribute or divert flow then you are absolutely correct. I'm just playing Devil's advocate since it wasn't mentioned (which it didn't need to be so I'll shut up now).

 

[russ_watters]

As an upper bound, start with a Bernoulli's equation calculation. Then see if the number you get is high enough to even bother worrying about pump curves and system dynamics.

With a 1/4" gap around the perimeter of an 8" pipe, I'm betting not...

 

[tyroman]

Good idea,

The max flow would be seen if the break occurred in the pipe above ground, no flow downstream of the break occurred and the system pressure remained at 84 psi during the leak.

Using the approximate orifice discharge formula from Cameron for d/D > 0.3

Q = {19.636 K d^2 h^1/2}*{[ 1 / (1-(d/D)^4) ]^1/2}

(Note, the second term above (sq rt of 1 divided by 1 less the fourth power of the d/D ratio) is a correcting factor for relatively large orifices... d/D > 0.3 -- in our case, this amounts to a factor of only 1.008)

where;
Q = flow - gpm
d = dia of orifice - inches
h = diff head at orifice - ft
D = dia of pipe in which orifice is placed - inches
K = discharge coefficient -

(Some simplifying assumptions and rounding has been done)
circumference of 8" pipe = 25.13"
with a 360 deg, 1/4" gap, area for flow is 6.28 sq in

-IF- we can -ASSUME- the annular gap is equivalent to a sharp or square edged round orifice of the same area, then;

equivalent orifice dia (d) = 2.83" (d/D = 0.3538)
h = (84 psi)(2.31) = 194.04 ft of head
D = 8"
K = .61

and Q = 1347 gpm

Dan,
Recognizing that this is an approximation of the MAXIMUM flow that could occur if the break had been above ground, do you think this might be significant enough to pursue the issue further?

 

[russ_watters]

Thanks for doing the dirty work for me. ;) Typically, the max flow velocity you would put through a pipe is 10 ft/sec which corresponds to about 1500 gpm in an 8" pipe. So if there isn't any downstream flow, it is possible that you could get 1347 gpm out of a break of that size.

 

[Dan Sponaugle]

Finding the hydraulic characteristics of the Earth covering the broken pipe is going to be a guess at best. Would there be a simple correction factor or percent of found flow that could just be considered? God I love this stuff!

 

[stewartcs]

Thanks for doing the dirty work for me. ;) Typically, the max flow velocity you would put through a pipe is 10 ft/sec which corresponds to about 1500 gpm in an 8" pipe. So if there isn't any downstream flow, it is possible that you could get 1347 gpm out of a break of that size.

I think this is one of the key issues here, that is, if we are to assume it is a series piping system or a parallel one (the other issue being the resistance offered by the rock).

If the flow was solely through the "orifice" (i.e. crack) then you would probably get the previously calculated value of ~1300 GPM. However, since we can almost be certain that flow is continuing on down the pipe as well as leaking out at the "orifice", we are presented with a more complicated problem.

Can you submit a sketch of the piping system in question that shows the location of the break?

CS

 

[tyroman]

Dan,

As stewartcs says, we need more system info from you in order to help further...

Use the attached draft sketch if it will help. You can cut and paste as needed using MS Paint. Delete all the text from the sketch and re-arrange components as needed to depict as much info as possible. Equipment data can be described in the text of your post, with your sketch attached for reference.

Depending on your relationship to the company operating the system, this info may be hard to come by... just get what you can.