fire water pipe rupture calculation

[jrpower]

I have a fire protection piping system with 3" and 4" schedule 40 piping that I am trying to calculate the flow rate from various sizes of a pipe crack/breaks up through a full guillotine rupture of the pipe. I am trying to use simple calculational methods to estimate the break flow rates without getting the exact pipe lengths of the system. The pump pressure is about 150 psi and the break is going to atmosphere. I also have the pump curve data for the pump (see below).

For a pipe break that is not a full guillotine break, from the Crane Technical Paper No. 410 I am using the following equation Q = 236 x C x d1^2 x (dP / rho)^0.5 (Crane's Eqn 2-23), where C = Cd / (1 - B^4)^0.5 and B = d1 / d2 where d1 is the inner diameter of the pipe and d2 is going to be the oriface or in this case the crack size, and Cd~0.6 for flat plate orifaces for water at 60 deg F. I am getting very reasonable numbers for my flow rates with this methodology and am satisfied with these estimates, BUT...

For the full guillotine rupture of the pipe, I need an equation that is reasonable and not overly conservative. I have tried using Darcy's formula for pipe's Q = 236 x D^2 x (dP /K x rho)^0.5 (Crane's Eqn 3-19), where it is assumed that K=1. But when I use this method, I find that the flow rate is extremely large when compared to some computer modeling numbers that I have in hand.

Can anyone suggest a methodology/equation/way to calculate the flow rates of these guillotine type pipe breaks?

Thanks for any assistance or insight you may be able to provide, JR

Here is the Pump Curve info I have been able to obtain:

head (ft) flow (gpm)
292.37 0
286.6 500
277.12 1000
260.03 1500
231.51 2000
187.86 2500
124.97 3000
39.33 3500

 

[stanier]

You could download PSIM and model the system before and after the event.

http://www.pumpsystemsmatter.org/content_detail.aspx?id=110

Better still invest in dynamic system modelling package such as Impulse.

http://www.aft.com.

"Sharing knowledge is the way to immortality"
His Holiness the Dalai Lama.

http://waterhammer.hopout.com.au/

 

[TD2K]

I don't think you can neglect piping hydraulics though it obviously complicates things.

I agree with the second equation you are using but you are implicitly assuming any upstream piping losses are insignificant compared to the break. I don't think that's realistic when you only have an exit loss of 1.0.

What is your main fire water header: 8", 10"? Even if you had a very short piece of 3" pipe coming off the main header to the break, you would then also have an entrance loss (from the 6" for example into the 3") in addition to the exit loss. Using 0.5 as the entrance loss that gives you a total K of 1.5, not 1. The 3" piping at high flow has a friction factor of maybe 0.017. If you have 10' of 3" piping, that gives a K of nearly 0.7. That's not insignificant compared to an exit K of 1.0 and an entrance K of 0.5. Assume 50' of piping before the break occurs and the flow is significantly lower compared to a clean break of the 3" at the main header.

If we ignore all that and say it's only the exit loss (the 3" piping is sheared off right at the main header), then the pump runs down the curve until the flow from the pump = the flow through the opening. For a 3" opening, I estimate for your pump curve that's about 2,100 gpm (I'm assuming the pump's suction pressure is 0 psig because you didn't provide any data on that). Is that in the area of what you are coming up with?

2100 gpm in a 3" line is 90 ft/sec and with any piping, your line losses would quickly become controlling. That's why I think you aren't buying your numbers.

 

[jrpower]

TD2K, You are correct in saying that the Main Fire header is larger. It is a 12" header then to a 10" header that branches off to 6" headers then down to 4" branches that break down further to then 1", 2" and 3" branches with sprinkler heads.

As for the pump's suction pressure, there are a couple of sizable water storage tanks that I didn't even think about until now since I did consider the suction to be 0 psig.

How did you estimate the 2,100 gpm?

The computer model numbers that I have that were generated a while ago gave a 3" pipe break a flow rate of about 1,800-1,900 gpm which is in my opinion close to 2,100 gpm, using the calculation above, Q = 236 x D^2 x (dP /K x rho)^0.5 and setting K=1, I got a flow rate of 3,447 gpm which is extremely too high and too conservative and for 4" piping the computer generated a value of about 2500-2600 gpm and using the equation, I came up with 5936 gpm.

Thanks for the assistance and any more insight that you have, JR

 

[TD2K]

I was wondering if you had a pressurized water supply to the firewater pumps when you said the pressure is 150 psig (at 150 psi dP across a 3" sch 40 pipe clean break gives me 3444 gpm, basically the same as your 3447 gpm).

However, if your suction pressure is essentially 0 psig, your pump curve doesn't give you 150 psig discharge pressure. At 1500 gpm pump flow, the head is 260 feet which is a differential dP of about 100 psi which gives you 100 psig discharge pressure for a 0 psig suction pressure. To get 150 psig discharge pressure, you'd need a head of about 350 feet.

To estimate the flow, I simply used your formula Q = 236 * d^2 * (dP/(K * rho)). Assume a flow through the pump, use the corresponding head at that flow to calculate the pump discharge pressure and then calculate the flow through the orifice. Adjust the estimate till the 2 are 'about' the same.

I must have made a mistake last night, not sure where as I didn't save all my numbers. Using the above approach today, I get about 2500 gpm.

At 2500 gpm, the head is 188 feet. That gives a discharge pressure of 81 psig (0 psig suction). Assuming all that pressure drop is taken across the 3" break, Q = 2530 gpm, pretty good agreement.

I think the lower flows you are getting with your model is due to the pressure drop through the 4" upstream piping. At 1800 gpm, the dP through 6" piping is 8.4 psi/100' and through 4" piping is about 65 psi/100' (I had to estimate the 4" as Crane's numbers don't go that high).

Take a look at your computer model. There must be a way to see the pressure profile from the pump through the various piping before you get to the 3" 'break'.

 

[77JQX]

I'm with TD2K. To get the flow from a beam break, you need to include the friction in the pipe between the pump and the break. That becomes significant at the high flows found in a beam break. I'd use equations 3-5 for the pipe, and 3-14 for the entrance, exit, and fittings.