How Can I Calculate Fluid Flow from a Ruptured Pipe?

[construction dude]

I need help. My associate called from the job site and said,
"This building we're inspecting in Alaska had a 1/2" pipe freeze and then completely broke open at the compression ring. Water was freely running over the weekend. How many gallons per minute do you think was being dumped?"

Assume water pressure is 50 psi (it was a commercial building located in the city) Given the equation, we can always adjust if we find out it should be 60 psi or something else.

Assume it was clean water

How do I simply calculate the rate water was being lost?

Thanks in advance for your help!

 

[KSCphysics]

try usin bernoulli's equation..

$$p_{1}+\rho gy_{1} + \frac{1}{2} \rho v_{1}^2= p_{2} + \rho gy_{2} + \frac{1}{2} \rho v_{2}^2$$

 

[construction dude]

I don't know how to use bernoulli's equation.

I want to find flow rate. As I stated, all I know is the diameter (and therefore the crossectional area of the pipe). I'm assuming that municipal water pressure is 50 psi. I don't understand why gravity is an issue. I don't know the pressure drop between node 1 and node 2. I don't know the difference between velocities at node 1 and node 2. Heck, I don't even know fluid density. Can I assume 1 since it is clean water?

I'm not being lazy, I just don't know what the heck I'm doing, Please, can some one help me here?

 

[Michael D. Sewell]

Yeah, I'll help. You just figure about 4 gallons per minute, unless it is near the beginning of the system, then it could be 3 times that much. It depends on how many feet of pipe it flows through, and how many fittings and what kind of fittings. I have done quite a few flow tests; seldom have I gotten much more than 4 gallons per minute.

If you give me the information on pressure, type of pipe, length of pipe, number and type of fittings, I can give you a better estimate.
-Mike

 

[construction dude]

Thanks Michael!

Pipe is 1/2" copper and let's assume no line loss due to elbows, fittings, etc... I don't know how far the break was from the water main leading into the building.

Does it make a difference if the pipe is horizontal or vertical at the rupture point? I don't know which it was.

What is the equation to calculate the flow. If my associate can verify the PSI and measure the length from the water main to the break, then he can plug in those numbers later.

Thanks for your help!

 

[Michael D. Sewell]

Thanks Michael!

Pipe is 1/2" copper and let's assume no line loss due to elbows, fittings, etc... I don't know how far the break was from the water main leading into the building.

Does it make a difference if the pipe is horizontal or vertical at the rupture point? I don't know which it was.

What is the equation to calculate the flow. If my associate can verify the PSI and measure the length from the water main to the break, then he can plug in those numbers later.

Thanks for your help!

Laminar flow and no friction loss would give you over 34 gals/min. I doubt that this is the situation here, but I'd need more information to tell you.

The horizontal or vertical part really only applies like this:
How high above the pressure gauge is the break? What we want is pressure at the break, not at the gauge.

This is not meant to be a criticism, but you have already rejected Bernoulli's equation; and the equation that you need is an empirical one based on Bernoulli's equation and Torrecelli's theorem(same thing really), which is much more difficult to work with.

If you can get your hands on a good book on plumbing, you will find flow tables that include losses for height, length, fittings, and valves. Then you can solve your problem without much sweat. Otherwise all I can do for you is make a wild guess, unless I have more information. I don't think that me telling you between 4 and 34 gals is what you want.

Your other way to do this(and this is really the best way anyway) is to:
1.) Take a bucket and determine it's volume.

2.)At the job site(or your location if you must), time how long it takes to fill the bucket with water under the same conditions that were present at the time of the leak.

3.)Divide the volume of the bucket by the time in seconds that it takes to fill.
Multiply this figure by 60 secs/min and that is your flow rate per minute.

I have to leave to check on a construction job of my own, so I won't be able to help you any more for several hours. If you need help sooner, you could try to reach Russ Waters on this forum, I'm sure he can help you if he has time. He's an HVAC guy, and a mechanical engineer(and a sharp one at that).

If I can be of any further assistance let me know.
-Mike

P.S. Hire yourself a good engineer, you'll be glad you did. In the long run, a good engineer doesn't cost you a nickel.