Hydraulic grid calcs (fire sprinkler)... how does it work?

[frostrap]

Hello all, this is my first post here and I'm hoping you will be able to help me in my search for an answer.

I am a fire sprinkler designer. I also enjoy math (took math through calculus, but stopped short of differential equations). I have a pretty good grasp on calcing trees and simple loops by hand, but am interested in knowing more about the math behind how complex grids are calculated.

I have been searching for answers for a long time now, but apparently haven't been looking in the right direction because I haven't found any clear answers. (The descriptions of the process that I have found have been vague.)

So far what I have learned is that it would be extremely time consuming to calculate a gridded system by hand. However, I am nonetheless interested in knowing how to do such a thing for my own sake.

Do any of you have any resources in the way of books or un-compiled software, or written algorithms that I could study to help me understand more specifically how a grid is calculated?

Thanks!

Joe

 

[MortenA]

I saved an old article from chemical engineering 1995 by T. W. cochran titled "Simplifying piping network analysys". This should work for simple piping networks (e.i. rings with "shotcuts".

You could take a look at this.

The "real" simulators uses differential equations solved by use of eigenvectors and stuff like that (its +15 years since i leared this and even then i found it difficult).

Best regards

Morten

 

[chicopee]

First,you should understand NFPA 13 (sprinkler system)which is prerequisite to the next NFPA 231C(rack storage protection) before involving yourself with the worksheets used in the industry.
Secondly you should understand about sprinlker and hydrant flow tests to insure that you have adequate water to the sprinklers.
thirdly,if you are still interested, I'll fax you some examples in about two to three weeks.

 

[BigInch]

For a basic understanding of loops and gridded system hydraulic analysis search for Hardy-Cross method. No differential calculus req'd.

"I think it would be a good idea."
- Mahatma Gandhi (1869-1948),
when asked about Western civilization

 

[frostrap]

Thanks for your replys!

Morten, I am interested in seeing that article. I'll see if I can dig it up.

Chicopee, I am familiar with NFPA 13 (live in it every day), and though I typically do my calcs in HASS, I do know how to do trees and simple loops by hand using calc sheets. If you have any examples describing the calculation of a gridded system I'd love to see them.

BigInch, I have searched under the Hardy-Cross method and have gotten some reasults, but am hoping to find some examples or descriptions of the process that go beyond explaining a basic loop.

I get a little confused about the process once the grid being calced has more than one "loop" in it.


I can figure this loop out:

----------
| |
----| |
| O
| |
----------


And I understand this grid conceptually, but I am confused about how to apply hardy-cross correctly:

---------------------
| | |
----| | |
| O O
| | |
---------------------

 

[BigInch]

Each loop has an unbalanced flow and adjustments to all pipes in a loop are made. That is done in turn for each loop in the system. Thus, any pipes that are common to several loops have their flow adjusted several times, one time for each loop.

"I think it would be a good idea."
- Mahatma Gandhi (1869-1948),
when asked about Western civilization

 

[frostrap]

I totally get where you're coming from BigInch.

Is there a way that I can post an image or somethere here so that I can use that to explain my confusion?

 

[BigInch]

You can post an image by clicking the text to the right of the paper clip on Step 3 when you post a reply.

"...or upload your file
to ENGINEERING.com"

OR

Just send it to me.

Google "virtualpipeline" and you'll get my e-mail address on the first hit.

"I think it would be a good idea."
- Mahatma Gandhi (1869-1948),
when asked about Western civilization

 

[frostrap]

Alright, maybe you can walk me through the example I through together.

The example shows a simple grid with a single sprinkler at node 6 that is flowing 20gpm at 10psi. Water is entering the system at node 1.

Ignoring the line from node 4 to node 8, this is a relatively simple system to solve using Hardy-Cross. I know a the pressure at node 6. First I would I assume a flow through the path 6-5-4-3-2 and another flow through path 6-7-8-9-2. I would figure friction losses through each path and determine the resulting pressure at node 2. If the pressures don't equal within some acceptable limmit, I adjust the flows through each leg of the loop and start over. This repeats until an acceptable balance is found.

The problem is that my mind gets blown as soon as the line from node 4 to node 8 is added. I get confused when trying to pick a starting point and when trying to choose where to flow the water.

This is my thought process when adding the piece from node 8 to 4 into the loop:

Since I already calced the loop ignoring the piece from 4 to 8, I presumable know the pressure at 4 and 8. Let's assume node 8 has higher pressure than node 4. I would expect water to flow from 8 to 4. So, I would subtract some flow through path 8-7-6 and send it instead through path 8-4-5-6. (Things are starting to come apart in my mind.) I would then have to go through the same balancing process that I described earlier to see if the new flows checked out.

Ok that's about as far as I ever get. Can someone help me untangle my brain? The idea of what we are trying to achieve is in my head, but I can't for the life of me get my mind around the actual process step by step.

How would you approach the solution?

Thank you all for your help so far! I've been trying to get help with this for months!

- Joe

 

[RWF7437]

The short answer: Get EPANet2 ( it's free ):

http://www.epanet.com/downloads

Longer answer:

All water pipe networks, and many others, can be analyzed using the Hardy Cross method. This is an iterative solution (fancy way of saying trial and error ) to the problem. It depends on the fact that around each loop om the system the headlosses must be the same AND the flows in to the loop must be equal to the flows out of the loop. Get EPANet and read the documentation and look at the examples and this will all become clearer. No need for higher math, matrix algebra, Black Magic or witchcraft.

good luck

 

[frostrap]

Good, I was concerned about having to use witchcraft.

I'll check out that site, thank you for the resource!

Any other resources that you folks might have would be fantastic, thanks!

- Joe

 

[BigInch]

I thought you wanted to understand how it works, or do you just want to do data entry?

"The problem is that my mind gets blown as soon as the line from node 4 to node 8 is added. I get confused when trying to pick a starting point and when trying to choose where to flow the water." You're going to have that problem with epanet too. You start at the water source and flow to wherever sprinkler is open. That's all there is too it. First pick the most direct route between the two, calculate the pressure drops along that route assuming all flow follows that route (zero flow in other pipes). If you get to zero pressure, redistribute some parts of the flows into branches, or reduce all the flows.

Once the initial flows are set up, you have to go around and around in a logical manner from pipe to pipe until the errors are small enough to be acceptable. A spreadsheet (using the Churchill flow equation) can easily be written to solve a 3 or 4 loop system. Each iteration takes a couple of lines, new flows, new errors, new balanced flows. Copy and paste each line, until you have acceptable errors on the bottom line.





"I think it would be a good idea."
- Mahatma Gandhi (1869-1948),
when asked about Western civilization