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System resistance curve modelling

System resistance curve modelling

System resistance curve modelling

(OP)
Hey guys, quick question, probably very simple, to do with construction of a system resistance curve in a firewater deluge system model. (So I'm trying to generate the characteristic curve, I already have the OEM pump curve and the actual pump curve from a recent round of testing).

I'm aware that if you have pipes in series, you simply sum up the friction losses for each section and call it a day. However, if I have a branching, open system (and ignoring the static and pressure heads for now) how do I create the total system curve?

The system I'm modelling draws from the ocean and discharges to atmospheric pressure through a large number of nozzles at essentially the same elevation (it's a deluge system).

My thoughts at the moment are to select the branch path (and by that I mean from the very first junction point on the pump discharge line, all the way to ONE particular nozzle) with the highest resistance and then add that on as if it's a simple single pipes in series model. Corrections and suggestions welcome.

Also, as a point of curiosity if in this system I had pipes running in parallel, then rejoining, and then having the system branch off as above, how then do you account for the pressure drop over that segment in the total system curve? Are the parallel branches added together? I'm not quite clear on this one.

RE: System resistance curve modelling

I find it helpful to model each branch and compute the pressure drop for a representative but completely arbitrary flow, then compute a Cv for that branch.

For water, the units of Cv are gpm / sqrt(psid) .
Its inverse may be thought of as a flow resistance.

<tangent>
( The usual textbook definition for Cv is confusing, because it doesn't mention the square root.

{ "... Cv is the volume (in US gallons) of water at 60°F that will flow per minute through a valve with a pressure drop of 1 psi across the valve."
}

See, using 1 psid as the pressure drop is confusing, because 1 is its own square root.

I would like to see the textbooks use phrasing that makes it clear that you can measure the Cv of any pipe or device at any flow by measuring the flow and dividing it by the square root of the pressure drop that you can measure.

)
</tangent>

Then, you can use an electrical analogy to solve for the network's fluid resistance at the pump. Kirchoff's rules apply, even though the 'resistors' are square-law devices.

With the network's equivalent Cv, you can plot a system resistance curve at the pump, and graphically find its intersection with the pump curve.

Of course that technique goes to hell if the pipes are not flowing full, and becomes a little more tricky if there are things like elevated discharge orifices that don't discharge all the time, but with everything on the same elevation, the problem is relatively simple to solve.


Mike Halloran
Pembroke Pines, FL, USA

RE: System resistance curve modelling

I don't think it's that simple an issue.

Assuming that your system is a fixed deluge - i.e. that when you turn it on all your nozzles are flowing water together, then IMO you don't really have a system curve, but a fixed delivery point as the flow won't change, as it should be number of nozzles times flow from a nozzle.

The tricky bit is making the design able to flow the same flow from each nozzle which all have a different resistance from the pressure source.

Again it is a big assumption, but systems like this normally have some sort of variable resistance intended to even out the flow between braches and nozzles. This can be pipe size restriction, variable control valves or variable nozzle orifices to make the flow the same even though the pressure immediately upstream of the nozzle varies between nozzles. It usually takes a bit of time during commissioning to get the flow the same or similar through each nozzle.

Hence take the furthest nozzle away and assume no "artificial" restrictions such as needle valves etc, work out the resistance to flow from that one to achieve the required flow and then work backwards adding the flow from each branch at the fixed pressure needed to run the one furthest away summing your series losses.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

RE: System resistance curve modelling

In any system there will be one controlling path with the highest pressure drop.
Assume flow rates to all nozzles.
calculate the pressure drop in all legs
add the pressure drops up along any path
the largest one is the critical path, so to speak
If you are happy with the inlet pressure required, and can adjust the nozzles for the flowrates that you have assumed, you're basically finished.

If you can't adjust the nozzles for flow rates, then you will have to calculate new flowrates in each branch, given the inlet pressure to the branch at its connection point. Then you will have to redistribute the feeding flowrates to equal the outlet flows. Then recalculate the pressure drop etc.

It is what can be a long iteration process.
Do you know about EPAnet? It's free. Or AFT pipe flow.
Take it from me, get a program, or get out of the business right now.

I hate Windowz 8!!!!

RE: System resistance curve modelling

It is messy because the flow out each of your nozzles is a function of the dP across the nozzle and the flow area. Tiny changes from nozzle to nozzle can have a huge impact on total flow rate.

I would take a few of the lines and calculate a dP based on nominal flow rate (it is an iterative exercise). From that I'd get an average dP from the pump to a nozzle and an average flow rate, multiply the flow rate times number of nozzles, add a safety factor, and buy a pump that could do that much flow into that much back pressure. I haven't had a lot of luck getting commercial models to match reality in minimal backpressure scenarios. I usually do this kind of problem by hand (i.e., in MathCad) and put in a pretty healthy safety factor (125% of predicted hp is my usual).

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

RE: System resistance curve modelling

The other way to do this is to significantly oversize your header and branch / loop system such that the pressure drop in the pipework is a small fraction (10-15%) of the overall pressure drop where the nozzle takes the remaining 85 - 90% of the pressure drop and essentially the same pressure exists at all parts of your system. Then it's a relatively simple addition of the flow through your nozzle at some assumed pressure from your pump times the number of nozzles.

Then add 25% extra as my esteemed other posters note above.

Trying to optimise pipe size to do it another way is sometimes just too hard and takes too long depending on the number of nozzles and branches you have. You might spend double what you save during commissioning running around setting different flow rates in different branches whilst you're getting soaked with water...

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

RE: System resistance curve modelling

Back in the day, I used the Hardy Cross Method when designing fire protection systems.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

RE: System resistance curve modelling

(OP)
Thanks guys. BigInch seems to have nailed exactly what I'm after. Thanks everyone for your input.

RE: System resistance curve modelling

You mean the, "Get a program, (I'll add, "Find someone who's got one"), or get out of the business right now", part ... I presume.

I hate Windowz 8!!!!

RE: System resistance curve modelling

(OP)
Nah we usually just contract this stuff out and let a 3rd party use HYENA to model the systems, I just wanted to get an idea of changes to the system curve with some quick excel calcs. Was interested in the 'critical path' stuff.

RE: System resistance curve modelling

I would plot on a semi log hydraulic graph based on the Hazen William equation to plot the performance curve that you are seeking. Select the longest line between the pump intake line and the furthest nozzle which you will plot the flow rate of water (horizontal axis) vs. friction loss. The equation preferably used in fire science is the Hazen William equation. Each segment of pipe with different dia. can be plotted individually by assuming a flow rate ( such as 1000 gpm) for which there will be friction loss (in this case psi for unit). Only one point for each straight line is necessary. These lines can be added to ultimately give a performance curve of the system. Be careful when you plot these lines on the graph paper because some lines will be in series and others maybe in parallel. Lines in series will have a common flow rate whereas lines in parallel will have equal pressure drop when you plot them to be added. The semie log paper should be based on the equation mentioned above and attached is a copy of the semi log graph. Notice the horizontal axis which is based on the N=1.85. There are flow rate vs. psi tables for varying pipe sizes and these tables are based on 100' long pipes. Don't forget to add the equivalent lengths for the fittings and valves and to add the extra length at the intake to the pump. Using this technique is fast and easy with no need for iterations or the Hardy cross method.

RE: System resistance curve modelling

I was working on big boats a while back.

I got to choose an orifice associated with only one of multiple possible sinks, part of the engine exhaust system. The boatbuilder laid out the plumbing according to his whim or lore, and the engine manufacturer selected the pump, and decreed a range of acceptable pressures after the heat exchanger downstream of the pump.

I used to do it BigInch's way or Zdas04's way, but iterative solutions presented huge logistical problems, what with getting to the boat, getting the boat to deep water, running it flat out for a while, and getting someone else to pay for the crew and for the fuel consumed.

Adjustable anythings are bad on boats, because random twiddlers will move them, and because the class societies insist that adjustments cannot be wired in place or otherwise locked, so that random twiddlers _can_ move them.

I started using the Cv or its inverse and modeling the system as an electrical network so that I could get my orifice right, or close enough, before the engines were started, so I only had to go to the boat and deal with an irate billionaire if I screwed up.

I also had some success with 'Streamlines', a free DOS program (the manual costs $75, cheap). It requires ANSI.SYS (remember that?) or an equivalent. I have been able to make it run under WindowsXP. So far I have not been able to make it work under Wine and Linux.

Mike Halloran
Pembroke Pines, FL, USA

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