Pump Operator Math

As is tradition at my FD, we just completed another round of annual promotional exam testing for positions of Captain, Engineer, and Inspector. Every year we study, cram, take classes, what ever, all for the chance at scoring good enough to get on the promotional list.

This got me to thinking...

I've been an Engineer at CJC for several years now; six years since being permanently promoted, nearly seven if you count the nine months I was temporarily promoted. I've also had experience operating pumps and aerials at St. Joe Fire and at Camdenton Fire, as well as a few part time fire department jobs I worked at over the years. I think I get the job done - well, at least I haven't had too many complaints for over- or under-pumping a line. (The one under-pumping complaint I can think of as I write this was attributed to a kink in the line, which I handled shortly after the attack began.)

I actually have been studying pump operations since I was about ten or eleven years old, when my dad was a fireman on the Brookfield Vol. Fire Co. in Brookfield, CT. One Saturday after we got the yard work done I asked him how he knows what to pump the fire hoses at. He asked me if I wanted the short or long answer. I said to hit me with the short answer, and he said, "150 & pump." I guess I looked genuinely confused, cuz he was grinning when I asked exactly what that means. He then said it appears I want the long answer, and for that, perhaps a trip to the firehouse was in order. We spent the afternoon up there, and he taught me the theory of FL and why we need to know what we are going to flow, and even set up some demonstrations for me using one of the pumpers and a pitot gage. I was hooked!

Over the years, I have had the honor of helping younger members study for the upcoming exam. Lately, the exams cover less of the math and more of the policies and SOGs at our department. I can't complain, although, in my less-than-humble opinion, knowing the math - by this I mean KNOWING IT COLD - is the bread and butter of pump operating. Yes, engineers do other jobs too, like running aerials and other support apparatus, however, this post will be confined to the general topic of pump operating.

Why is pumping a line at the proper pressure important? The answer seems simple enough - so you can supply the proper flow to the crew and they can then put the fire out in a quick, safe, and orderly manner.

While that answer is seemingly simple enough, there are several factors a pump operator must consider:

• hose size
• length of hoselay
• needed fire flow
• nozzle type
• nozzle flow rating
• nozzle operating pressure
• friction loss
• elevation pressure loss OR gain
• appliance loss
• standpipe friction loss
• sprinkler connections
• pumping an aerial fly-pipe (at my FD we pump it at either 160# or 180#, depending on which truck we are dealing with, due to their nozzle types)

Quite a lot to think about, ain't it - especially when you are the driver of a pumper arriving at a well established fire in a large apartment building at double-dark-thirty.

Hose size - by this I am referring to the internal diameter of the hose. Each size has its own friction loss properties. The length of the hose lay also effects the friction loss. So does the flow of water through the hose.

What type of nozzle are you pumping to? For handlines, a smooth bore is generally pumped at 50 psi; if pumping a master stream appliance with a smooth bore tip on it, you pump it generally at 80 psi. A standard fog nozzle operates at 100psi. However, there are several models of fog nozzles available now that operate at lower pressures, such as 80 psi, 75 psi, and 50 psi. Confused yet? It's ok, so am I sometimes. Just try to relax, remember to breathe, and think it through, one step at a time.

Ok, so now let's talk friction loss. The formula is: FL=CxQ²xL. "C" is the hose "Coefficient", also referred to as the "Constant" or the "C-Factor". It doesn't matter really, it is the same thing. It just depends on who is teaching the class you are taking. Basically we have to trust that the taped-glasses wearing, pocket protector using, propeller-head types know what they are doing (they do) and they have spent years coming up with this stuff. "Q²"is the GPM (flow, in gallons per minute) divided by 100. "L" is the length of the hose line divided by 100.

Wow... if THAT ain't a mouthful...

Ok. Now we need to know what we are flowing. The fog nozzles on my engine company are rated for 200 GPM @ 100 psi of nozzle pressure (aka: NP). The nozzles on my FD's truck company are rated for 150 GPM @ 50 psi NP. (Frankly, I wish we had those fog nozzles too, along with a good set of smooth bore nozzles, but we don't, not yet.) See what I meant about what type of nozzle and what operating pressure they work at? Just two different companies in the same department with drastically different nozzles. FWIW, there is another engine company at my FD that has the same nozzles my company does. Both pumpers are water pumpers. There are two other engine companies that are CAFS pumpers, and they have TOTALLY different nozzle types. We'll skip that for now.

Our SOG's call for an initial attack line to be able to flow 160 GPM. This is easily attainable with our 1.75" lines. Now begs the question, But Ken! You just said your engine company's nozzles are rated for 200 GPM @ 100 psi! How do you pump it for 160 GPM?"  I'm glad you asked. I simply figure the friction loss for the length of line for 160 GPM, then add 100 psi to it for the NP.

(For those of you keeping score, that means for 160 GPM I pump the 150' lines at 160 psi and the 200' lines at 180 psi. For the 200 GPM, I pump the 150' lines at 190-195 psi and the 200' lines at 210-215 psi. Both of my engine's 2.5" preconnects are pumped at 125 psi to start, which is 250 GPM.)

So, is this exactly 160 GPM? No, it's not. But it's worked for me for years when pumping this style of nozzle. I should note that where obvious larger flows are needed, I pump it at the higher pressure for the 200 GPM. If this doesn't work, then it's time to consider larger lines & master streams. You may ask, Well, Ken, how can you KNOW what you are flowing when you think you're flowing 160 GPM? We can hook up to a calibrated flow meter and then we will KNOW what we are flowing. We don't have one, though, so we're good with shooting from the hip.

Here is a chart of the FL in 1.75" hose for various flows:

• 100 GPM = 15.5 PSI/100 FT
• 125 GPM = 24 PSI/100 FT
• 150 GPM = 35 PSI/100 FT
• 160 GPM = 40 PSI/100 FT
• 170 GPM = 45 PSI/100 FT
• 180 GPM = 50 PSI/100 FT
• 185 GPM = 53 PSI/100 FT
• 200 GPM = 62 PSI/100 FT
• 210 GPM = 68 PSI/100 FT
• 250 GPM = 96 PSI/100 FT

Here is a rule for FL - in any size hose - that I want you to tuck away for potential future use:

WHEN THE FLOW RATE DOUBLES, THE FRICTION LOSS INCREASES FOUR TIMES!

Look at the flows of 100 & 125 GPM, their respective FL #'s are 15.5 & 24 PSI for every 100 ft of hose you are pumping through. Now look at the 200 & 250 GPM - their FL #'s are 62 & 96 PSI for every 100 ft of hose you are pumping through. Why is this important? Well, I have seen some folks out there throughout my career who incorrectly presumed that since a nozzle is stamped for, say, 200 GPM at 100 psi, that you only had to pump the line at 100 PSI, no matter how long the lay was. They were seriously underpumping lines - making it inherently UNSAFE for the crews, and frequently being told to increase the pressure by crews using the lines.

A little off topic, but still related and very important - the 1.75" hose line, while it is capable of flowing high flows, is a very squirrelly line to handle when you kick up the GPMs and have higher nozzle pressures. We can discuss more on this later. (Or, feel free to contact me and I'll be happy to share my thoughts.) My point is, if you are going to flow higher flows, either use lower pressure nozzles or larger lines, or both.

Here is a chart of the FL in 2.5" hose for various flows:

• 200 GPM = 8 PSI/100 FT
• 210 GPM = 9 PSI/100 FT
• 225 GPM = 10 PSI/100 FT
• 250 GPM = 12.5 PSI/100 FT
• 265 GPM = 14 PSI/100 FT
• 300 GPM = 18 PSI/100 FT
• 325 GPM = 21 PSI/100 FT
• 350 GPM = 25 PSI/100 FT
• 400 GPM = 32 PSI/100 FT
• 500 GPM = 50 PSI/100 FT
• 750 GPM = 113 PSI/100 FT

Here is a chart of the FL in 5" hose for various flows:

• 250 GPM = 0.5 PSI/100 FT
• 500 GPM = 2 PSI/100 FT
• 600 GPM = 3 PSI/100 FT
• 700 GPM = 4 PSI/100 FT
• 750 GPM = 4.5 PSI/100 FT
• 800 GPM = 5 PSI/100 FT
• 900 GPM = 7 PSI/100 FT
• 1000 GPM = 8 PSI/100 FT
• 1250 GPM = 12.5 PSI/100 FT
• 1500 GPM = 18 PSI/100 FT
• 1750 GPM = 25 PSI/100 FT
• 2000 GPM = 32 PSI/100 FT

While there are other common sizes of fire hoses within the United States Fire Service, these are the sizes used at my FD, and are what I am familiar with.

Okay, that's enough for one day. Thanks for reading. Any questions, please feel free to contact me.

Stay safe, and God bless you.

Ken