Pump Operator Math, Part 2

The other day, I posted a blog about Pump Operator Math. It has occurred to me that I didn't cover as much as I should have, and for that I apologize. I freely admit that I got busy and that I prematurely (keep your mind out of the gutter) posted it before it should have been.

Ok, so the other day I listed several factors:

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

But I didn't cover them all. I stopped at friction loss.

Oops. My bad.

So, let's talk about Elevation Loss (or gain) which in the formulas is represented by EL. Science has proven that for every ten feet of elevation, there is a pressure difference of 4.34#, but in the fire service, we like to try to keep things simpler, so we rounded up to 5#/10ft. If you are pumping up a hill, you will loose five psi for every ten feet of elevation. Conversely, if you are pumping down a hill, you will gain five psi for every ten feet of elevation. Fairly simple, isn't it.

Now for street applications. For this example we are pumping a 2.5" line that is 200ft flowing 250 GPM through a standard fog nozzle which operates at 100 psi, so the standard pump pressure is 125 psi. The house is on a slight hill, and is about ten feet above the roadway. We'll need to add 5 psi, so we're now pumping at 130psi. Say this fire is on the second floor of the house - we'll need to add another 5 psi, so now we're up to 135 psi.

What if that house was down the hill? I'd ask how far down. Say, for example, the house is 30 ft below the road we parked our pumper on, but the fire is on the second floor. Ok, 125 psi - 15 psi + 5 psi = 115 psi. Not too confusing, is it.

Ok. Let's move on to Appliance Loss (AL in the formulas). Appliance losses are caused by using varuios appliances in your set-up. They cause additional turbulence within the appliances themselves that rob flow by increased friction. Wyes, siamese connections, and water thief valves are common examples. Other appliances are master stream devices (deck guns, fly-pipes, and portable monitors).

• AL for Wyes, Siamese, & Water Thief's: Flow < 350 GPM, AL = 0
• AL for Wyes, Siamese, & Water Thief's: Flow > 350 GPM, AL = 10 psi
• Master Stream Applilances: AL = 25 psi

Ok, so, now we are told we have to pump a fly-pipe. At my FD we have simplified it: for the aerial's water pipe system, the elevation, friction loss, and appliance loss is 80 psi. This was figured at full elevation. We don't reduce it if the aerial is not at full elevation. What's the worst thing that'll happen - with no EL, more GPM will flow and the fire will go out faster - I'm good with that! So, we add the nozzle pressure (80 or 100, depending on the nozzle that is on the pipe) to the 80 and pump it at either 160 or 180 psi. That's not counting the friction loss from the pumper to the inlet; we'll hafta add that in, too.

For sprinker systems, at my FD, our SOP is we pump them at 150 psi at the panel. Period. We don't have any high-rise buildings, but do have several mid-rises. The prescribed 150 psi will handle anything we have. If any readers out there have experience pumping sprinkler systems in high-rise buildings, please leave a comment on how your FD covers this.

On standpipe systems, we need to do a little more thinking. For starters, what is the expected flow rate that you'll need to support? You'll need to pump your supply line(s) properly to overcome friction loss for that flow. For the standpipe system itself, at my FD we figure 25 psi for the friction loss. I was told in a class many moons ago that this figure comes from the "propeller-heads" and to accept it. Ok - who am I to argue? ;^) If the crews are operating above ground level, we'll need to remember to add 5 psi for each floor above the ground. (Standpipe PDP = FL (to the connection) + FL (standpipe system) + EL + FL (attack hose) + NP).

Did I miss anything? Probably. But, I feel better now, having covered more of the basics.

FWIW, here's are the coefficients for the most common sizes of fire hose:

• 3/4"   =  1100
• 1"      =    150
• 1.5"   =     24
• 1.75" =     15.5
• 2"      =       8*
• 2.5"   =       2
• 3"      =       0.8**
• 4"      =       0.2
• 5"      =       0.08

(* - 1.5" couplings; ** - 2.5" couplings)


Remember, we need to know the flow desired before we can figure friction loss. Fog nozzles have their flow ratings stamped on them.

The formula to figure GPM for solid tip/smooth bore nozzles is GPM = 29.7 x d² x sqrtNP. The 29.7 is another propeller-head constant; the d² is the square of the diameter of the nozzle tip; and the sqrtNP is the square root of the nozzle pressure. FWIW, the three common nozzle pressures are 100, 80, and 50 psi. Their square roots are 10, 8.94, and 7.07, respectively.

While I am practically giving you the answers to a lot of this, I want you to work SOME of it out! At least I'm giving you the tools!

 While it may LOOK intimidating, it really isn't. Remember, these things are built by people. You can do it! I have faith!