
04112011, 02:39 PM #1
 Join Date
 May 2010
 Posts
 2
Complex relay with hoses of varying diameter
Ok, here is my question. I was recently asked to calculate the PDP on a relay operation. Being the supplying pumper I need to pump 1550 gpm through a 3" with 2 1/2" couplings and a 4" line, the distance was 500'. I came up with a method that I thought would work for calculating the friction loss and I was wondering if this would have worked.
With out a given pump chart with the calculated friction losses for this configuration of a Siamese set up, I originally split the flow in half and calculated the friction loss in each hose section which inturn had different numbers. I had trouble with this concept because I know if I pumped the 4” at the same pressure of the 3” I would be giving them too much water, which isn’t bad, but it would be too high of pressure.
The method I came up with was to look at the friction loss chart reference the PSI and GPM numbers until the friction loss in 100’ for both sizes was similar enough, within 510 psi, and the sum of the two GPM’s equaled 1500.
I brought this theory and method to my training officer and he said that he hadn’t seen that method before and wasn’t sure if it would work or not. Everyone else that I’ve asked couldn’t answer definitively one way or another. Could someone please let me know if this method is flawed or if it truly works? I could supply the numbers for the friction loss if you need them.

04112011, 05:44 PM #2
 Join Date
 May 2000
 Location
 Wisconsin
 Posts
 29
lots of assumptions
First off assume the formula friction loss (FL) = C*Q^2*L is correct with C the coefficient of friction for the hose size, Q is the flow in hundreds of gallons per minute and the value will be squared, and L is the length of hose in hundreds of feet.
One way to look at this problem is to pick a discharge pressure and work backwords, or pick a flow and see what happens. So for the sake of trying something assume 100 psi discharge pressure for each line.
Line 1 is 500 feet of four inch hose (Coefficient 0.2) we will pump the line at 100 psi if we solve for Q the flow we find
100= 0.2*(Q^2)*5 do a little algebra and rearrange you get
square root (100/.02*5)= Q = 10 as in 10 hundred gallons per minute or 1000 gallons per minute
Line 2 is 500 feet of three inch hose (Coefficient 0.8) we will also pump this line at 100 psi, solve for Q the flow
100=0.8*(Q^2)*5 do a little algebra and rearrange you get
square root (100/0.8*5)=Q = 5 as in 5 hundred gallons per minute or 500 gpm
So if you were pumping this theoretical relay and you needed to flow 1550 gpm through a length of four inch hose and a length of three inch hose 100 psi discharge pressure should account for the friction loss, you should also account for a residual intake pressure for the pumper you are supplying so add 20 or 30 pounds for that, plus maybe some pressure for a siamese appliance or so. So my initial pressure to start out would probably be 125 psi., get water flowing in the system and adjust as necessary.
On the practical side if I pulled up my engine and hooked into this system at o dark thirty I would look at my pump chart for four inch, treat the three inch hose as four inch, split flow for the four inch and estimate high for the number, by that expect to flow 900 gpm per hose, add 25 pounds to that friction loss (my pump chart 81 pounds+25=106), fill the hose with water, and throttle up to my guestimate pressure, and wait for the guy downstream to ask for more or less. But this number is really a slightly scientific wild *** guess.
So yes your method of finding the pressure works. It is basically doing what I did with formulas by looking at a chart. The caveat is that numbers derived from charts or formulas without actual testing are just estimates to get you in the right ballpark.Last edited by Rhinofire; 04112011 at 05:47 PM. Reason: clarification

04112011, 07:09 PM #3
 Join Date
 Jan 2007
 Location
 Pa Wilds
 Posts
 605
Smithnatester: Rhino is right on with his treatment of the formula except that it needs to be solved for the combined "C" value. It just so happened that his choice of flows was really close to what you needed in the problem. If you are regularly faced with feeding parallel lines of different diameters, then the following might be helpful: A 3" line handles about 1/2 the flow of a 4" line. (See Rhino's example for 100 psi loss and 500 gpm in the 3", with 1,000 gpm in the 4" line) A 5" line handles about 3 1/2 times the flow in a 3" with 2 1/2" couplings. If you decide to evaluate your particular hose, you will find the friction loss (c value) can change with the pressure, because some hoses stretch in diameter as the pressure is raised. Using Rhino's figures for a flow of 1500 gpm with a friction loss of 100 psi, then the combined value of C would be 0.08889. Putting the desired flow of 1550 gpm into the equation we get a friction loss of 106.8 psi for the hose arrangement. Feeding two master streams with 1 3/4" tips would require a total flow of 1640 gpm. Using the C value calculated above your 500 ft. lay would have a friction loss of 120 psi or an engine pressure on the supply engine of 150 psi and an incoming engine pressure at the attack engine of 30 psi. It is nice to do the numbers to see how well the theory works, but in the real world...Make The Darn Think Work. Throttle up and keep everyone happy. Use the radio or hand signals...Just get the job done!

04132011, 03:31 AM #4
 Join Date
 May 2010
 Posts
 2
Rihnofire and KuhShise: thanks for the help. i know that i just need to get the wet stuff on the red stuff however i can. i just was currious about formulas to put me in the ball park for the necessary pressure and that i'm not overloading one hose line or losing most of the water out of the intake pressure relief valve on the attack pumper.
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