Friction Loss Formulas

Different ways to calculate Friction Loss (FL), Appliance FL, Elevation loss

Fire Hydraulics

 
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NFPA 1002

 

Fire Apparatus Driver/Operator

Standard For Fire Apparatus Driver

Minimum job performance requirements for firefighters who drive and operate fire apparatus.

   

 

NFPA 1914

 

Testing FD Aerial Devices

Specifies minimum inspection and testing requirements for aerial devices to insure a minimum degree of safety for continued use.

Applicable to aerial ladders, platforms and water towers.

   

 

NFPA 1911

 

Fire Pumps

Service Tests of Fire Pump Systems on Fire Apparatus

Establishes site, environmental, and equipment requirements for proper pump system performance testing as well as frequency and procedures.

   

 

Friction Loss

 

Friction Loss In Fire Hose:

Friction loss (FL) is the most important variable to be considered in fire ground hydraulics. Each appliance, fitting, coupling, section of hose and everything else through which water flows will impede the flow through friction. All of these factors may vary with condition, design, manufacturer, and age of hose and appliances: therefore, no exact allowances can be made for friction loss. Use of parallel lines of hose reduces friction loss to approximately 28% of what it is with a single line, for the same flow of water. Friction loss in 3" hose with 2 ½" couplings is about 40% that of 2 ½ " hose. Thus, with the same engine pressure (EP), it is possible to use a line of 3” hose two and one half times as long as one of 2 ½, to get the same nozzle pressure (NP) with the same size nozzle. Having 2 ½ “ couplings on a 3” hose only increases friction loss by about 5%: using the same size couplings on both 2 ½ “ and 3 “ hose makes it possible to use these sizes interchangeably. Pumps provide rated capacity (100%)  at 150 psi net pump pressure and only 70% of rated capacity at 200 psi net pump pressure and at 250 psi net pump pressure, the pump will discharge 50% of rated pump capacity. By the use of formulas bellow, it is evident that the friction loss in a hose is based on the quantity of water flowing. Friction loss will remain constant as long as the GPM remain the same. Regardless of the pressure the friction loss in a given flow is approximately constant.

FL =C Q²L

FL = friction loss in psi

C = friction loss coefficient

Q = quantity of water flowing or flow rate in gpm

L = hose length inhundreds of feet

 

Q = gpm/ 100

Q = hundreds of gpm

GPM = actual flow through hose

100 = a constant

 

L = hose length/100

L = hose length in hundreds of feet

hose length = actual length of hose

100 = a constant

 

Hose Diameter and Type (inches) Coefficient (C)
3/4 inch booster 1100
1'' booster 150
1 1/4 ''booster 80
1 1/2 ''rubber lined 24
1 3/4 with 1 1/2'' couplings 15.5
2 1/2'' rubber lined with 1 1/2'' couplings 8
2 1/2 rubber lined 2
2 3/4'' with 3'' couplings 1.5
3'' with 2 1/2'' couplings 0.8
3'' with 3'' couplings 0.677
3 1/2'' 0.34
4'' 0.2
4 1/2'' 0.1
5'' 0.08
6'' 0.05
4'' standpipe 0.374
5'' standpipe 0.126
6'' standpipe 0.052

 

Different way to calculate Friction Loss (for 2 1/2'' hose) is to use formula  FL = 2Q2 + Q  for flows  greater  than 100 GPM and FL = 2Q2+ ½ Q for flows less than 100 GPM.

To get FL for hose larger or smaller in diameter than 2 1/2'', first you find FL for 2 1/2'' by using the formula above, than the result should be multiplied or divided  (whether multiplication or division is used is up to personal preference) by the appropriate conversion factor from the table:

 

Diameter and Type (single line) Divide by Multiply by
3/4'' booster 0.0029 344
1 booster 0.011 91
1 1/4'' rubber lined 0.025 40
1 1/2''  rubber lined 0.074 13.50
1 3/4 '' rubber lined 0.16 5.95
2'' rubber lined 0.34 2.94
3'' rubber lined 2.60 0.385
3'' rubber lined with 2 1/2'' couplings 2.50 0.40
3 1/2'' rubber lined 5.80 0.172
4'' rubber lined 11 0.09
4 1/2'' rubber lined 19.50 0.051
5'' rubber lined 32 0.031
6'' rubber lined 83.33 0.012
1 1/4'' unlined linen 0.0157 63.60
1 1/2'' unlined linen 0.039 25.60
2'' unlined linen 0.16 6.25
2 1/2'' unlined linen 0.14 2.13
SIAMESED LINES OF EQUAL LENGTH Divide by Multiply by
Two 2 1/2'' 3.60 0.28
Three 2 1/2'' 7.75 0.129
Two 3'' 9.35 0.107
One 3'', One 2 1/2'' 6.10 0.164
Two 2 1/2'', One 3'' 11.50 0.087
Two 3'',One 2 1/2'' 15 0.067
STANDPIPES Divide by Multiply by
4'' 7.50 0.133
5'' 22 0.045
6'' 52 0.019
     

 

FIND FRICTION LOSS:  ( USE 2Q² + Q  or CQ² L )

 

 

Rate of Friction Loss Increase (ROI)

ROI = V² /

V = new velocity flow

v = old velocity flow

 

New Friction Loss  ( NFL ) resulting from an INCREASE in the Velocity Flow

NFL = ( V² / v² ) FL

NFL = New Friction Loss

V = new velocity flow

v = old velocity flow

FL = old friction loss

 

Relationship Between Different Size Hose Lines (equivalent length -  EL)

EL = ( C1 / C2 ) L

EL = equivalent length

C1 = coefficient of smaller line

C2 = coefficient of larger line

L = hose length in hundrends of feet ( length / 100 )

 

Friction Loss Coefficients for SIAMESED Lines of EQUAL Lengths

 

Two 2 1/2'' 0.5
Three 2 1/2'' 0.22
Two 3'' with 2 1/2'' couplings 0.2
One 3'' with 2 1/2'' couplings, one 2 1/2'' 0.3
One 3'' with 3'' couplings, one 2 1/2'' 0.27
Two 2 1/2'', One 3''  with 2 1/2'' couplings 0.16
Two 3'' with 2 1/2'' couplings, one 2 1/2'' 0.12
STANDPIPES  
4'' 0.374
5'' 0.126
6'' 0.052

 

 

 


 

 

APPLIANCES

 

 

> than 350 GPM  Friction loss = 25 psi 

Siameses and wyes - less than 350 GPM Friction loss  = 0 psi 

Siameses and wyes = greater than 350 GPM Friction loss = 10 psi

Clappered Siamese(ladder trucks) = 10 psi

Portable Monitor = 25 psi

Wagon Battery = 25 psi

Hush pumpers  "deck" gun = 15 psi

Pierce pumpers "deck" gun = 25 psi

Seagraves pumpers "deck" gun = 30 psi

American LaFrance "deck" gun = 60 psi

Ladder Pipe = 80 psi (Note: Please check your department SOP and ladder specs.)

Standpipe = 25 psi 

Sprinkler Inlet whether or not fire is showing pump at 150 psi (Note: Please check your department SOP).

 

 

   

 

ELEVATION   PRESSURE

 

 

Elevation Pressure = 0.5 H

Elevation Pressure = Elevation pressure in psi

0.5 = A constant

H = Height in feet

(Total Height minus 10, than divide by half, or number of stories minus 1)

5 psi per floor or 5 psi per 10 feet ( It is 4.5 psi but we are using 5 psi)

Mountain slopes - use 5 psi per 100' of hose layout ( Again, it is 4.5 psi but we are using 5 psi in the field )

 

PRINCIPLES OF FRICTION LOSS

 

 

1. IF ALL OTHER CONDITIONS ARE THE SAME, FRICTION LOSS VARIES DIRECTLY WITH THE LENGTH OF HOSE OR PIPE.  Double the length, double the friction loss.

2. WHEN HOSE, ETC. ARE THE SAME SIZE, FRICTION LOSS VARIES APPROXIMATELY WITH SQUARE OF THE INCREASE IN THE VELOCITY OF THE FLOW.  Double the speed of the water and increase friction loss by four times.

3. FOR THE SAME DISCHARGE, FRICTION LOSS VARIES INVERSELY AS THE FIFTH POWER OF THE DIAMETER OF THE HOSE.  At a given GPM, friction loss is cut by four times when you increase the diameter of hose from 2 1/2'' to a 5'' hose.

4. FOR A GIVEN VELOCITY, FRICTION LOSS IS APPROXIMATELY THE SAME, REGARDLESS OF THE PRESSURE OF THE WATER.  Friction loss is VELOCITY based.  The faster you move it, the more friction loss occurs.

At a given quantity of flow, friction loss in nearly independent of pressure.  The velocity of water through a hose line, not pressure, causes friction loss. Other factors affecting friction loss in hose line include: rough lininings in the hose, sharp bends or kinks, appliances, improperly seated gaskets, partially closed valves, etc.

MUNICIPAL HOSE GUIDE

 

MUNICIPAL HOSE GUIDE pdf