Chapter III

Fire Ground

Formulas

FIREGROUND FORMULAS

CHAPTER 3

The science of hydraulic engineering requires the application of theoretical and highly precise

mathematical formulas. Principles and theories can generally be expressed as numerical

equations, and these used to make determinations of unknowns. Naturally, the securing of

absolutely correct answers to problems is an integral part of such a science.

The task of supplying water for any operation on the fireground does not demand such

exactitude. In the interest of speed and ease it is highly desirable to apply less complicated

formulas and practical rules. In order to create such formulas, it becomes necessary to "round

off" numbers so that they may be easily memorized. However, when this manipulation is made,

the accuracy of the formula is reduced, and the resultant becomes more of an approximation than

a calculation, and such is accepted by the fire service as a means to accomplish a goal. Rules can

be established to serve as guide lines in particular operations, and if they have their foundation

built on hydraulic fact, can be generalized to suit a number of applications.

The D.C. Fire and EMS Department has instituted a set of formulas and rules for its fireground

operations, and they are found within this chapter. Although not precise, the directives and

allowances set forth are sufficiently accurate to provide effective firefighting streams.

Although the deliveries obtained by the use of the following formula will vary to some extent, it

is sufficiently accurate for all practical purposes. It shall be used on the fireground in calculating

the engine pressure.

E.P. = N.P. plus F.L. plus or minus E

Where,

E.P. Is the engine pressure in pounds per square inch.

N.P. Is the nozzle pressure for the appliance used.

F.L. Is the total friction loss allowance in the hose line or lines supplying the appliance

or assembly plus any allowance for friction loss in the appliance, assembly, or

standpipe.

E. If the elevation allowance due to the location of the nozzle in relation to the

pump.

III-1

The nozzle pressure for the appliance used shall be selected from the "Nozzle Pressure and

Friction loss charts".

The friction loss in hose will vary with the amount of water flowing through the line and with the

size of hose. A different friction loss for each size hose, even when delivering the same amount

of water, is also necessary. The "Nozzle Pressure and Friction Loss Charts" that follow, give the

friction loss for all the deliveries likely to be encountered on the fireground. These charts are

separated according to the size of hose. When calculating the friction loss, the friction loss per

100 feet which applies is selected from these charts. Then the length of the line being used is

divided by 100 to give the number of 100 foot lengths of hose. This is multiplied by the amount

of friction loss selected from the chart. The total friction loss for the supply line or lines is then

known. The allowance for friction loss in the appliance, assembly, or standpipe is taken from the

"Friction Loss Allowance Chart". The sum of these two figures gives the total friction loss to be

used in the formula for Engine Pressure.

The elevation shall be added or subtracted, depending upon the position of the nozzle. One half

pound shall be added for each foot of elevation that the nozzle is above the level of the pump.

One half pound shall be deducted for each foot that the nozzle is below the level of the pump.

Five pounds shall be added/subtracted for each story above/below the level of the pump. When

calculating elevation for the ladder pipe, the extension of the ladder shall be used as the basis for

calculation. (The error will be relatively small).

When a pumper is relaying water to another pumper, there is no nozzle or tip in the line between

them for which a nozzle pressure is needed. However, it is desired that the water arrive at the

next pumper in line with sufficient pressure to allow efficient operation. It has been determined

that when there are more than two pumpers in line, an allowance of 20 pounds for this intake

pressure is suitable. Therefore, pump operators in a relayed lire of more than two pumpers, with

the exception of the operator of the pump nearest the fire, shall calculate their pump pressure

using the relay formula of:

.

E.P. = 20 plus F.L. plus or minus E.

Where,

E.P. Is the engine pressure in pounds per square inch.

20 psi Is the allowance for the pressure at the intake of the next pumper in line.

F.L. Is the total friction loss allowance in the hose

line or lines between the pump under consideration

and the next one in line.

E. Is the elevation allowance due to the elevation differential between the

pump under consideration and the next one in 1ine.

III-2

MAXIMUM LAYOUT

Maximum layout is the distance that the pump can supply the proper pressure and gallonage for

efficient operation. When considering pressure, calculate the friction loss for GPM’s required

without exceeding the supply hoses ability to contain the pressure, ( hose is tested at 200 psi) .

Also consider when suppling water the pumps capacity, (1250 OR 1500 GPM) the pump is most

efficient at capacity with 150 psi discharge. From the above two statements the following items

shall be considered when working with layouts; GPM, PUMP DISCHARGE PRESSURE.

AND DISTANCE OF LAYOUT. An example of such a situation would be a 1250 gpm wagon

laying 800' of dual 3" lines suppling 800 gallons to the next wagon. Using the relay formula we

find the following:

F.L. = split the water through both lines:

800 divided by 2 = 400

400 gallons through one 3" line per 100" = 16 psi

16 psi times 8 (800' lines) = 128 psi

128 + 20 = 148 psi

E.P. = 148 psi (plus or minus elevation)

With this problem we find that the pump can supply the lay out without exceeding the rated

supply hose pressure and the pumps capacity. If the gpm's or length of the layout were different

we would have passed the point to where the pump could operate efficiently and safely. To meet

or exceed the pump capacity or the hoses pressure on layouts consider adding another supply line

or increasing the size of the supply lines until the friction loss calculation is in the proper range

of the pump. The following chart gives examples of fire ground calculated maximum lay outs

when pumping the capacity of the pump.

1250 GPM 1500 GPM

DUAL 3" LINES 350 FT 250 FT

3" / 4" LINES 800 FT 600 FT

The TWO PUMP OPERATION is written so that a pressure of 125 pounds is used by the

pumper at the source of supply (150 pounds when supplying the hydrant valve), unless

conditions are present which would cause a change (refer to relaying water in the fire ground

operations section). A TWO PUMP OPERATION with a long layout or a large flow of water

will require the use of the relay formula when calculating the engine pressure for the pump at the

source of supply.

III-3

When calculating the engine pressure to supply two lines from a wye or gated wye the flow in

the single hose line to the wye, or gated wye, and the pressure required for only one line from the

wye, or gated wye, are used as a basis of calculation. If the lines from the wye or gated wye

require different pressures, the line requiring the higher pressure is used.

When calculating the engine pressure for siamese or trimese lines of unequal length and same

size, the average length is used as a basis for calculation.

When calculating the engine pressure for siamese or trimese lines of unequal length and unequal

size you will have a percentage delivered through each line based on the cross sectional area. An

example is dual supply lines consisting of one 3" and one 4" which will naturally deliver more

water through: the 4" line. For fire ground calculation you can say that 30% of the water being

supplied s delivered through the 3" line and 70% of the water is being delivered through the 4 "

1ine.

Example: A pumper is flowing 1,000 gallons through dual lines consisting of 800' of 3"and

800' of 4".

Gallons delivered Friction loss

per line per 100'

3" line = 300 gal. 8 psi

4" line = 700 gal. 10 psi

From the above you will use 10 psi per 100 ft. of supply line plus 20 psi for the intake pressure at

the next engine.

E.P. = 20 + (8 x 10) E.

E.P. = 100 psi

The maximum operating engine pressure shall be 300 PSI and layouts shall be controlled so that

no pumper will be required to operate above this pressure.

Where two or more pumping apparatus are supplying water to a heavy duty device or relaying

water, each pumper shall deliver a proportional share of water based on the number of lines each

pumper is supplying. (i.e. If three lines of equal diameter are supplying water to a device and one

pumper is supplying one line then 1/3 of the water is being supplied by this pumper and the other

2/3 is being supplied by the other pumper).

III-4

FORMAT FOR CALCULATING ENGINE PRESSURE

FORMULA: E.P. = N.P. + F.L. E.

E.P.= Engine pressure in psi

N.P.= Nozzle pressure in psi for the appliance being used

F.L.= Friction loss in psi in 3/4 , 11/2 , 1 3/4 or 2 1/2" hose

F.L.= Friction loss in psi in the 3" and/or 4" hose

E. = Elevation allowance in psi due to the location of the nozzle in

relation to the pump

Example: An 1 ½" line on the fifth floor working from the standpipe through 200' of 1 ½"hose.

The wagon is pumping on the standpipe through 300' of 2 ½" hose.

Solution: p.s.i.

N.P. = 100

F.L. = 200 divided by 100 equals 2

2 times 30 psi equals 60

F.L. = 300 divided by 100 equals 3

3 times 5 psi equals 15

F.L.A.= Standpipe connection 25

E. = 4 times 5 psi equals 20

E.P. = 220 psi

Example: A 350' of 1 ½" line working on the 4th floor, and a 200' of 1 ½" line working on the

2nd floor.

Solution: p.s.i.

N.P.= 100

F.L.= 350 divided by 100 equals 3.5

3.5 times 30 equals (longest line) 105

E = 3 times 5 psi equals 15

E.P. = 220 psi

III-5

Example: A 200' of 1 1/2" line working in a basement. (one level below the pump)

Solution: p.s.i.

N.P.= 100

F.L .= 200 divided by 100 equals 2

2 times.30 equals 60

E. = 1 times 5 psi equals -5

E.P.= 155

Note: When totaling friction loss always round off to the higher number.

III - 6

FRICTION LOSS CHART D.C.F.D.

Friction loss per 100'

Number and size of lines.

G. P. M.

1

2-1/2"

HOSE

2

3"

HOSE

1 2

3

3-1/2"

HOSE

1

2

4"

HOSE

1

2

1-3"

1-4"

UP TO 125 5

>125/215 10 5

250/275 15 7

275/325 20 10

325/350 25 12

350/375 30 14 5

375/425 35 9 18 6

425/450 40 10 20 7

450/475 45 11 22 8

475/500 50 12 25 6 8 5

500/550 55 15 30 8 10 6

550/600 18 36 9 12 7

600/650 22 42 10 14 8

650/700 25 49 12 5 16 10

700/750 28 56 14 6 19 5 11 5

750/800 64 16 7 22 6 13 7

800/900 81 20 9 27 7 16 9

900/1000 25 10 34 9 20 10

1000/1100 30 13 41 10 24 6 13

1200/1300 42 18 11 34 8 20

1300/1400 49 21 16 39 10 20

1400/1500 56 25 19 45 11 24

1500/1600 64 28 21 51 13 26

1600/1700 72 32 58 16 28

1700/1800 81 36 64 16 32

1900/2000 44 80 20 40

III-7

NOZZLE PRESSURE CHART

Friction per 100 ft. in psi’s

APPLIANCE NOZZLE

PRESSURE GPM

3/4"

LINE

1-1/2"

LINE

2-I/2"

LINE

SMALL LINE (3/4"NOZZLE) 100 psi 13 30

1-1/2" FOG NOZZLE (CVFSS) 75 psi 125 40

1-1/2” cut off w/ 7/8 smoothbore 50 psi 160 60

1-1/2” cut off w/ 15/16 smoothbore 50 psi 180 75

1-1/2" REVOLVING DIST.

NOZZLE 100 psi 115 30

2-1/12 FOG NOZZLE (CVFSS) 75 psi 250 12

LOW VELOCITY FOG

APPLICATOR 100 psi 115 30 3

EDUCTOR (FOAM POSITION) 200 psi 95 5

1" TIP (SMOOTH BORE) 50 psi 210 10

1-1/8" TIP 50 psi 265 15

1-1/4" TIP 50 psi 325 22

LUCUS VALVE (AMMONIA

FLUSH) 50 psi 200 10

PERI-JET 120 psi 200 10

PERIPHERAL JET SYPHON 120 psi 420 40

2-1/2" REVOLVING DIST.

NOZZLE 100 psi 425 40

IMPERIAL 500 (CVFSS) 100 psi 500

1-3/8' TIP (SMOOTH BORE) 80 psi 500

1-1/2" TIP 80 psi 600

1-5/8" TIP 80 psi 700

1-3/4' TIP 80 psi 800

2' TIP 80 psi 1000

JN-200 FOG NOZZLE (30 DEG.) 80 psi 600

JN-200 FOG NOZZLE (90 DEG.) 80 psi 1000

III-8

FRICTION LOSS CHART (CONT)

CELLAR PIPE 50 PSI

LADDER PIPE ASSEMBLY

(SIAMESE, 10OFT 3" HOSE,

LADDER, PIPE

50 PSI

STANDPIPE 25 PSI

MONITOR NOZZLE OR

WAGON PIPE 20 PSI

Pre piped Ladder Pipe (Seagrave) 115 PSI

E.P. FOR SPRINKLER SYSTEMS 125 PSI

E.P. FOR

SPRINKLER/STANDPIPE 175 PSI

HEAVY DUTY FOG

JN-200 FOG NOZZLE

When calculating the engine pressure necessary to supply the JN-200, consider the variable gallonage. With the

red marks in line (30 degrees), delivery and formula are the same as 1-1/2"tip. With maximum opening (90

degrees), delivery and formula are the same as 2" tip. Other settings require intermediate tip equivalencies.

NOTE: when supplying the wagon pipe through hose connected to either the siamese or its base, or a wagon

pipe siamese provided on apparatus, use the engine pressure formula with nozzle pressure and friction loss

allowance for tip being used plus friction loss allowance for wagon pipe.

When supplying the wagon pipe through a piping system leading from the discharge of the pump, the pump

pressure recommended by the Training Academy for each individual piece of apparatus shall be used.

ENGINE PRESSURE FOR SPRINKLER SYSTEMS

Use 125 psi engine pressure unless otherwise ordered.

ENGINE PRESSURE FOR COMBINATION SPRINKLER/STANDPIPE SYSTEMS

Use 175 psi engine pressure until notified that a higher pressure is needed.

ENGINE PRESSURE FOR METRO STANDPIPE SYSTEMS

When charging a Metro standpipe you shall consider the design of the system and which system is being

supplied

III-9

Particular attention shall be given when supplying a tunnel standpipe system due to the facts that they are

equipped with an exhauster at the end of system to expel air in a faster manner. This added pressure is gained

from-the drop in elevation which is why the exhausters are in place to help expel and to relieve the pressure

created when filling a system so damage does not occur. The exhauster may take up to five minutes to fully

expel the trapped air in the system as they are being filled with water, at which point the system is filled with

water. The exhausters close due to the fact that the water has a greater pressure which closes the valve that

allows the air to be expelled.

The following steps shall be used as a guide line when charging a

metro tunnel system:

1. Connect supply lines from hydrant to wagon and wagon to standpipe siamese. (two supply lines)

2. Note static pressure from hydrant.

3. Allow water to fill standpipe system with hydrant pressure only.

4. When your gauges read the same pressure as the original static pressure the system is full.

5. Using the friction loss formula calculate the proper Engine Pressure.

Elevation and length of systems run are available on a plate attached to the standpipe system riser at the

connection to assist in calculating friction loss.

Surface and aerial stations also have dry standpipe systems and should be filled with water in the same manor as

noted above.

Sub-Surface stations shall be supplemented by pumping apparatus with the consideration of the elevation that

will be gained when calculating Engine Pressure.

ENGINE PRESSURE FOR THE EDUCTOR

To function properly in the foam position, the eductor requires a flow of at least 95 gpm. Playpipes which

deliver less than 95 gpm cannot be used with the eductor in the "Foam" position. When the eductor is placed in

service, the pressure at the eductor should be 200 psi and the length of line limited to 200 feet. When the

eductor is being supplied by a 3" hose, friction loss in the supply line is determined by the gpm discharged by

the 1-1/2"nozzle. In the "water" position, the friction loss in the eductor is negligible and shall be disregarded.

Because of the high friction loss in the 1-1/2" discharge piping of some hose wagons, the engine pressure

required for the preconnected eductor to function properly may be as high as 230 psi. When using 125 gpm

nozzles with 95 gpm foam eductor the foam solution may have a proportion of foam other than 6%. Operators

should be aware that this may cause more/less frequent changing of foam cans. Different manufactured foams

may recommend various percentages in utilizing that specific foam. Review the specifications of the individual

foam used for proper percentages and application for maximum effectiveness.

III-10

III-11