Fire Hydraulics Formulas

Different Fire Hydraulics Formulas Commonly Used in Fire Service

Fire Streams Formula

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.

   

 

Formulas

 

Nozzle Reaction (NR)

NR = 1.5 x D2 x NP

 

Nozzle Reaction (FOG)

NR = 0.05 x GPM x √NP

Above formula assumes that the opening has a discharge factor of 1, such as smooth bore nozzle.  For other opening, another factor must be used:

Open Butt = .9      Hydrant Butt = .9      Sprinkler Head = .8

Momentary Nozzle Reaction ( 20% more than stabilized stream)

MNR = 1.88 D² P

MNR = momentary nozzle reaction

D = diameter

P = pressure

 

Flow

GPM = 29.7 x D2 x √NP

GPM = 29.7 x D2 x √NP x 0.9 (unrestricted orfice, such as hydrant)

 

Sprinkle Head (when pressure is known)

Q = 1/2 P + 15

 

Friction Loss

FL = CQ2L   or   FL = 2Q2 + Q (> 100 GPM)     or    FL = 2Q2 +½Q   (< 100 GPM)

 

Pump Discharge Pressure (PDP) or Engine Pressure (EP)

PDP ( EP ) = NP + FL + AP +/- EL

AP = Appliance

EL = Elevation

PDP(E P)highrise = NP + FL (to connection/standpipe) + 25psi (connection/standpipe)  + 5 psi per floor (above first floor) + FL ( hose in high rise)

 

 

 

 

   

 

Fire Streams Related Formulas

 

 

Horizontal Reach of a Solid Hose Stream

S = √(HF)√(P)

S = distance

HF = horizontal factor

P = nozzle pressure

Values of Horizontal Factors (note: base is 1/2''tip and factor 56,than there is  a increase of 6 for each 1/8'' in tip size)

1/2'' 5/8'' 3/4'' 7/8'' 1'' 1 1/8'' 1 1/4'' 1 3/8'' 1 1/2'' 1 5/8'' 1 3/4'' 2''
56 62 68 74 80 86 92 98 104 110 116 128

 

Vertical Reach of a Solid Hose Stream

S = √(VF)√(P)

S = distance

VF = vertical factor

P = nozzle pressure

Values of Vertical Factors (note:base is 1/2'' tip and factor 85, than there is a increase of 5 for each 1/8'' in tip size)

1/2'' 5/8'' 3/4'' 7/8'' 1'' 1 1/8'' 1 1/4'' 1 3/8'' 1 1/2'' 1 5/8'' 1 3/4'' 2''
85 90 95 100 105 110 115 120 125 130 135 145

 

 

 

 

Horizontal Reach of a Solid Hose Stream (second formula)

This formula is useful for tip sizes of 3/4'' and bigger with Nozzle Pressure (NP) over 30 PSI.(NOTE: For nozzle tips bigger than 3/4'' you MUST add 5 to the 26 for EACH 1/8'' increase in tip size)

S = 1/2 P + 26     (note: add 5 for each 1/8'' increase in tip size)

 

 

Velocity Flow

V = 8 √H     (when head is known)

V = velocity flow in feet per second

H = head

V = 12.14 √P  (when pressure is known)

 

Comparing the velocity flow in the hose with the velocity flow at the nozzle tip

VD² = vd²

V = velocity flow trough the hose

D = diameter of the hose

v = velocity flow from the nozzle tip

d = tip size

 

   

Area Formulas

 

Square

Area = side X side

Rectangle

Area = length X width

Triangle

Area = base X height / 2

Circle

Area =  .7854 X diameter2

Area = 3.1416 X radius2

 

Velocity formula

Velocity = 8√Height

Velocity = 12.1√NP 

 

Normal Atmospheric Pressure

29.92  Hg'' or 14.7 psi

Water weighs

approx.62.5 lbs per cubic foot

One Gallon of Water

weighs 8.35 lbs

One Gallon of Water

contains 231 cubic inches

One cubic foot of Water

contains 1728 cubic inches.

Stream Penetration Formula

A / B + C / D

Gallons to Volume Formula

V = gallons / 7.48

Weight to Gallons Formula

G = weight / 8.35

Gallons in a Hose Formula

G = 0.0408 D(inch) L (feet)

Gallons in Tank Formula

G = 5.875 D² H

Gallon Capacity Formula

G = 7.48 V

Right Triangle Formula

C² = A² + B²

Volume (cubic inch to cubic feet)

V = cubic inches / 1728

Maximum Efficient Water

capacity of fire hose:

1'' hose = 30gpm

1 1/2'' hose = 100 gpm

2 1/2'' hose = 250gpm

3'' hose = 500 gpm

3 1/2 '' hose = 750 gpm

Maximum Lift

H = 1.13Hg