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Metric Pump Math

Flow from a solid stream nozzle

L/min = 0.067 x d² x √NP

d Diameter of orifice in mm
NP Nozzle pressure in kPa

Nozzle reaction for solid stream nozzles

NR = 1.57 x d² x NP
lbs (force) / diameter (inches) / pressure (PSI)
NR = 0.0015 x d² x NP
newtons (force) / diameter (mm) / pressure (kPa)

1 lb = 4.448 newtons

Nozzle reaction for fog stream nozzles

NR = 0.0505 x Q x √NP
lbs (force) / flow (GPM) / pressure (PSI)
NR = 0.0156 x Q x √NP
newtons (force) / flow (LPM) / pressure (kPa)

Friction loss

FL = C (LPM/100)² (meters/100)

FL = C x Q² x L

FL Friction loss in kPa
C Friction loss co-efficient
Q Flow in 100s of LPM (LPM/100)
L Hose length in 100s of meters (length/100)

For a wyed hoseline, calculate Q as

(LPM line A + LPM line B) / 100

Appliance friction loss

Insignificant when flowing through appliances < 1,400 LPM

  • 70 kPa for each appliance other than master streams
  • 175 kPa for all master stream appliances

Elevation pressure

10 kPa per meter
40 kPa per story

EP = 10 x H

H Height in meters

EP = 40 (stories - 1)

Siamesed hoselines

When 2 hoselines of equal length are siamesed to supply a fire stream, friction loss is approximately 25% of a single hoseline at the same nozzle pressure.

When 3 hoselines of equal length are siamesed to supply a fire stream, friction loss is approximately 10% of a single hoseline at the same pressure.

Pump Discharge Pressure (PDP)

PDP = NP + TPL

NP Nozzle pressure
TPL Total pressure loss (FL attack + FL supply + APP loss)

Net pump discharge pressure (NPDP)

NPDP = PDP - supply/intake pressure

Dynamic pump intake calculation

Compound % dropAdditional supply available
0-10%3x current flow
11-15%2x current flow
16-25%Same as current flow
> 25%More water available buy less than current flow

Shuttle operations

UT + TTF + FT + RT = TRT

UT Unload/dump time
TTF Time to travel (to fill site)
FT Fill time
RT Return time
TRT Total run time