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 % drop Additional 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