# Pump MathComment on this page

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 |