Applied Mathematics
What the exam tests
Applied Mathematics tests fireground arithmetic: area, volume, flow, pressure, friction loss, nozzle reaction and ladder geometry. Units and sensible rounding matter.
Core rules
- Volume of a rectangular tank = length × breadth × height; 1 m³ = 1,000 L.
- Flow rate = volume ÷ time; time = volume ÷ flow.
- Pump pressure = nozzle pressure + friction loss + elevation, in bar or psi.
- Nozzle reaction is approximately related to flow and the square root of nozzle pressure; use the formula supplied in the question rather than memory.
- Ladder problems use Pythagoras: ladder length² = vertical height² + horizontal distance².
- Show units at every step and convert millimetres to metres before calculating.
Worked example
A tank is 3 m long, 2 m wide and 1.5 m deep. Volume = 3 × 2 × 1.5 = 9 m³ = 9,000 L. If a branch flows 450 L/min, duration = 9,000 / 450 = 20 minutes. Reasoning: calculate volume first, convert to litres, then divide by flow. If a 20% reserve is required, usable water is 7,200 L, giving 16 minutes.
Traps
Mixing litres and cubic metres; adding friction loss twice; using internal dimensions for a tank that is not full; forgetting elevation when the branch is above the pump; rounding too early.