39_Formula_Booklet_-_Fire_Engineering_Science_v3.0_for_2020_21

Introduction

• Prepared by Richard Fowler for the Institution of Fire Engineers (IFE) to assist students in Fire Engineering Science papers.

• Designed to complement other learning, consolidating essential formulas for student’s understanding and applications.

Index

• Section 1: L3 Diploma – Fire Engineering Science

  • Equations of Linear Motion

  • Newton’s Laws of Motion

  • Mass, Weight, and Momentum

  • Work, Energy, and Power

  • Hydraulics

  • Mathematics

  • Equilibrium in Mechanical Systems

  • Electricity

  • Heat

  • The Gas Laws

  • Transformer Ratios

• Section 2: L4 Certificate – Fire Engineering Science

  • Hydraulics

  • Liquid Flow in Open Channels

  • Measuring Flow through an Open Channel

  • Electricity

  • Fire Dynamics (Law’s Law)

  • Recommended Calculator

Section 1: L3 Diploma – Fire Engineering Science

1. Equations of Linear Motion

• Key Equations:

  • v = u + at

  • s = (u + v)/2 * t

  • s = ut + 1/2 at^2

  • s = v t - 1/2 at^2

  • v^2 = u^2 + 2as

• Variables:

  • v = Final velocity (m/s)

  • u = Initial velocity (m/s)

  • a = Acceleration (m/s²)

  • t = Time (s)

  • s = Distance (m)

2. Newton’s Laws of Motion

• First Law: An object remains at rest or in uniform motion unless acted upon by an external force.

• Second Law: Acceleration is proportional to the net force acting on it (F = ma).

• Third Law: For every action, there is an equal and opposite reaction.

3. Mass, Weight, and Momentum

• Force Equation: F = m x a

  • F = Force (N)

  • m = Mass (kg)

  • a = Acceleration (m/s²)

• Momentum Equation: p = mv

  • p = Momentum (kg·m/s)

4. Work, Energy, and Power

• Power Equation: P = W/t

  • W = Work done (J)

  • P = Power (W)

• Kinetic Energy Equation: KE = 1/2 mv^2

• Potential Energy Equation: PE = mgH

5. Hydraulics

• Pressure Equation: P = ρgH

• Flow Rate through Nozzle: L = 2/3d²√P

6. Mathematics

• Area of Circle: A = πr²

• Volume of Cylinder: V = πr²h

• Volume of Sphere: V = 4/3πr³

7. Equilibrium in Mechanical Systems

• Conditions of Equilibrium:

  • For straight motion, net force = 0.

  • For rotation, net moment = 0.

8. Electricity

• Ohm's Law: V = IR

• Power Calculation: P = IV

9. Heat

• Heat Change Equation: c = ∆Q/∆T

• Specific Heat Capacity: C = ∆Q/m × ∆t

10. The Gas Laws

• Boyle’s Law: P1V1 = P2V2

• Charles’s Law: V1/T1 = V2/T2

• Ideal Gas Law: PV = nRT

11. Transformer Ratios

• Transformer Equation: VP/VS = NP/NS = IS/IP

Section 2: L4 Certificate – Fire Engineering Science

12. Hydraulics

• Bernoulli’s Equation: P1 + ρgH1 + 1/2 ρv1² = P2 + ρgH2 + 1/2 ρv2²

13. Liquid Flow in Open Channels

• Flow Rate Equation: Q = v × A

14. Measuring Flow through an Open Channel

• Rectangular Weir Flow Equation: Q = 2/3 × C × L × (2g × H)^{1/2}

15. Electricity (Advanced)

• Inductive and Capacitive Reactance: XL = 2πfL (Inductor), XC = 1/(2πfC) (Capacitor)

16. Fire Dynamics

• Law’s Law:

  • tf = k × L / (Aw × At)^{1/2}

  • Where tf = fire resistance time (min).

17. Recommended Calculator

• Recommended Model: Casio fx-85GT Plus or fx-85GTX

• Key Functions to Practice: Fractions, result toggling, memory clearing.