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# T207 exam equations

### T207 exam equations 2018

Title | Equation |
---|---|

Change in thermal energy (B4P19)(pdf P811) ... m = Mass, c = Specific heat capacity of the material, ΔT = Change in temperature | ΔQ = mcΔT |

Linear model of thermal expansion (B1p88)(PDFp88) ... X = Dimension, ΔT = Change in temperature, α = Linear temperature coefficient | ΔX = X-X_0 = X_0αΔT |

Bernoulli's equation (B4p111)(PDFp903) … Ev=Energy per unit volume, p=Pressure, ρ=Density, v=Speed, g=Gravity, h=Height | Ev=p+0.5ρv^2+ ρgh |

Magnetic force (B3b2p23)(PDFp639) ... B=Magnetic flux density, I=current, l=length, θ=Angle current makes with magnetic field | F=BIl sinθ |

Newton’s second law of motion (Precise) (B3b1p81)(PDFp545) ... d(mv) = Rate of change of momentum, dt = Rate of change of time | F = d(mv)/dt |

Newton’s second law (Simple) (B3b1p81)(PDFp545) ... F = Force, m = Mass, a = Acceleration | F = ma |

Frictional Force (B3b1p117)(PDFp581) ... F=Force, µ=Coeffiecient of friction, R=Reaction force | F=µR |

Aero drag equation (B3b2p92)(PDFp708) ... FD = Drag force, ρ = Density, v = Speed, C_D = Drag coefficient, A = Wing area | FD=(0.5ρv^2)C_D A |

Aero Lift equation (B3b2p91)(PDFp707) ... FD = Drag force, ρ = Density, v = Speed, C_L = Lift coefficient, A = Wing area | FD = (0.5ρv^2)C_L A |

Thin Ring or thin walled hollow cylinder (B3b1p100)(PDFp564) … m = mass, r = radius | I = Σmr^2 |

Moment of inertia of a thick Ring or thin walled hollow cylinder (B3b1p100)(PDFp564) â¦ m = mass, r_o = radius outer, r_i = radius inner | I = 0.5m(r_o^2+r_i^2) |

Archand Wear Equation (B4p153)(PDFp945) … k = Wear coefficient, Q = Measured volume of material worn, per metre of sliding distance, H = Hardness of the softer surface, W = Normal load | k = QH/W |

Fracture Mechanics Equation (B5b2p52)(PDFp1202) … σ = Stress, a = Crack length, Y = E.g. Long edge crack in a finite-width plate etc. | K₁= Yσ√(πa) |

Fracture Toughness (B2b2p77)(PDFp367) … G_c = Toughness, E = Young's modulus, a_c = Critical crack length | K_c = √(EG_c) = σ√(πa_c) |

Total Kinetic Energy (B4p17)(PDFp808) … (Sum of trans’l and rot’l kinetic energies), m = Mass, v = Speed, I = Moment of inertia, ω = Angular speed | K_total = 0.5mv² + 0.5Iω² |

Natural Log of Arrhenius's Law (B1p113)(PDFp113) … r = Rate, Ea = Activation energy, k = Boltzmann constant, T = Temperature (y=mx + c) | ln r = (-Ea/k)1/T + lnr_o |

Mass Flow Rate (B4p112)(PDFp903) … ρ = Density, v = Speed, A = Area | m = ρvA |

Engineers Bending Equation (B4p112)(PDFp903) … M = Bending moment, I = Second moment of area, σ = Stress, y = distance, E = Young's modulus, R = Radius of curvature | M/I = σ/y = E/R |

Power – Linear (B3b1p106)(PDFp570) … F = Force, v = Velocity | P = Fv |

Electrical Power (B3b2p36)(PDFp651) … I = Current, V = Voltage | P = IV |

Power - Rotation (B3b1p106)(PDFp570) … Γ = Torque, ω = Angular speed | P = Γω |

Power Lost to Heat (B3b2p47)(PDFp662) … I = Current, R = Resistance | Ptherm = I^2R |

Volumetric Flow Rate (B4p112)(PDFp903) … v = Speed, A = Area | Q = vA |

Arrhenius's Law (B1p107)(PDFp107) … r = Rate, Ea = Activation energy, k = Boltzmann constant, T = Temperature | r = r_o exp(-Ea/kT) |

Kinematic Equations for Rectilinear Motion (B3b1p31)(PDFp495) … s = Distance, u = Initial speed, a = Acceleration, t = Time | s = ut + 0.5at^2 |

Period of Oscillation (B3b1p42)(PDFp506) … T = Time, ω = Angular speed | T = 2π/ω |

Homologous Temperature (B5b2p77)(PDFp1226) … T = Operating temperature, T_m = Melting point, (If TH value is above 0.4Tm then creep will occur) | T_H = T/T_m |

Gravitational Potential Energy (B4p17)(PDFp808) … m = Mass, g = Gravity, h = Height | U_grav = mgh |

Tangential Speed (B3b1p18)(PDFp482) … r = Radius, ω = Angular speed | v = rω |

Kinematic Equations for Rectilinear Motion (B3b1p31)(PDFp495) … v = Final speed, u = Initial speed, a = Acceleration, t = Time | v = u + at |

Kinematic Viscosity (B4p164)(PDFp955) … η = Dynamic viscosity, ρ = Density | v = η/ρ |

Kinematic Equations for Rectilinear Motion (B3b1p31)(PDFp495) â¦ v = Final speed, u = Initial speed, a = Acceleration, s = displacement | v^2 = u^2 +2as |

Acceleration â Rotational (B3b1p106)(PDFp570) â¦ dÏ = Change in angular speed, dt = Change in time | α = dω/dt |

Shear Drag Torque due to the Shear Force (B4p117)(PDFp908) â¦ (Linked to Petrov's Equation by P = ÎÏ ) Î· = Dynamic viscosity, r = Shaft radius, L = Axial bearing length, Ï = Shaft speed, C_r = Radial clearance | Î = 2ÏÎ·rÂ³LÏ/C_r |

Torque Second Law (B3b1p106)(PDFp570) … I = Moment of inertia, α = Angular acceleration | Γ = Iα |

Motor Torque (B3b2p37)(PDFp652) … Γ_s = Stall torque, ω = Angular speed, ω_n = No load speed | Γ = Γ_s(1 - ω/ω_n) |

Strain Equation (B2b2p63)(PDFp355) â¦ Îµ = Strain, Îl = Extension, l = Original length | ε = Δl/l |

Thermo-dynamic Efficiency (B4p24)(PDFp815) … T_1 = Temperature in, T_2 = Temperature out | η = 1 - (T_2/T_1) |

Motor Efficiency Equation (B3b2p47)(PDFp662) … P_out = Power out, P_in = Power in | η = P_out/P_in |

Angular Displacement (B3b1p29)(PDFp493) … ω = Final angular speed, ω_i = Initial angular speed, α = Angular acceleration | θ = (ω² - ω_i²)/2α |

Net Displacement (B3b1p27)(PDFp491) … ω = Angular speed, t = Time | θ = ωt |

Toughness (B2b2p77)(PDFp367) … G_c = Toughness, E = Young's modulus, a = Crack length | σ = √EG_c/πa |

Stress Equation (B2b2p63)(PDFp353) … σ = Stress, F = Force, A = Area | σ = F/A |

Hoop Stress in a Thin Cylinder … p = Pressure, r = Radius, t = Wall thickness | σ_hoop = pr/t |

Hall-Petch Equation … σ_t = Strength, σ_0 = Constant for a given material, K = Constant for a given material, d = Grain Size | σ_t = σ_₀ + kd^(-1/2) |

Shear Stress (B4p162)(PDFp953) … τ = Applied shear stress, G = Shear modulus of the material, γ = Shear strain | τ = Gγ |

Shear Stress (B4p163)(PDFp954) … τ = Applied shear stress, η = Coefficient of dynamic viscosity, dγ/dt = Rate of shear strain | τ = η dγ/dt |

Angular Speed (B3b1p29)(PDFp493) … ω_i = Initial angular speed, α = Angular acceleration, t = Time | ω = ω_i + αt |

Bending moments. (B2b1p32)(PDFp166) ... W=point load, L= distance between supports V_A and V_B, a= distance between V_A and W, similar for b | V_A = (Wb)/L and V_B = (Wa)/L |