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# T207 Exam Notes

### T207 Engineering Study Notes

Term | Definition |
---|---|

Bernoulli's Principle | Holds that for fluids in an ideal state, pressure and density are inversely related. Assumptions: 1) points 1 and 2 lie on a streamline 2) fluid has constant density 3) flow is steady 4) no friction |

Temperature Dependent Effects - Accelerating | Example: Heat curable glues. Modelled in terms of the fraction of the particles that have much higher than average thermal energy. Y-Axis = Viscosity. |

Temperature Dependent Effects - Gradual | Example: Convection in a domestic water system. Modelled in terms of the average thermal energy of the particles of the system. Y-Axis = Resistance. |

Temperature Dependent Effects - Sudden | Example: An electric kettle automatic switch-off. Modelled in terms of the balance between disorder generated by the vibration of atoms and order induced by inter-particle forces. Y-Axis = Crystal Atom Spacing. |

Full Film Lubrication | Surfaces are completely separated by a constant film of lubricant. The only frictional resistance is that of the fluid's viscosity resisting shear deformation caused by the relative movement of the two surfaces. Example. Skis on snow. |

Cell Potential | E(cell) = E(metalA)-E(metalB). Positive answer = Metal B corrodes. Negative answer = Metal A corrodes. |

Required for Corrosion | Anode - (More Active Material). Cathode - (Less Active Material). Current - (Flow of Ions). Electrolyte - (Host for Flow of Ions). |

Motor Effect | A simple electric motor can be built using a coil of wire that is free to rotate between two opposite magnetic poles. When an electric current flows through the coil, the coil experiences a force and moves. |

Forces on a Plane | Weight = gravity. It acts downward. Lift = force that acts at a right angle to the wings-differences in air pressure. Thrust = force that propels forwards-Engines. Drag = force that pulls backwards-friction and air pressure . |

Thermal Efficiency | Indicates the extent to which the energy added by heat is converted to work output. |

Friction | A force between two surfaces that are sliding, or trying to slide, across each other. Small imperfections in the surfaces move against each other and may form weak bonds. This pulls on the surfaces and slows them down. |

Block on an Inclined Plane | tan(θ) = sin(θ)/cos(θ). µ=tan(θ). θ=tan-¹(µ). Draw a Triangle akin to the diagram to show all the working out. |

Abrasive Wear | Occurs between two surfaces that are in relative motion. Happens because the asperities of each surface gouge material out as they move. Over time the material is worn away. |

Power Absorbed | P=Γω |

Creep | Requires three conditions to occur; time, heat and stress. Occurs when Homologous Temperature,Th>0.4 Tm. Th=T/Tm. |

Fracture in Metals | Caused by: Stress concentration, Speed of loading, Temperature, Thermal shock. |

Thermal Stresses | When there is a temperature change, but some constraint prevents expansion. |

Wear Mechanisms | abrasion, adhesion, fatigue, oxidation. |

Galvanising | when the zinc layer stops oxygen, water or salt from attacking the iron. An advantage is that a scratch will still slow corrosion, as Zn is higher in the series. |

Electroplating | Depositing a thin layer of metal on the object being protected. Requires the object being protected to be the negative terminal, surrounded by a solution of the ions of the tin. The negative charge attracts positive ions. |

Sacrificial Protection | This method works by taking a metal higher up the reactivity series. This is connected to the iron/steel and donates its electrons to any iron ions that might have formed, stopping it from corroding. |

Innovation by context | The fruit of the creative process going on in the mind of the engineer when solving a problem, clever change in the design of a computer program that allows it to run faster something revolutionary like the jet engine. Example - Clockwork Radio. |

Innovation by development | About changing the bit that doesn't work, or that could work better, to improve the function of the whole for reasons of cost, performance, ease of manufacture or competitive edge. Example - Black and Decker Workmate. |

Routine solutions | Involve configuration or reconfiguration of existing devices or components, without innovation, because something is broken or needs to be re-positioned, or there is simply a better way to do it. Example - Adjustment of Hubble Telescope mirror. |

Elastic Collision | In which both conservation of momentum and conservation of kinetic energy are observed. e.g. Snooker Balls |

Inelastic Collision | In which the colliding objects stick together after the collision. e.g.Two balls of wet clay |

Hammer Forces | Impulse = change of momentum. and, Impulse = average force x contact time. and, change of momentum = momentum out - momentum in = (m V2 - m V1) = m (V2 - V1) |

Creep | A constant stress situation that is below yield. It is extremely prevalent in higher temperature conditions. Usually tested with a wire of a given size that has a constant load and the elongation is measured over time. |

Fatigue | Due to cyclic/alternating loading that can be at any stress level. The loading is repeated until the number of cycles imparted causes failure. |

Stress corrosion | Characterised by cracks propagating along grain boundaries. three factors: 1-Tensile stresses. 2- Corrosive medium . 3 - Material susceptible to stress corrosion. |

Linear Model for Thermal Expansion | ∆X = X-X₀ = X₀α∆T. X = Dimension. ∆T = Change in temperature. α = Linear temperature coefficient. |

Arrhenius's Law | r = r₀ exp(-Ea/kT. r = Rate. Ea = Activation energy. k = Boltzmann constant. T = Temperature. |

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

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

Stress Equation | σ = F/A. σ = Stress. F = Force. A = Area. |

Strain Equation | ε = ∆l/l. ε = Strain. ∆l = Extension. l = Original length. |

Toughness | σ = √EGc/πa. Gc = Toughness. E = Young's modulus. a = Crack length. |

Fracture Toughness | Kc = √EGc = σ√πac. Gc = Toughness. E = Young's modulus. ac = Critical crack length. |

Tangential Speed | v = rω. r = Radius. ω = Angular speed. |

Net Displacement | θ = ωt. ω = Angular speed. t = Time. |

Angular Speed | ω = ωi + αt. ωi = Initial angular speed. α = Angular acceleration. t = Time. |

Angular Displacement | θ = (ω² - ωi²)/2α. ω = Final angular speed. ωi = Initial angular speed. α = Angular acceleration. |

Kinematic Equations for Rectilinear Motion | (v = u + at) (v² = u² + 2as) (s = ut + 0.5at²) s = Distance. v = Final speed. u = Initial speed. a = Acceleration. t = Time. |

Time rotating | T = 2π/ω. T = Time. ω = Angular speed. |

Force | F = ma. F = Force. m = Mass. a = Acceleration. |

Torque Second Law | Γ = Iα. I = Moment of inertia. α = Angular acceleration. |

Linear Power | P = Fv. F = Force. v = Velocity. |

Rotational Power | P = Γω. Γ = Torque. ω = Angular speed. |

Rotational Acceleration | α = dω/dt. dw = Change in angular speed. dt = Change in time. |

Frictional Force | F = µR. µ = Coefficient of friction. R = Reaction force. |

Power Lost to Heat | Ptherm = I²R. I = Current. R = Resistance. |

Gravitational Potential Energy | Ugrav = mgh. m = Mass. g = Gravity. h = Height. |

Change in Thermal Energy | ∆Q = mc∆T. m = Mass. c = Specific heat capacity of the material. ∆T = Change in temperature. |

Mass Flow Rate | m = ρvA. ρ = Density. v = Speed. A = Area. |

Archand Wear Equation | k = QH/W. k = Wear coefficient. Q = Measured volume of material worn per metre of sliding distance. H = Hardness of the softer surface. W = Normal load. |

Petrov's Equation | Γ = 2πηr³Lω/Cr. where: η = Dynamic viscosity. r = Shaft radius. L = Axial bearing length. ω = Shaft speed. Cr = Radial clearance. This equation is linked to Petrov's Equation by P = Γω, making Petrov's Equation: (P = 2πηr³Lω²/Cr) |

Hall-Petch Equation | σt = σ₀ + kd⁻½. σt = Strength. σ₀ = Constant for a given material. K = Constant for a given material. d = Grain Size. |

Fracture Mechanics | K₁= Yσ√πa. σ = Stress. a = Crack length. Y = Material Constant, (Long edge crack in a finite-width plate etc.) |

Brittle Fracture | rapid crack growth. low energy release. no plastic deformation. little/no plastic deformation prior to fracture. sharp corner/ notches/ fatigue crack. cleavage or intergranular fracture. nonmetals such as glass, ceramics and hard plastics. |

Bimetallic switch (Composite body) | Made of two or more materials with different properties. generates internal constraint when T changes. When heated, one layer will be trying to expand more than the other - If neither metal yields, the strip will bend. |

Thermo-dynamic Efficiency | η = 1 - (T₂/T₁). T₁= Temperature in. T₂= Temperature out. |

Hoop Stress in a Thin Cylinder | σhoop = pr/t. p = Pressure. r = Radius. t = Wall thickness. |

Circle Equations | (A=pi*r^2) (C=2*pi*r) (d=2r) (r=c/2*pi) |

Hydrodynamic Lubrication | Self-generating, full film lubrication. The relative velocity of the surfaces dragging the lubricant create wedge shaped pressure fields that balance any applied load. Greater load= a thinner wedge and a greater pressure field-e.g. bearings in a gearbox |

Conditions for hydrodynamic lubrication | 1) relative velocity between the two surfaces. 2) a convergent shape of the oil film. 3) lubricant of sufficient viscosity. |

Advantages of hydrodynamic lubrication | Very low friction. Lower wear. Run cooler. less friction. |

Disdvantages of hydrodynamic lubrication | Require forced lubrication to maintain the full film. The correct viscosity of oil is required to avoid contact between metal pieces . |

Reduce torque (power absorbed) in Petrov's Equation | Γ = 2πηr³Lω/Cr. Reduce any of the parameters on the top and power absorbed will reduce: a reduction of'r' will have the biggest effect. Or you can increase the clearance on the bottom. |