Catalog / Mechanical Engineering Cheatsheet
Mechanical Engineering Cheatsheet
A comprehensive cheat sheet covering essential formulas, concepts, and principles in mechanical engineering.
Thermodynamics
Basic Concepts
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Zeroth Law |
If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. |
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First Law |
Energy cannot be created or destroyed, only converted from one form to another. ΔU = Q - W |
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Second Law |
The total entropy of an isolated system can only increase over time. ΔS ≥ 0 |
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Third Law |
As temperature approaches absolute zero, the entropy of a system approaches a minimum or zero. |
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Enthalpy (H) |
H = U + PV, where U is internal energy, P is pressure, and V is volume. |
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Specific Heat (c) |
The amount of heat required to raise the temperature of one unit mass of a substance by one degree. Q = mcΔT |
Thermodynamic Processes
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Isothermal |
Constant temperature. ΔT = 0, Q = W |
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Adiabatic |
No heat transfer. Q = 0, ΔU = -W |
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Isobaric |
Constant pressure. ΔP = 0, W = PΔV |
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Isochoric (Isometric) |
Constant volume. ΔV = 0, W = 0, ΔU = Q |
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Polytropic |
Process described by PV^n = constant, where n is the polytropic index. W = (P2V2 - P1V1) / (1-n) |
Cycles
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Carnot Cycle |
Theoretical thermodynamic cycle with the highest possible efficiency. Efficiency = 1 - (Tc/Th) |
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Otto Cycle |
Idealized cycle for spark-ignition internal combustion engines. Efficiency = 1 - (1/r^(k-1)) |
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Diesel Cycle |
Idealized cycle for compression-ignition internal combustion engines. Efficiency = 1 - (1/r^(k-1)) * ((rc^k - 1) / (k*(rc-1))) |
Fluid Mechanics
Fluid Properties
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Density (ρ) |
Mass per unit volume. ρ = m/V |
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Specific Weight (γ) |
Weight per unit volume. γ = ρg |
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Viscosity (μ) |
Resistance to flow. τ = μ(du/dy) |
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Kinematic Viscosity (ν) |
Ratio of viscosity to density. ν = μ/ρ |
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Surface Tension (σ) |
Force per unit length acting at the interface between two fluids. F = σL |
Fluid Statics
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Pressure (P) |
Force per unit area. P = F/A |
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Hydrostatic Pressure |
Pressure due to the weight of a fluid column. P = ρgh |
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Buoyancy |
Upward force exerted by a fluid on an immersed object. Fb = ρVg |
Fluid Dynamics
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Continuity Equation |
A1V1 = A2V2 (for incompressible fluids) |
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Bernoulli’s Equation |
P + (1/2)ρV^2 + ρgh = constant |
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Reynolds Number (Re) |
Dimensionless number indicating whether flow is laminar or turbulent. Re = (ρVD)/μ |
Solid Mechanics
Stress and Strain
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Stress (σ) |
Force per unit area. σ = F/A |
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Strain (ε) |
Deformation per unit length. ε = ΔL/L |
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Young’s Modulus (E) |
Measure of stiffness of a material. E = σ/ε |
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Shear Stress (τ) |
Stress parallel to the surface. τ = F/A |
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Shear Strain (γ) |
Angular deformation. γ = Δx/L |
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Shear Modulus (G) |
Measure of a material’s resistance to shear deformation. G = τ/γ |
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Poisson’s Ratio (ν) |
Ratio of lateral strain to axial strain. ν = -ε_lateral/ε_axial |
Beams
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Bending Stress (σ) |
σ = My/I, where M is bending moment, y is distance from neutral axis, and I is moment of inertia. |
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Shear Stress in Beams (τ) |
τ = VQ/Ib, where V is shear force, Q is first moment of area, I is moment of inertia, and b is width. |
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Deflection of Beams (δ) |
Depends on loading and support conditions. Common formulas are available for various cases. |
Torsion
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Torsional Shear Stress (τ) |
τ = Tρ/J, where T is torque, ρ is radial distance, and J is polar moment of inertia. |
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Angle of Twist (θ) |
θ = TL/GJ, where L is length, G is shear modulus, and J is polar moment of inertia. |
Dynamics and Vibrations
Kinematics
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Displacement (s) |
Change in position. Measured in meters (m). |
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Velocity (v) |
Rate of change of displacement. v = ds/dt. Measured in meters per second (m/s). |
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Acceleration (a) |
Rate of change of velocity. a = dv/dt. Measured in meters per second squared (m/s²). |
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Uniform Acceleration Equations |
v = u + at, s = ut + (1/2)at², v² = u² + 2as |
Kinetics
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Newton’s Second Law |
F = ma, where F is force, m is mass, and a is acceleration. |
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Work (W) |
W = Fd cos(θ), where F is force, d is displacement, and θ is the angle between them. |
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Kinetic Energy (KE) |
KE = (1/2)mv², where m is mass and v is velocity. |
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Potential Energy (PE) |
PE = mgh, where m is mass, g is acceleration due to gravity, and h is height. |
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Power (P) |
P = W/t, where W is work and t is time. Also, P = Fv. |
Vibrations
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Natural Frequency (ωn) |
ωn = √(k/m), where k is spring stiffness and m is mass. |
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Damping Ratio (ζ) |
ζ = c / (2√(mk)), where c is damping coefficient. |
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Damped Frequency (ωd) |
ωd = ωn√(1 - ζ²) |