Mechanical Formulae

ENGINEERING MECHANICS

TermsFormulae
PowerForce x Velocity
MomentForce x Distance
Area moment of inertia of circular section about centroid\frac{\pi}{64}\times D^{4}
Area moment of inertia of rectangular section about centroid\frac{bd^{3}}{12}
Area moment of inertia of triangular section about centroid\frac{bh^{3}}{36}
Area moment of inertia of triangular section about base\frac{bh^{3}}{12}
Mass moment of inertia of disc type rotating object
(about axis of rotation)
\frac{mr^{2}}{2}
Mass moment of inertia of rimmed type rotating object
(about axis of rotation)
mr^{2}
Polar moment of inertia\frac{\pi}{32}\times D^{4}
Radius of gyration\sqrt{\frac{I}{A}} , where I = moment of inertia, A = Area
Kinetic energy of linear motion½ mv² where m = mass, v = velocity
Kinetic energy of rotating motion½ Iω² where I = mass moment of inertia, ω = angular velocity
Potential energymass x acceleration due to gravity x height -> mgh
Momentummass x velocity
Angular momentummass moment of inertia about axis of rotation x angular velocity -> Iω
Centroid of circlex = b / 2, y = d / 2
Centroid of quadrant circlex = 4r / 3π, y = 4r / 3π
Centroid of trianglex = b / 3, y = h / 3
b = breadth, d = depth, D = diameter, r = radius, m = mass

THERMODYNAMICS / THERMAL ENGINEERING

TermsFormulae
Gas equationPV = mRT or
Pν = RT or
PV = nRT
Number of molesMass / Molecular weight
Specific heat ratio or adiabatic index\frac{C_{p}}{C_{v}}
Specific heat at constant pressure\frac{\gamma R}{\gamma-1}
Specific heat at constant volume\frac{R}{\gamma-1}
Gas constantC_{p}-C_{v}
P = pressure, V = volume, T = Temperature, ν = specific volume, n = number of moles, R = gas constant, C_{p} , C_{v} are specific heat at constant pressure and volume, \gamma = Specific heat ratio or adiabatic index

HEAT AND MASS TRANSFER

TermsFormulae
Thermal diffusivity\frac{K}{\rho C_{p}}
Heat fluxheat transfer / area
K = thermal conductivity, C_{p} = specific heat at constant pressure, ρ = density

FLUID MECHANICS

TermsFormulae
Mass densitymass / volume
Specific volume1 / mass density
Specific gravitydensity of the fluid / density of the standard fluid or
specific weight of the fluid / specific weight of standard fluid

STRENGTH OF MATERIALS

TermsFormulae
Stressforce / area
Strainchange in length / original length
Young’s modulus or modulus of elasticitystress / strain
Modulus of rigidity or shear modulusshear stress / shear strain
Bulk modulusdirect stress / volumetric strain
Section modulusmoment of inertia about neutral axis / maximum distance from the neutral axis to outer fiber of the cross section
Polar moduluspolar moment of inertia / radius of the shaft
Stiffnessload / deflection

THEORY OF MACHINES

TermsFormulae
Gear ratiopinion speed / wheel speed or number of wheel teeth / number of pinion teeth
Frequencycycles / second
Modulepitch circle diameter / number of teeth

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