Basic symbols

Symbol	Name of the symbol	Unit
$ $	bolt	$\mathrm{ }$
$ $	type of strut mounting	$\mathrm{ }$
$A$	amplitude	$\mathrm{m}$
$A$	function $ A $	$\mathrm{ }$
$A_b$	cross‐sectional area of the bolts	$\mathrm{mm^2}$
$B$	function $ B $	$\mathrm{ }$
$C$	function $ C $	$\mathrm{ }$
$C_1$	coefficient $ C_1 $	$\mathrm{}$
$C_2$	coefficient $ C_2 $	$\mathrm{}$
$C_3$	coefficient $ C_3 $	$\mathrm{}$
$C_4$	coefficient $ C_4 $	$\mathrm{}$
$C_5$	coefficient $ C_5 $	$\mathrm{}$
$C_c$	coefficient according to load	$\mathrm{ }$
$D$	diameter of the shaft	$\mathrm{mm}$
$D$	basic major diameter of internal thread (nominal diameter)	$\mathrm{mm}$
$D$	diameter, larger diameter	$\mathrm{mm}$
$D$	function $ D $	$\mathrm{ }$
$D_1$	basic minor diameter of internal thread	$\mathrm{mm}$
$D_2$	basic pitch diameter of internal thread	$\mathrm{mm}$
$E$	Young's modulus	$\mathrm{MPa}$
$E$	function $ E $	$\mathrm{ }$
$E_k$	kinetic energy	$\mathrm{J}$
$E_k$	rotational kinetic energy	$\mathrm{J}$
$E_p$	gravitational potential energy	$\mathrm{J}$
$E_p$	elastic potential energy	$\mathrm{J}$
$F$	force	$\mathrm{N}$
$F$	gravitational force between two bodies	$\mathrm{N}$
$F$	function $ F $	$\mathrm{ }$
$F_f$	friction force	$\mathrm{N}$
$F_{max}$	maximal (critical) force	$\mathrm{N}$
$G$	gravitational constant	$\mathrm{m^3\cdot kg^{-1}\cdot s^{-2}}$
$G$	function $ G $	$\mathrm{ }$
$H$	height of fundamental triangle	$\mathrm{mm}$
$H$	width, larger width	$\mathrm{mm}$
$H$	geopotential altitude	$\mathrm{m}$
$H_b$	lower limit geopotential altitude	$\mathrm{m}$
$H_p$	pressure scale height	$\mathrm{m}$
$I$	exponent $ I $	$\mathrm{ }$
$I$	second moment of area	$\mathrm{mm^4}$
$I$	moment of inertia	$\mathrm{kg\cdot m^2}$
$I$	moment of Inertia for a simple pendulum	$\mathrm{kg\cdot m^2}$
$I_0$	reference sound intensity	$\mathrm{W/m^2}$
$I_1$	measured sound intensity	$\mathrm{W/m^2}$
$J$	exponent $ J $	$\mathrm{ }$
$J$	impulse	$\mathrm{kg\cdot m/s}$
$J^o$	exponent $ J^o $	$\mathrm{ }$
$K_t$	stress concentration factor	$\mathrm{ }$
$K_{tg}$	stress concentration factor with the nominal stress based on gross area	$\mathrm{ }$
$K_{tn}$	stress concentration factor with the nominal stress based on net area	$\mathrm{ }$
$K_{ts}$	stress concentration factor for shear stress	$\mathrm{ }$
$L$	strut length	$\mathrm{mm}$
$L$	angular momentum	$\mathrm{kg\cdot m^2/s}$
$L$	sound intensity level	$\mathrm{dB}$
$L_v$	voltage level	$\mathrm{dB}$
$M$	air molar mass at sea level	$\mathrm{kg\cdot kmol^{-1}}$
$M$	moment	$\mathrm{Nm}$
$M$	moment of force	$\mathrm{Nm}$
$M$	rotational force	$\mathrm{Nm}$
$N_A$	Avogadro constant	$\mathrm{kmol^{-1}}$
$P$	pitch	$\mathrm{mm}$
$P$	load, force	$\mathrm{N}$
$P_{SV}$	saturated vapor pressure	$\mathrm{Pa}$
$P_{all-B}$	allowable bearing stress	$\mathrm{MPa}$
$R$	specific gas constant	$\mathrm{J\cdot K^{-1}\cdot kg^{-1}}$
$R$	specific gas constant of ordinary water	$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$R^*$	universal gas constant	$\mathrm{J\cdot K^{-1}\cdot kmol^{-1}}$
$S$	Sutherland's empirical coefficients $ S $	$\mathrm{K}$
$S$	profile area	$\mathrm{mm^2}$
$S_F$	safety factor	$\mathrm{ }$
$S_{y}$	the minimum yield strength	$\mathrm{MPa}$
$T$	temperature $ T $	$\mathrm{K}$
$T$	torque	$\mathrm{Nm}$
$T$	period	$\mathrm{s^{-1}}$
$T$	the water temperature	$\mathrm{°C}$
$T^*$	temperature reducing quantity	$\mathrm{K}$
$T_b$	lower limit temperature	$\mathrm{K}$
$T_{SV}$	saturated vapor temperature	$\mathrm{°C}$
$V_0$	reference voltage	$\mathrm{V}$
$V_1$	measured voltage	$\mathrm{V}$
$W$	work	$\mathrm{J}$
$W$	work done by rotational force	$\mathrm{J}$
$\text{Region}$	region	$\mathrm{ }$
$a$	speed of Sound	$\mathrm{m/s}$
$a$	acceleration	$\mathrm{m/s{^2}}$
$a$	wave acceleration	$\mathrm{m/s^2}$
$b$	width key	$\mathrm{mm}$
$c$	extreme fiber distance	$\mathrm{mm}$
$c_p$	specific isobaric heat capacity	$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$c_ν$	specific isochoric heat capacity	$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$d$	basic major diameter of external thread (nominal diameter)	$\mathrm{mm}$
$d$	diameter	$\mathrm{mm}$
$d$	width	$\mathrm{mm}$
$d_1$	basic minor diameter of external thread	$\mathrm{mm}$
$d_2$	basic pitch diameter of external thread	$\mathrm{mm}$
$d_3$	basic smaller diameter of external thread	$\mathrm{mm}$
$e$	eccentricity	$\mathrm{mm}$
$f$	frequency	$\mathrm{Hz}$
$g$	gravitational acceleration	$\mathrm{m/s^2}$
$h$	height key	$\mathrm{mm}$
$h$	thickness	$\mathrm{mm}$
$h$	specific enthalpy	$\mathrm{J\cdot kg^{-1}}$
$h$	height	$\mathrm{m}$
$h$	height above sea level	$\mathrm{m}$
$i$	gyration radius	$\mathrm{mm}$
$k$	spring constant	$\mathrm{N/m}$
$l$	mean free path of air particles	$\mathrm{m}$
$l$	length key	$\mathrm{mm}$
$l_t$	tolerance of key length	$\mathrm{mm}$
$m$	the mass of the body	$\mathrm{kg}$
$m_1$	the mass of the body 1	$\mathrm{kg}$
$m_2$	the mass of the body 2	$\mathrm{kg}$
$n$	air number density	$\mathrm{m^{-3}}$
$n$	coefficient $ n $	$\mathrm{ }$
$n^o$	coefficient $ n^o $	$\mathrm{ }$
$p$	the water pressure	$\mathrm{Pa}$
$p$	momentum	$\mathrm{kg\cdot m/s}$
$p^*$	pressure reducing quantity	$\mathrm{Pa}$
$p_b$	lower limit pressure	$\mathrm{Pa}$
$p_{air}$	atmospheric pressure air	$\mathrm{Pa}$
$r$	nominal earth's radius	$\mathrm{m}$
$r$	radius of curvature of hole, arc, notch	$\mathrm{mm}$
$r$	the distance between the centers of the masses	$\mathrm{m}$
$r$	position vector	$\mathrm{m}$
$r$	distance from the axis of rotation	$\mathrm{m}$
$r_1$	max. rounding the key	$\mathrm{mm}$
$r_2$	groove rounding	$\mathrm{mm}$
$s$	specific entropy	$\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$s$	distance	$\mathrm{m}$
$t$	depth in the shaft	$\mathrm{mm}$
$t$	depth of groove, notch	$\mathrm{mm}$
$t$	temperature	$\mathrm{°C}$
$t_1$	depth in the hub	$\mathrm{mm}$
$t_t$	tolerance of the groove height in the shaft	$\mathrm{mm}$
$t_{1t}$	tolerance of the groove height in the hub	$\mathrm{mm}$
$u$	specific internal energy	$\mathrm{J\cdot kg^{-1}}$
$v$	velocity	$\mathrm{m/s}$
$v$	velocity of sound	$\mathrm{m/s}$
$v$	wave speed	$\mathrm{m/s}$
$v̄$	mean air-particle speed	$\mathrm{m/s}$
$w$	speed of sound	$\mathrm{m\cdot s^{-1}}$
$x$	deformation	$\mathrm{m}$
$Δs$	distance	$\mathrm{m}$
$Δt$	time	$\mathrm{s}$
$Δv$	velocity	$\mathrm{m/s}$
$Δθ$	angle	$\mathrm{rad}$
$Δω$	angular velocity	$\mathrm{rad/s}$
$α$	angular acceleration	$\mathrm{rad/s^2}$
$α_p$	relative pressure coefficient	$\mathrm{K^{-1}}$
$α_ν$	isobaric cubic expansion coefficient	$\mathrm{K^{-1}}$
$β$	transformed pressure	$\mathrm{ }$
$β$	coefficient for buckling	$\mathrm{ }$
$β$	temperature gradient $ β $	$\mathrm{K\cdot m^{-1}}$
$β_p$	isothermal stress coefficient	$\mathrm{kg\cdot m^{-3}}$
$β_s$	Sutherland's empirical coefficients $ β_s $	$\mathrm{kg\cdot m^{-1}\cdot s^{-1}\cdot K^{-1/2}}$
$γ$	dimensionless Gibbs free energy	$\mathrm{ }$
$γ^o$	ideal-gas part	$\mathrm{ }$
$γ^o_{ππ}$	second partial derivative of $ γ^o $ with respect to $ π $	$\mathrm{ }$
$γ^o_{πτ}$	cross derivative of $ γ^o $ with respect to $ π $ and temperature $ τ $	$\mathrm{ }$
$γ^o_{ττ}$	second partial derivative of $ γ^o $ with respect to $ τ $	$\mathrm{ }$
$γ^o_π$	derivative of $ γ^o $ with respect to the dimensionless pressure $ π $	$\mathrm{ }$
$γ^o_τ$	partial derivative of $ γ^o $ with respect to $ τ $	$\mathrm{ }$
$γ^r$	residual part	$\mathrm{ }$
$γ^r_{ππ}$	second partial derivative of $ γ^r $ with respect to $ π $	$\mathrm{ }$
$γ^r_{πτ}$	cross derivative of $ γ^r $ with respect to $ π $ and temperature $ τ $	$\mathrm{ }$
$γ^r_{ττ}$	second partial derivative of $ γ^r $ with respect to $ τ $	$\mathrm{ }$
$γ^r_π$	derivative of $ γ^r $ with respect to the dimensionless pressure $ π $	$\mathrm{ }$
$γ^r_τ$	partial derivative of $ γ^r $ with respect to $ τ $	$\mathrm{ }$
$γ_{air}$	specific weight air	$\mathrm{kg\cdot m^{-2}\cdot s^{-2}}$
$γ_{ππ}$	second partial derivative of $ γ $ with respect to $ π $	$\mathrm{ }$
$γ_{πτ}$	cross derivative of $ γ $ with respect to $ π $ and temperature $ τ $	$\mathrm{ }$
$γ_{ττ}$	second partial derivative of $ γ $ with respect to $ τ $	$\mathrm{ }$
$γ_π$	derivative of $ γ $ with respect to the dimensionless pressure $ π $	$\mathrm{ }$
$γ_τ$	partial derivative of $ γ $ with respect to $ τ $	$\mathrm{ }$
$δ$	reduced density	$\mathrm{ }$
$ζ$	loss coefficient	$\mathrm{ }$
$η$	eccentricity parameter	$\mathrm{ }$
$θ$	reduced temperature	$\mathrm{ }$
$θ$	angle	$\mathrm{rad}$
$θ$	transformed temperature	$\mathrm{ }$
$κ$	adiabatic index	$\mathrm{ }$
$κ_T$	isothermal compressibility	$\mathrm{Pa^{-1}}$
$λ$	thermal conductivity	$\mathrm{W\cdot m^{-1}\cdot K^{-1}}$
$λ$	slenderness ratio	$\mathrm{ }$
$μ$	dynamic viscosity	$\mathrm{kg\cdot m^{-1}\cdot s^{-1}}$
$μ$	discharge coefficient	$\mathrm{ }$
$μ$	coefficient of friction	$\mathrm{ }$
$ν$	kinematic viscosity	$\mathrm{m^2\cdot s^{-1}}$
$ν$	Poisson's ratio	$\mathrm{ }$
$ν$	specific volume	$\mathrm{m^3\cdot kg^{-1}}$
$π$	reduced pressure	$\mathrm{ }$
$ρ$	mass density	$\mathrm{kg\cdot m^{-3}}$
$ρ^*$	mass density reducing quantity	$\mathrm{kg\cdot m^{-3}}$
$ρ_{air}$	density air	$\mathrm{kg/m^3}$
$σ$	effective collision diameter of an air molecule	$\mathrm{m}$
$σ$	normal stress	$\mathrm{MPa}$
$σ_{all-A}$	allowable axial stress	$\mathrm{MPa}$
$σ_{all-B}$	allowable bending stress	$\mathrm{MPa}$
$σ_{all-C}$	allowable combined stress	$\mathrm{MPa}$
$σ_{max}$	maximum normal stress	$\mathrm{MPa}$
$σ_{nom}$	nominal or reference normal stress	$\mathrm{MPa}$
$τ$	inverse reduced temperature	$\mathrm{ }$
$τ_{all-S}$	allowable shear stress	$\mathrm{MPa}$
$τ_{max}$	maximum shear stress	$\mathrm{MPa}$
$τ_{nom}$	nominal or reference shear stress	$\mathrm{MPa}$
$φ$	latitude	$\mathrm{°}$
$φ$	dimensionless Helmholtz free energy	$\mathrm{ }$
$φ_{δδ}$	second partial derivative of $ φ $ with respect to $ δ $	$\mathrm{ }$
$φ_{δτ}$	cross derivative of $ φ $ with respect to $ δ $ and temperature $ τ $	$\mathrm{ }$
$φ_{ττ}$	second partial derivative of $ φ $ with respect to $ τ $	$\mathrm{ }$
$φ_δ$	derivative of $ φ $ with respect to the dimensionless density $ δ $	$\mathrm{ }$
$φ_τ$	partial derivative of $ φ $ with respect to $ τ $	$\mathrm{ }$
$ω$	air-particle collision frequency	$\mathrm{Hz}$
$ω$	angular velocity	$\mathrm{rad/s}$
$ω$	angular frequency	$\mathrm{rad/s}$