# Basic symbols

Symbol Name of the symbol Unit
 bolt $\mathrm{ }$
 type of strut mounting $\mathrm{ }$
$A$ 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 $\mathrm{kg\cdot m^2}$
$J$ 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 $\mathrm{kg\cdot m^2/s}$
$M$ 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 $\mathrm{Nm}$
$T$ the water temperature $\mathrm{°C}$
$T^*$ temperature reducing quantity $\mathrm{K}$
$T_b$ lower limit temperature $\mathrm{K}$
$T_{SV}$ saturated vapor temperature $\mathrm{°C}$
$W$ work $\mathrm{J}$
$W$ work done by rotational force $\mathrm{J}$
$\text{Region}$ region $\mathrm{ }$
$a$ speed of Sound $\mathrm{m/s}$
$a$ acceleration $\mathrm{m/s{^2}}$
$b$ 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 $\mathrm{mm}$
$g$ 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 $\mathrm{m/s}$
$v̄$ 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 $\mathrm{rad/s}$