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Basic symbols

Symbol Name of the symbol Unit
$ $ bolt $\mathrm{ }$
$A$ 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 $\mathrm{mm}$
$E$ function $ E $ $\mathrm{ }$
$F$ function $ F $ $\mathrm{ }$
$G$ 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 $ $\mathrm{ }$
$J$ exponent $ J $ $\mathrm{ }$
$J^o$ 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 $\mathrm{ }$
$M$ air molar mass at sea level $\mathrm{kg\cdot kmol^{-1}}$
$M$ moment $\mathrm{Nm}$
$N_A$ 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 $ $\mathrm{K}$
$S_F$ 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 $\mathrm{°C}$
$\text{Region}$ region $\mathrm{ }$
$a$ speed of Sound $\mathrm{m/s}$
$b$ width key $\mathrm{mm}$
$c_p$ 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 $\mathrm{mm}$
$g$ 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 above sea level $\mathrm{m}$
$l$ mean free path of air particles $\mathrm{m}$
$l$ length key $\mathrm{mm}$
$l_t$ tolerance of key length $\mathrm{mm}$
$n$ air number density $\mathrm{m^{-3}}$
$n$ coefficient $ n $ $\mathrm{ }$
$n^o$ coefficient $ n^o $ $\mathrm{ }$
$p$ the water pressure $\mathrm{Pa}$
$p^*$ 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 $\mathrm{mm}$
$r_1$ max. rounding the key $\mathrm{mm}$
$r_2$ groove rounding $\mathrm{mm}$
$s$ specific entropy $\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$t$ depth in the shaft $\mathrm{mm}$
$t$ depth of groove, notch $\mathrm{mm}$
$t_1$ 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 $\mathrm{J\cdot kg^{-1}}$
$v̄$ mean air-particle speed $\mathrm{m/s}$
$w$ speed of sound $\mathrm{m\cdot s^{-1}}$
$α_p$ relative pressure coefficient $\mathrm{K^{-1}}$
$α_ν$ isobaric cubic expansion coefficient $\mathrm{K^{-1}}$
$β$ transformed pressure $\mathrm{ }$
$β$ 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 $\mathrm{ }$
$θ$ reduced temperature $\mathrm{ }$
$θ$ transformed temperature $\mathrm{ }$
$κ$ adiabatic index $\mathrm{ }$
$κ_T$ isothermal compressibility $\mathrm{Pa^{-1}}$
$λ$ thermal conductivity $\mathrm{W\cdot m^{-1}\cdot K^{-1}}$
$μ$ dynamic viscosity $\mathrm{kg\cdot m^{-1}\cdot s^{-1}}$
$μ$ discharge coefficient $\mathrm{ }$
$ν$ 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 $\mathrm{Hz}$