Cableizer ®

Archimedes' constant $\pi$

The constant $\pi$ represents the area of the unit circle, the half-period of trigonometric functions, and many other things in mathematics.

Symbol
$\pi$

Default
3.141592653589793

Used in
$A_{ab}$
Cross-sectional area armour bedding [mm$^2$]
$A_{ar}$
Cross-sectional area armour [mm$^2$]
$A_c$
Cross-sectional area conductor [mm$^2$]
$A_{comp}$
Cross-sectional area compartment [m$^2$]
$A_d$
Cross-sectional area duct wall [mm$^2$]
$A_{d,fill}$
Free cross-sectional area inside duct [mm$^2$]
$A_{di}$
Duct surface (inner) [m$^2$]
$A_{do}$
Duct surface (outer) [m$^2$]
$A_e$
Surface of object [m$^2$]
$A_{encl}$
Cross-sectional area enclosure [mm$^2$]
$A_{er}$
Surface of object [m$^2$]
$A_f$
Cross-sectional area filler [mm$^2$]
$A_{foj}$
Cross-sectional area protective jacket [mm$^2$]
$A_{hsf}$
Cross-sectional area fluid [mm$^2$]
$A_{hsi}$
Cross-sectional area pipe insulation [mm$^2$]
$A_{hsj}$
Cross-sectional area protective jacket [mm$^2$]
$A_{hsp}$
Cross-sectional area fluid-filled pipe [mm$^2$]
$A_i$
Cross-sectional area insulation [mm$^2$]
$A_{i,t}$
Cross-sectional area insulation (IEC 60853) [mm$^2$]
$A_j$
Cross-sectional area jacket [mm$^2$]
$A_{prot}$
Cross-sectional area protective cover [mm$^2$]
$A_{sc}$
Cross-sectional area screen [mm$^2$]
$A_{scb}$
Cross-sectional area screen bedding [mm$^2$]
$A_{scs}$
Cross-sectional area screen serving [mm$^2$]
$A_{sh}$
Cross-sectional area sheath [mm$^2$]
$A_{shj}$
Cross-sectional area sheath jacket [mm$^2$]
$A_{sp}$
Cross-sectional area steel pipe [mm$^2$]
$A_{sw}$
Cross-sectional area skid wires [mm$^2$]
$A_t$
Cross-sectional area (inner) tunnel [m$^2$]
$A_{tape}$
Cross-sectional area tapes [mm$^2$]
$\beta_1$
Substitution coefficient $\beta_1$ for eddy-currents
$\beta_X$
Crossing angle [rad] [rad]
$C_{ag}$
Capacitance armour - ground [F/m]
$C_b$
Capacitance insulation [F/m]
$c_c$
Distance conductor axis—cable axis [mm]
$C_{cs}$
Capacitance conductor - shield [F/m]
$C_E$
Capacitance to earth [F/m]
$C_{g3}$
Factor C3 pipe
$C_{sa}$
Capacitance shield - armour [F/m]
$C_{sg}$
Capacitance shield - ground [F/m]
$d_{ar}$
Mean diameter armour [mm]
$d_{c,t}$
External diameter conductor, transient [mm]
$D_e$
External diameter object [mm]
$D_{eq}$
Equivalent diameter of a group of round objects [mm]
$D_f$
Diameter over filler [mm]
$d_f$
Diameter armour wire [mm]
$d_x$
Equivalent diameter conductor [mm]
$\delta_{ar}$
Equivalent thickness of armour [mm]
$\Delta \theta_{0x,h}$
Temperature rise of the conductor by source h [K]
$\Delta \theta_{e,t}$
Transient temperature rise outer surface [K]
$\Delta \theta_{kp}$
Temperature rise by object k [K]
$\Delta \theta_{kp,t}$
Transient temperature rise outer surface by object k [K]
$\Delta \theta_{uh}$
Temperature rise by crossing heat sources z [K]
$Do_t$
Diameter (outer) tunnel [m]
$F_{\alpha}$
Inclination derating factor [p.u.]
$F_{eq}$
Factor for envelope circle for a group of equal circles
$F_{ij}$
View factor object—object
$F_{lay,3c}$
Effective length per unit lay length twisted conductors
$F_{lay,ar}$
Effective length per unit lay length armour
$F_{lay,c}$
Effective length per unit lay length conductor strands
$F_{lay,sc}$
Effective length per unit lay length screen wires
$F_{lay,sw}$
Effective length per unit lay length skid wires
$F_m$
Mutual radiation coefficient
$F_x$
Geometrical distance factor for multi-core cables
$G$
Conductance [S/m]
$G_1$
Geometric factor $G_1$
$G_2$
Geometric factor $G_2$ cables with separate sheaths
$g_{dry}$
Geometric constant of circle drying zone [p.u.]
$GMR_c$
Geometric mean radius conductor [m]
$GMR_{sp}$
Geometric mean radius steel pipe [m]
$H_1$
Inductance $H_1$ armour [H/m]
$H_2$
Inductance $H_2$ armour [H/m]
$h_{ground}$
Heat transfer coefficient part of pipe in contact with ground [W/(K.m$^2$)]
$h_t$
Height (inner) [m]
$H_x$
Magnetic field x [mH]
$H_y$
Magnetic field y [mH]
$I_c$
Conductor current [A]
$I_{EMF}$
Phase current for EMF calculation [A]
$K_A$
Coefficient K in air
$K_{par}$
Constant $K_{par}$ (Ovuworie)
$K_{vermeer}$
Vermeer constant for convection heat transfer
$L_a$
Self inductance conductor [H/m]
$L_i$
Inductance conductor i [H/m]
$L_m$
Inductance (mean) [H/m]
$\lambda_i$
Parameter $\lambda$ for linear density of dielectric losses
$\omega$
Angular frequency [rad/s]
$p_{soil}$
Depth of image source
$\phi_{ar}$
Angle between armour and cable axis [rad]
$Q_{i,t1}$
Thermal capacitance insulation, 1st portion (IEC 60853) [J/(m.K)]
$Q_{i,t2}$
Thermal capacitance insulation, 2nd portion (IEC 60853) [J/(m.K)]
$q_x$
Factor characteristic diameter
$r_b$
Equivalent radius backfill [mm]
$R_{co}$
Standard DC resistance of conductor [$\Omega$/km]
$R_{sky}$
Resistance skywire [$\Omega$/m]
$\rho_{ar}$
Specific electrical resistivity armour material [$\Omega$.m]
$\rho_c$
Electrical resistivity conductor material [$\Omega$.m]
$S_{ar}$
Circumference armour [mm]
$T_1$
Thermal resistance conductor—sheath [K.m/W]
$T_2$
Thermal resistance armour bedding [K.m/W]
$T_3$
Thermal resistance jacket [K.m/W]
$T_{4c}$
Thermal resistance backfill correction Neher [K.m/W]
$T_{4d}$
Thermal resistance daily load cycle [K.m/W]
$T_{4db}$
Thermal resistance backfill correction [K.m/W]
$T_{4i}$
Thermal resistance medium in the duct [K.m/W]
$T_{4ii}$
Thermal resistance duct wall [K.m/W]
$T_{4iii}$
Thermal resistance ambient [K.m/W]
$T_{4pii}$
Thermal resistance pipe wall [K.m/W]
$T_{4piii}$
Thermal resistance pipe—ambient [K.m/W]
$T_{4ss}$
Thermal resistance steady-state [K.m/W]
$T_{4w}$
Thermal resistance weekly load cycle [K.m/W]
$T_{4y}$
Thermal resistance yearly load cycle [K.m/W]
$T_{ab}$
Thermal resistance armour bedding [K.m/W]
$T_{ab,1}$
Thermal resistance armour bedding 1 [K.m/W]
$T_{ab,2}$
Thermal resistance armour bedding 2 [K.m/W]
$T_{at}$
Thermal resistance convection air—tunnel [K.m/W]
$T_{conv,ce}$
Thermal resistance convection conductor—enclosure [K.m/W]
$T_{cs}$
Thermal resistance conductor shield [K.m/W]
$T_{ct}$
Thermal resistance conductor tape [K.m/W]
$T_{dsh}$
Thermal resistance corrugation filling [K.m/W]
$T_e$
External thermal resistance of tunnel [K.m/W]
$T_f$
Thermal resistance filler [K.m/W]
$T_{foj}$
Thermal resistance protective jacket [K.m/W]
$T_{hsi}$
Thermal resistance pipe insulation [K.m/W]
$T_{hsj}$
Thermal resistance protective jacket [K.m/W]
$T_{hsp}$
Thermal resistance fluid-filled pipe [K.m/W]
$T_i$
Thermal resistance insulation [K.m/W]
$T_{ins}$
Thermal resistance insulation [K.m/W]
$T_{is}$
Thermal resistance insulation screen [K.m/W]
$T_j$
Thermal resistance jacket [K.m/W]
$T_{jj}$
Thermal resistance additional layer [K.m/W]
$T_{prot}$
Thermal resistance protective cover [K.m/W]
$T_{riser}$
Thermal resistance riser [K.m/W]
$T_{sa}$
Thermal resistance convection object—air [K.m/W]
$T_{scb}$
Thermal resistance screen bedding [K.m/W]
$T_{scs}$
Thermal resistance screen serving [K.m/W]
$T_{shj}$
Thermal resistance sheath jacket [K.m/W]
$T_{st}$
Thermal resistance radiation object—tunnel [K.m/W]
$T_{tr}$
Thermal resistance trough [K.m/W]
$T_{tw}$
Thermal resistance wall [K.m/W]
$T_{wall}$
Thermal resistance pipe wall [K.m/W]
$\theta_{gas}$
Gas temperature [°C]
$U_{partially}$
OHTC pipe partially buried [W/(K.m$^2$)]
$U_{wall}$
OHTC pipe wall [W/(K.m$^2$)]
$V_{comp}$
Gas volume [m$^3$]
$W_{conv,ce}$
Convective heat transfer conductor→enclosure [W/m]
$W_{conv,ext}$
Convective heat transfer riser—air [W/m]
$W_{conv,gd}$
Convective heat transfer gas—duct [W/m]
$W_{conv,int}$
Convective heat transfer cable→riser [W/m]
$W_{conv,og}$
Convective heat transfer cable→gas [W/m]
$W_{conv,sa}$
Convective heat transfer, surface→air [W/m]
$W_{de}$
Losses outside of riser [W/m]
$W_{rad,ce}$
Radiation heat transfer conductor→enclosure [W/m]
$W_{rad,ext}$
Radiation heat transfer riser—air [W/m]
$W_{rad,sa}$
Radiation heat transfer surface—air [W/m]
$X_1$
Positive sequence reactance [$\Omega$/m]
$X_a$
Self reactance conductor [$\Omega$/m]
$X_{ap}$
Equivalent mutual reactance between conductors [$\Omega$/m]
$X_{ar}$
Self reactance armour [$\Omega$/m]
$X_c$
Mutual reactance between middle and outer cables in flat formation with earth return [$\Omega$/m]
$X_{cp}$
Zero-sequence reactance steel pipe [$\Omega$/m]
$X_d$
Reactance steel pipe [$\Omega$/m]
$X_e$
Self reactance screen/sheath [$\Omega$/m]
$X_{ij}$
Mutual reactance between conductors i + j [$\Omega$/m]
$X_L$
Mutual reactance between outer cables in flat formation [$\Omega$/m]
$X_m$
Mutual reactance between conductors flat formation without transposition [$\Omega$/m]
$X_{mut}$
Mutual reactance [$\Omega$/m]
$x_p$
Factor for proximity effect of conductors
$x_s$
Factor for skin effect on conductor
$X_s$
Self reactance screen/sheath [$\Omega$/m]
$X_{S1}$
Reactance section 1 [$\Omega$/m]
$X_{S2}$
Reactance section 2 [$\Omega$/m]
$X_{S3}$
Reactance section 3 [$\Omega$/m]
$X_{sky}$
Reactance skywire [$\Omega$/m]
$Z_{ct}$
Self impedance earth continuity conductor [$\Omega$/m]
$Z_{kp}$
Impedance between cable k and p in ground [$\Omega$/m]
$Z_{mt}$
Equivalent mutual impedance between earth continuity conductor and any cable [$\Omega$/m]
$\zeta_{er}$
Radiation shape factor touching cables
$\mathcal{Z}_1$
Impedance conductor outer surface [$\Omega$/m]
$\mathcal{Z}_2$
Impedance insulation conductor—screen [$\Omega$/m]
$\mathcal{Z}_{34}$
Impedance insulation shield—armour [$\Omega$/m]
$\mathcal{Z}_{3,s}$
Impedance shield inner surface [$\Omega$/m]
$\mathcal{Z}_{3,sc}$
Impedance screen inner surface [$\Omega$/m]
$\mathcal{Z}_{3,sh}$
Impedance sheath inner surface [$\Omega$/m]
$\mathcal{Z}_{4,s}$
Mutual impedance shield [$\Omega$/m]
$\mathcal{Z}_{4,sc}$
Mutual impedance screen [$\Omega$/m]
$\mathcal{Z}_{4,sh}$
Mutual impedance sheath [$\Omega$/m]
$\mathcal{Z}_{56}$
Impedance jacket [$\Omega$/m]
$\mathcal{Z}_{5,s}$
Impedance shield outer surface [$\Omega$/m]
$\mathcal{Z}_{5,sc}$
Impedance screen outer surface [$\Omega$/m]
$\mathcal{Z}_{5,sh}$
Impedance sheath outer surface [$\Omega$/m]
$\mathcal{Z}_6$
Impedance insulation screen—sheath [$\Omega$/m]
$\mathcal{Z}_g$
Impedance earth return in ground [$\Omega$/m]
$\mathcal{Z}_{gm}$
Impedance mutual earth return in ground [$\Omega$/m]
$\mathcal{Z}_{pin}$
Impedance armour inner surface [$\Omega$/m]
$\mathcal{Z}_{pmut}$
Mutual impedance armour [$\Omega$/m]
$\mathcal{Z}_{pout}$
Impedance armour outer surface [$\Omega$/m]