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 of armour bedding [mm$^2$]

$A_{ar}$

Cross-sectional area of armour [mm$^2$]

$A_c$

Cross-sectional area of conductor [mm$^2$]

$A_{comp}$

Cross-sectional area of compartment [m$^2$]

$A_d$

Cross-sectional area of duct wall [mm$^2$]

$A_{d,fill}$

Free cross-sectional area inside duct [mm$^2$]

$A_{di}$

Surface of duct inner wall [m$^2$]

$A_{do}$

Surface of duct outer wall [m$^2$]

$A_e$

Surface of object [m$^2$]

$A_{encl}$

Cross-sectional area of enclosure [mm$^2$]

$A_{er}$

Surface of object [m$^2$]

$A_f$

Cross-sectional area of filler [mm$^2$]

$A_{hsf}$

Cross-sectional area of fluid [mm$^2$]

$A_{hsi}$

Cross-sectional area of insulation [mm$^2$]

$A_{hsj}$

Cross-sectional area of outer jacket [mm$^2$]

$A_{hsp}$

Cross-sectional area of fluid-filled pipe [mm$^2$]

$A_i$

Cross-sectional area of insulation [mm$^2$]

$A_{it}$

Cross-sectional area of insulation (IEC 60853) [mm$^2$]

$A_j$

Cross-sectional area of jacket [mm$^2$]

$A_{prot}$

Cross-sectional area of protective cover [mm$^2$]

$A_{sc}$

Cross-sectional area of screen [mm$^2$]

$A_{scb}$

Cross-sectional area of screen bedding [mm$^2$]

$A_{scs}$

Cross-sectional area of screen serving [mm$^2$]

$A_{sh}$

Cross-sectional area of sheath [mm$^2$]

$A_{shj}$

Cross-sectional area of sheath jacket [mm$^2$]

$A_{skid}$

Cross-sectional area of skid wires [mm$^2$]

$A_{sp}$

Cross-sectional area of steel pipe [mm$^2$]

$A_t$

Cross-sectional area of the tunnel [m$^2$]

$A_{tape}$

Cross-sectional area of bedding/serving tapes [mm$^2$]

$\beta_1$

Substitution coefficient $\beta_1$ for eddy-currents

$\beta_X$

Crossing angle [rad] [rad]

$C_b$

Capacitance of insulation [F/m]

$c_c$

Distance between the axis of a conductor and the cable center [mm]

$C_E$

Capacitance to earth [F/m]

$C_{g3}$

Factor C3 for partially buried pipes

$d_{ct}$

External diameter of conductor for transient calculations [mm]

$D_e$

External diameter of object [mm]

$D_{eq}$

Equivalent diameter of a group of round objects [mm]

$D_f$

External diameter of the filler [mm]

$d_x$

Equivalent diameter of a 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 of outer surface [K]

$\Delta \theta_{kp}$

Temperature rise by buried object k [K]

$\Delta \theta_{kp,t}$

Transient temperature rise of outer surface by object k [K]

$\Delta \theta_{uh}$

Temperature rise by crossing heat sources at z [K]

$Do_t$

Tunnel/trough outer diameter [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 of twisted conductors

$F_{lay,ar}$

Effective length per unit lay length of armour

$F_{lay,c}$

Effective length per unit lay length of conductor strands

$F_{lay,sc}$

Effective length per unit lay length of screen wires

$F_m$

Radiation coefficient mutual

$F_x$

Geometrical distance factor for multi-core cables

$G$

Conductance [S/m]

$G_1$

Geometric factor $G_1$

$G_2$

Geometric factor $G_2$ for cables with separate sheaths

$g_{dry}$

Geometric constant of circle with dried-out soil [p.u.]

$GMR_c$

Geometric mean radius of conductor [mm]

$H_1$

Component of inductance $H_1$ of armour [H/m]

$H_2$

Component of inductance $H_2$ of armour [H/m]

$h_{ground}$

Heat transfer coefficient buried part of wall to soil [W/(K.m$^2$)]

$h_t$

Inner height [m]

$H_x$

Magnetic field x-component [mH]

$H_y$

Magnetic field y-component [mH]

$I_c$

Conductor current [A]

$I_{EMF}$

Phase current for EMF calculation [A]

$K_A$

Coefficient K to calculate in air

$K_{par}$

Constant $K_{par}$ (Ovuworie)

$K_{vermeer}$

Vermeer constant for convection heat transfer

$L_1$

Inductance of phase 1 [H/m]

$L_2$

Inductance of phase 2 [H/m]

$L_3$

Inductance of phase 3 [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]

$Q_{it1}$

Thermal capacitance of insulation, 1st portion (IEC 60853) [J/(m.K)]

$Q_{it2}$

Thermal capacitance of insulation, 2nd portion (IEC 60853) [J/(m.K)]

$q_x$

Factor for characteristic diameter

$r_b$

Equivalent radius of backfill [mm]

$R_{co}$

Standard DC resistance of conductor [$\Omega$/km]

$T_1$

Thermal resistance between one conductor and sheath [K.m/W]

$T_2$

Thermal resistance of armour bedding [K.m/W]

$T_3$

Thermal resistance of jacket [K.m/W]

$T_{4d}$

Thermal resistance for daily load cycle [K.m/W]

$T_{4db}$

Correction of thermal resistance for backfill [K.m/W]

$T_{4i}$

Thermal resistance of medium in the duct [K.m/W]

$T_{4ii}$

Thermal resistance of the duct wall [K.m/W]

$T_{4iii}$

Thermal resistance to ambient [K.m/W]

$T_{4pii}$

Thermal resistance of the pipe wall [K.m/W]

$T_{4piii}$

Thermal resistance of the pipe to ambient [K.m/W]

$T_{4ss}$

Steady-state thermal resistance [K.m/W]

$T_{4w}$

Thermal resistance for weekly load cycle [K.m/W]

$T_{4y}$

Thermal resistance for yearly load cycle [K.m/W]

$T_{ab}$

Thermal resistance of armour bedding [K.m/W]

$T_{at}$

Thermal resistance by convection, air to tunnel [K.m/W]

$T_{conv,ce}$

Thermal resistance by convection, conductor to enclosure [K.m/W]

$T_{cs}$

Thermal resistance of conductor shield [K.m/W]

$T_{ct}$

Thermal resistance of conductor tape [K.m/W]

$T_{dsh}$

Thermal resistance of corrugation filling [K.m/W]

$T_e$

External thermal resistance of tunnel [K.m/W]

$T_{hsi}$

Thermal resistance of insulation [K.m/W]

$T_{hsj}$

Thermal resistance of outer jacket [K.m/W]

$T_{hsp}$

Thermal resistance of fluid-filled pipe [K.m/W]

$T_i$

Thermal resistance of insulation [K.m/W]

$T_{ins}$

Thermal resistance of insulation [K.m/W]

$T_{is}$

Thermal resistance of insulation screen [K.m/W]

$T_j$

Thermal resistance of jacket [K.m/W]

$T_{prot}$

Thermal resistance of protective cover [K.m/W]

$T_{riser}$

Thermal resistance of riser/J-tubes in air/water [K.m/W]

$T_{sa}$

Thermal resistance by convection, surface to air [K.m/W]

$T_{scb}$

Thermal resistance of screen bedding [K.m/W]

$T_{scs}$

Thermal resistance of screen serving [K.m/W]

$T_{shj}$

Thermal resistance of sheath jacket [K.m/W]

$T_{st}$

Radiation thermal resistance, surface to tunnel [K.m/W]

$T_{tr}$

Thermal resistance of trough [K.m/W]

$T_{tw}$

Thermal resistance of tunnel wall [K.m/W]

$T_{wall}$

Thermal resistance of pipe wall [K.m/W]

$\tau_{ar}$

Armour angle [rad]

$\theta_{gas}$

Gas temperature [°C]

$U_{partially}$

OHTC of partially buried pipe [W/(K.m$^2$)]

$U_{wall}$

OHTC of pipe wall [W/(K.m$^2$)]

$V_{comp}$

Gas volume [m$^3$]

$W_{conv,ce}$

Convection heat transfer, conductor to enclosure [W/m]

$W_{conv,da}$

Convection heat transfer, duct to air [W/m]

$W_{conv,gd}$

Convection heat transfer, gas to duct [W/m]

$W_{conv,od}$

Convection heat transfer, object to duct [W/m]

$W_{conv,og}$

Convection heat transfer, object to gas [W/m]

$W_{conv,sa}$

Convection heat transfer, surface to air [W/m]

$W_{de}$

Losses outside of riser/J-tube [W/m]

$W_{rad,ce}$

Radiation heat transfer, conductor to enclosure [W/m]

$W_{rad,da}$

Radiation heat transfer, duct to air [W/m]

$W_{rad,sa}$

Radiation heat transfer, surface to air [W/m]

$X_0$

Zero sequence reactance [$\Omega$/m]

$X_{ar}$

Self reactance of armour [$\Omega$/m]

$X_c$

Self reactance of conductor [$\Omega$/m]

$X_m$

Mutual reactance between conductors [$\Omega$/m]

$x_p$

Factor for proximity effect of conductors

$x_s$

Factor for skin effect on conductor

$X_s$

Self reactance of 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]

$z_{ar,i}$

Impedance of armour inner surface [$\Omega$/m]

$z_{ar,m}$

Mutual impedance of armour [$\Omega$/m]

$z_{ar,o}$

Impedance of armour outer surface [$\Omega$/m]

$z_{e1}$

Impedance of conductor outer surface [$\Omega$/m]

$z_{e2}$

Impedance of insulation between conductor and screen [$\Omega$/m]

$z_{earth}$

Impedance of earth return in ground [$\Omega$/m]

$z_{kp}$

Impedance between cable k and p in ground [$\Omega$/m]

$z_{os}$

Impedance of outersheath jacket [$\Omega$/m]

$z_{sc,i}$

Impedance of screen inner surface [$\Omega$/m]

$z_{sc,m}$

Mutual impedance of screen [$\Omega$/m]

$z_{sc,o}$

Impedance of screen outer surface [$\Omega$/m]

$z_{sc,sh}$

Impedance of insulation between screen and sheath [$\Omega$/m]

$z_{sh,i}$

Impedance of sheath inner surface [$\Omega$/m]

$z_{sh,m}$

Mutual impedance of sheath [$\Omega$/m]

$z_{sh,o}$

Impedance of sheath outer surface [$\Omega$/m]

$\zeta_{od}$

Radiation shape factor for touching cables