2.2　Symbols

a——mass velocity ratio；

A——cross-sectional area of pipe；

A1——cross-sectional area of pipe at cross-section 1；

A2——cross-sectional area of pipe at cross-section 2；

Ab——reinforcement area for the branch within the reinforcement zone；

Ah——reinforcement area for the run within the reinforcement zone；

Ai——flow area at cross-section i；

Ai-1——flow area at cross-section i-1；

Ap——pressure area；

Ar——required reinforcement area for opening of the run；

Aσ——bearing area；

Aw——fillet weld area within the reinforcement zone；

B——correction factor for steam compressibility；

b——ratio of pressure at piping start to that at piping end；

c——ratio of dynamic pressure to static pressure；

C——additional thickness allowing for corrosion，wear and mechanical strength；

C1——added value due to negative tolerancetolerance of pipe wall thickness；

C2——added value due to negative tolerance of steel plate thickness；

Di——inside diameter of pipe or pipe fittings；

Dib——inside diameter of the branch；

Dih——inside diameter of the run；

Dm——average diameter of reducer；

DN——nominal diameter of pipe or pipe fittings；

Do——outside diameter of pipe or pipe fittings；

Dob——outside diameter of the branch；

Doh——outside diameter of the run；

d——diameter of the minimum flow area of safety valve；

dg——inside diameter of gasket；

dH——pipe elevation variation；

dk——aperture diameter of orifice；

dm——average diameter at the point La apart from the curved section or average diameter of the pipe connected at the smaller end；

dp——medium pressure variation；

d1——dimension of longitudinal centerline of branch opening made in the run；

d2——inside diameter of pipe；

Ec——casting quality factor；

E20——modulus of elasticity of steels at 20℃；

Et——modulus of elasticity of steels at design temperature；

Et——elasticity modulus of pipe material at design temperature；

F——minimum flow area of safety valve；

f——reduction factor of stress range；

——area of orifice aperture in case of critical flow；

Fi——reaction force at cross-section i；

Fix——component force in x direction；

Fiz——component force in z direction；

Fk——area of orifice aperture in case of subcritical flow；

G——mass flow rate of medium；

g——gravitational acceleration；

Gi——flow rate of medium at cross-section i；

H——elevation difference between the start and the end of piping；

H1——elevation at the start of vertical pipe；

H2——elevation at the end of vertical pipe；

h——safety valve lift；

h1——enthalpy of medium at the start of piping；

h2——enthalpy of saturated water at pressure p；

hf——energy loss due to friction drag；

hi——minor axis radius of head；

hj——energy loss due to local resistance；

hn——enthalpy of saturated water at pressure pn；

hw——total resistance loss in piping；

I——correction factor for wall thickness of bends and elbows；

i——stress intensification factor；

K——coefficient；

K′——factor as a function of head structure；

K″——coefficient；

KPN——nominal pressure conversion coefficient；

Kr——resistance coefficient of pipe fittings；

k——adiabatic index；

L——developed length of pipe；

Lb——reinforcement zone of branch；

Lcb——effective bearing length of the branch；

Lch——half bearing length of the run；

Le——equivalent length of valves and pipe fittings；

Lh——"half width"of reinforcing zone；

Lw——weld joint height；

ΣLd——sum of the equivalent length of pipe fittings and valves on piping；

Ma——resultant moment loading on cross section due to dead weight and other sustained external loads；

Mb——resultant moment loading on the cross section due to occasional loads，such as thrusts from relief/safety valve loads，transient change in pressure and flow and earthquake；

Mc——resultant moment due to thermal expansion calculated based on the full compensation and modulus of elasticity of steel at 20℃；

Mj——resultant moment；j is a subscript；

Mxj，My j，Mzj——moments along coordinate planes x，y and z；

m——allowable negative tolerance of pipe wall thickness specified in the technical specifications；

——mass velocity of medium；

——mass velocity of medium at the start of piping after local change；

Ne——number of cycles within full temperature changeΔTe for which thermal expansion stress σe is calculated；

n——quantity of safety valves installed in parallel；

P——concentrated load at midspan；

Pt——allowable working pressure at design temperature；

PN——nominal pressure；

p——design pressure；

p0——stagnation pressure at the start；

p0k——stagnation pressure before the orifice；

p1——pressure at the start of piping；

p2——pressure at the end of piping；

p2k——pressure after the orifice；

pⅠ——static pressure at the end of piping before local change；

pⅡ——static pressure at the start of piping after local change；

pa——local atmospheric pressure；

pat——atmospheric pressure；

pd——dynamic pressure of medium carried inside the pipe；

pd1——dynamic pressure at the start of piping；

pd2——dynamic pressure at the end of piping；

pdⅠ——pressure at the end of piping before local change；

pdⅡ——pressure at the start of piping after local change；

pc——critical pressure；

pg——operating pressure；

pn——medium pressure in respective section；

pi——medium pressure at cross-section i；

pi-1——medium pressure at cross-section i-1；

p′——spatial pressure at the end；

p″——pressure head due to downstream pipe resistance and backpressure at pipe end；

Q——volume flow rate of medium；

Qs——reference volume flow rate at absolute pressure of 101.3 kPa and temperature of 20℃；

q——dead weight of piping per unit length；

qb——specific flow rate；

qc——coefficient；

R——bend radius of bends and elbows；

RE——thermal expansion force（or moment）applied on piping by the ends which is calculated with the full compensation value and the modulus of elasticity of steel at 20℃；

Re——Reynolds number；

Rn——gas constant；

——minimum tensile strength of steel at 20℃；

——minimum yield strength of steel at design temperature；

——minimum proof strength at 0.2% non-proportional elongation of steel at design temperature；

Rt——thrust or moment imposed on the equipment or end by the piping under operating condition during initial operating period；

R20——thrust or moment imposed on the equipment or end by the piping under cold state during initial operating period；

——thrust or moment imposed on the equipment or end by the piping after adaptive equalization under cold state；

r2——latent heat of vaporization at pressure pc；

——mean radius of branch pipe，mm；

rn——latent heat of vaporization of saturated water at pressure pn；

S——measured minimum wall thickness；

Sb——actual（measured）wall thickness or allowable minimum wall thickness of branch pipe connected to tee according to the purchase technical specifications；

Sb3——equivalent wall thickness of branch pipe；

Sc——calculated pipe wall thickness；

Sh——actual（measured）wall thickness or allowable minimum wall thickness of run pipe connected to tee according to the purchase technical specifications；

Sk——characteristic value of snow load；

Sm——required minimum wall thickness of piping；

Smb——required minimum wall thickness of the branch；

Smh——required minimum wall thickness of the run；

St——selected wall thickness of ellipsoidal head；

Svi——inside wall thickness of elbow without allowance；

Svo——outside wall thickness of elbow without allowance；

s′——entropy of saturated water at pressure pc；

s″——entropy of saturated steam at pressure pc；

——entropy of saturated water at pressure pc-Δp；

——entropy of saturated steam at pressure pc-Δp；

T——thickness；

To——stagnation temperature before orifice；

Tpd——calculated thickness under pressure；

t——operating temperature；

tamb——ambient temperature；

W——bending moment at pipe cross-section；

ω——weld strength reduction factor for longitudinal seam steel pipes under creep condition；

x——steam dryness；

xn——calculated dryness at at any point under pressure；

Y——correction factor；

α——angle of tee；

αc——critical pressure ratio；

αt——coefficient of linear expansion of steel from 20℃to the operating temperature；

α′——ratio of pressure at the start of piping to spatial pressure at the end of piping；

β——ratio of specific volume of medium at the end to that at the start；

βc——ratio of critical specific volume of medium to the specific volume at the start of piping；

———105h average creep rupture strength of steel at design temperature.

σeq——equivalent stress due to internal pressure；

σe——thermal expansion stress range；

［σ］s——reference stress corresponding to the nominal pressure.It refers to the allowable stress（MPa）of material at a specified temperature；

［σ］t——allowable stress of material at design temperature；

σeq——equivalent stress due to internal pressure；

σ1——sum of the axial stresses under operating condition due to sustained loads including internal pressure，dead weight and other sustained external loads；

σmax——maximum bending stress of horizontal straight pipe；

δmax——maximum bending deflection；

θ——semi-cone angle of reducer；

θb——chamfer angle；

ω——flow velocity of medium carried inside the pipe；

ωc——critical flow velocity；

ωi——flow velocity of medium at cross-section i；

ωi-1——flow velocity of medium at cross-section i—1；

ωm——average flow velocity of medium in piping；

φ′——factor as a function of head structure；

φ——deflection angle of steam flow with respect to the pipe axis；

γ——kinematic viscosity of medium；

γc——percentage of cold springing；

η——correction factor of allowable stress；

μ——dynamic viscosity of medium；

μ1，μ2——flow coefficient of safety valve，determined according to test results or manufacturer data；

μ1——flow coefficient；

μr——coefficient of snow load distribution on the top of piping.For rectangular piping，μr=1.For round piping，μr=0.4；

μz——friction factor；

υ——specific volume of medium；

υ0——specific volume at the start at stagnation conditions；

υ1——specific volume of medium at the start；

υ2——specific volume of medium at the end；

υc——critical specific volume；

υn——specific volume of steam and water mixture at any point；

υ″——specific volume of saturated steam at pressure pc；

——specific volume of saturated water at pressure pn；

——specific volume of saturated steam at pressure pn；

υⅡ——specific volume of steam at the start of piping after local change；

ξ——local resistance coefficient；

ξm——resistance coefficient corresponding to the flow velocity of medium before the orifice；

ξt——total resistance coefficient；

——resistance coefficient at larger end of reducer；

Σξ1——sum of local resistance coefficient of pipe；

Σξ——sum of the local resistance coefficient of pipe fittings and valves；

ε——equivalent roughness of pipe inner wall；

λ——friction coefficient of pipe；

λy——friction drag coefficient；

ρ——medium density；

ρ1——medium density at pipe inlet；

ρ2——medium density at pipe outlet；

ρe——medium density at the end of vertical pipe；

ρm——average density of boiling water in vertical pipe；

ρn——medium density in individual sections；

ΔP1——pressure loss of straight pipe due to friction drag；

ΔP2——pressure loss of piping due to local resistance；

ΔP——total pressure loss of piping；

Δp——difference between the pressure at the end of piping（p2（pc））and the closest pressure in the table of thermodynamic properties of water and steam；

ΔpⅠ-Ⅱ——steam resistance before and after local change；

Δpf——pressure loss of straight pipe due to friction drag；

Δpk——pressure loss due to local resistance；

Δpm——pressure drop across the orifice；

Δpt——total pressure loss of piping；

Xa，Ya，Za——coordinate values at the start（a）of calculated piping system；

Xb，Yb，Zb——coordinate values at the end（b）of calculated piping system；

ΔX，ΔY，ΔZ——full compensation for linear displacement of piping system along X，Y，and Z axes respectively；

ΔX20，ΔY20，ΔZ20——cold compensation for linear displacement of the calculated piping system or branch along X-axis，Y-axis，and Z-axis；

ΔXa，ΔYa，ΔZa——additional linear displacement at the start（a）of piping system along X，Y，and Z axes respectively；

ΔXb，ΔYb，ΔZb——additional linear displacement at the end（b）of piping system along X，Y，and Z axes respectively；

——cold springs of the calculated piping system or branch（ab）along X-axis，Y-axis and Z-axis；

——thermal elongation of piping system（ab）along X，Y，and Z axes respectively；

Δx——variation of steam dryness under isentropic expansion condition；

Δυ——increment of specific volume based on isentropic expansion within the range ofΔp.