A |
Required effective discharge area, inch2 |

A1 |
Exposed surface area, inch2 |

Ad |
Root diameter of thermowell, m |

B |
Diameter at tip, in |

b |
Fillet radius at root, m |

bs |
Fillet radius at base for stepped thermowell, m |

C |
Discharge coefficient |

CV |
Valve flow coefficient, US gallon per minute of water (60 ºF) at 1 psi pressure drop |

Cr |
Coefficient for critical flow equation, dimensionless |

Cs |
Speed of sound, m/s |

Cp |
Speed of sound in pipe wall, m/s |

D |
Internal pipe diameter (upstream) at flow temperature, mm |

D0 |
Internal pipe diameter (upstream) at ambient temperature, mm |

Dt |
Nominal size of sensing element, in |

D1 |
Inlet internal diameter of the pipe, mm |

D2 |
Outlet internal diameter of the pipe, mm |

Dd2 |
Outlet outside diameter of the pipe, m |

DP |
Pressure differential, P1-P2 , or differential pressure transmitter range, bar |

DPA |
Maximum allowable pressure drop, bar |

DPloss |
Pressure loss, bar |

DPn |
Differential pressure at normal flow rate, bar |

Dbh |
Bleed/Vent hole diameter, mm |

Dj |
Diameter of the jet, m |

d |
Valve inlet diameter or orifice (throat) diameter at flow temperature, mm |

db |
Bore diameter of thermowell |

d0 |
Orifice (throat) diameter at ambient temperature, mm |

E |
Module of Elasticity at 70 °F, psi-g |

Ef |
Acoustical efficiency factor, dimensionless |

Eref |
Reference value for module of elasticity, Pa-g |

Eps |
Gas expansion factor, ratio of flow coefficient for a gas to that for a liquid at the same Reynolds number, dimensionless |

F |
Environment Factor, dimensionless |

F1 |
Heat Absorption Factor, dimensionless |

F2 |
Coefficient for subcritical flow equation, dimensionless |

Fd |
Valve style modifier, dimensionless |

Fe |
Environmental factor for thermowell calculation, dimensionless |

FF |
Liquid critical pressure ratio factor, dimensionless |

Fk |
Ratio of specific heats factor, 1/K, dimensionless |

FL |
Liquid pressure recovery factor, dimensionless |

FLP |
Product of the liquid pressure recovery factor of a valve with attached fittings and the piping geometry factor, dimensionless |

Fp |
Piping geometry factor, dimensionless |

FR |
Reynolds number factor, dimensionless |

Fs |
Correction factor for steam quality, dimensionless |

fp |
Peak frequency, Hz |

fo |
Coincidence or Natural frequency, Hz |

fr |
Ring frequency, Hz |

fw |
Wake frequency, Hz |

Gf |
Liquid specific gravity (ratio of density of liquid at flowing temperature to density of water at 15.6 °C), dimensionless |

Gg |
Gas specific gravity (ratio of density of flowing gas to density of air with both at standard conditions, which is equal to the ratio of molecular weight of gas to the molecular weight of air), dimensionless |

Hc |
Mounting factor, dimensionless |

HS |
Segmental height at flow temperature, mm |

HS0 |
Segmental height at ambient temperature, mm |

HV |
Heat of vaporization, J/kg |

K |
Specific Heat Ratio, Cp/Cv dimensionless |

K1,K2,Kb1,Kb2 |
Effective velocity head coefficients, dimensionless |

KC |
Cavitation index, dimensionless |

KCD |
Relative capacity, CV/d2 |

KCV |
Valve cavitation index, dimensionless |

Kb |
Capacity correction factor due to back pressure, dimensionless |

Kcc |
Combination capacity factor for rupture disk at the relief valve inlet, dimensionless |

Kd |
Effective coefficient of discharge, dimensionless |

Kf |
Constant for thermowell calculation, dimensionless |

Kn |
Correction factor for Napier equation, dimensionless |

Kp |
Correction factor for overpressure, dimensionless |

Ksh |
Superheat steam correction factor, dimensionless |

Kv |
Correction factor for viscosity, dimensionless |

Kw |
Correction factor for back pressure, dimensionless |

L |
Maximum thermowell length or unsupported length of thermowell, in |

La |
"A"-weighted sound level, dB(A) |

Lg |
Correction for pipe Mach number dB |

Lpi |
Internal sound pressure level dB |

Ls |
Length of reduced-diameter shank for stepped thermowell, m |

M |
Molecular weight, atomic mass units |

MN |
Mach number in pipe, dimensionless |

MN0 |
Mach number in valve outlet, dimensionless |

Mj |
Mach number in the jet, dimensionless |

No |
Number of flow passages , dimensionless |

Ns |
Strouhal number |

Nsc |
Scruton number |

P |
Absolute static pressure, bar |

PC |
Absolute thermodynamic critical pressure, bar |

PV |
Absolute vapor pressure of liquid at inlet temperature, bar |

PVC, PVCC |
Absolute pressure in vena contracts at subsonic and critical flow conditions, Pa |

P2c, P2b, P2ce |
Border pressures for different noise regimes, Pa |

Pa |
Absolute outside pipe pressure, Pa |

Pb |
Total back pressure, psi-g |

Pb1 |
Constant back pressure, psi-g |

Pb2 |
Variable back pressure, psi-g |

Pb3 |
Built-up back pressure, psi-g |

Pcf |
Critical flow throat pressure, psi-a |

Pover |
Overpressure, % |

Ps |
Set pressure, psi-g |

Pup |
Upstream relieving pressure, psi-a |

R |
Limitation on Wake to Natural frequency ratio, dimensionless |

RO |
Density at flow conditions (upstream), kg/m3 |

ROm |
Density of well material at ambient temperature, kg/m3 |

ROp |
Density of pipe material, kg/m3 |

ROs |
Density of the thermowell sensor at ambient temperature, kg/m3 |

Rf |
Ratio of frequency at fluid temperature to frequency at 70 °F, dimensionless |

RS0 |
Segmental radius at ambient temperature, mm |

Re |
Valve (pipe) Reynolds number, dimensionless |

Remax, Ren |
Pipe Reynolds number at maximum and normal flow rate, dimensionless |

Rq |
Radius of upstream profile of Quarter of Circle (Quadrant Edge) orifice, mm |

S |
Maximum allowable working stress, Pa-g |

Sf |
Fatigue endurance limit, Pa-g |

SRF |
Scale reading factor, 10´Wn/Wmax |

St |
Water in steam, %wt |

T |
Flow temperature, K |

T1 |
Gas temperature at relieving conditions, °R |

T0 |
Ambient temperature, K |

Tc |
Thermodynamic critical temperature, K |

TL |
Transmission loss, dB |

TLfo |
Transmission loss at coincidence frequency, dB |

TLfr |
Transmission loss across the pipe wall at the ring frequency, dB |

Tw |
Vessel Wall Temperature, °R |

t |
Minimum tip thickness of thermowell, m |

U |
Velocity, m/s |

V |
Velocity, ft/s |

W |
Flow rate, kg/h |

Wmax, Wn |
Maximum and normal flow rate, kg/s |

Wa |
Sound power, W |

Wm, Wms |
Stream powers, W |

wall |
Pipe wall thickness, m |

X |
Ratio of pressure drop to absolute inlet pressure (DP/P1), dimensionless |

XT |
Pressure drop ratio factor, dimensionless |

XTP |
Value of XT for valve-fitting assembly, dimensionless |

Z |
Compressibility at operating conditions, dimensionless |

Zb |
Compressibility at base conditions, dimensionless |

ap, ape |
Linear expansion coefficient of pipe and primary element material, 1/ºC |

b |
Diameter ratio of orifice or throat and inside diameter of line |

DLf |
Correction value for cavitating flow, dB |

DTLfp |
Correction for ratio of peak frequency and coincidence frequency, dB |

h |
Acoustic efficiency factor, dimensionless |

m |
Absolute (dynamic) viscosity, Pa×s |

n |
Kinematic viscosity, centistokes |

ξ |
Damping factor, dimensionless |

Subscripts

0 |
First estimate |

1 |
Upstream conditions |

2 |
Downstream conditions |

VC |
Vena Contracta |

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Version 13.1

Published 1/28/2021 at 3:21 AM