3 Equations

 The following equations may be used to demonstrate the adequacy of the vent system.

  Equation (1) for all vapour mass flow rate from tank through PRVs:

 where:

• F = fire exposure factor according to section 8.5 of the IGC Code

• A = external surface area of Type C tank (m²)

• h_fg = latent heat of vaporization of cargo at 1.2 × MARVS (J/kg)

  Equation (2) for isenthalpic flashing mass flux of liquid through PRV orifice:

 where:

• h_fg = see equation (1)

• ρ_g = vapour density at 1.2 × MARVS and corresponding boiling temperature (kg/m ³)

• T_o = temperature (K)^footnote of cargo at 1.2 × MARVS

• c = liquid specific heat at 1.2 × MARVS and T_o (J/(kg K))

  Note: This expression is valid for multi component mixtures whose boiling point range does not exceed 100 K.

  Equation (3) for two-base mass flow rate through PRV is installed:

 where:

• G_v = is taken from Equation (2) (kg/(m²s) )

• K_w = PRV discharge coefficient on water (= 0.8 × measured K_d on air)

• A_v = actual orifice area of PRV (m ²)

  Equation (4) for Code PRV capacity for two-phase mass flow:

 where:

• G_QCC = Code PRV capacity of air at standard conditions in accordance with IGC Code 8.5.2 (m³/s )

• Q_IR = installed rated PRV capacity of air at T = 273K and p= 1.013bar (m³/s )

  Equation (5) for the calculation of the static pressure difference in a pipe section of constant diameter in which the mass flux (G_p) is constant:

 where:

• G_p = mass flux through pipe section

• v_e = two-phase specific volume at pipe section exit (m³/kg )

• v_i = two-phase specific volume at pipe section inlet (m³/kg)

• f = Fanning friction factor f = 0.005 for two-phase fully turbulent flow

• L = length of pipe section (m)

• D = diameter of pipe section (m)

• ΣN = sum of dynamic loss coefficients for fittings in the pipe section equivalent

• (Type values of N are given in Annex 2, Table 2 )

  Equation (5.1) For contractions, the difference in stagnation pressure is defined by:

 where:

• N = dynamic loss coefficients of the contraction

• G_p,e = mass flux at the exit of the contraction (kg/(m²s) )

• v_i = specific volume at the inlet of the contraction (m³/kg )

  Equation (6) for two-phase critical choking pressure at vent mast exit or at exit from any vent pipe section:

 where:

• G _p = as defined in equation (5)

• p _o = cargo vapour pressure in tank at inlet PRV (P_a )

• ρ_o = cargo liquid density in tank at inlet to PRV at p _o and T _o (kg/m³ )

• ω = compressible flow parameter in tank at inlet to PRV

 where:

• α_o = inlet void fraction or vapour volume fraction at inlet to PRV

• = 0, when assuming isenthalpic expansion of saturated liquid, at 1.2 × MARVS, through the PRV

• c = see equation (2)

• T _o = see equation (2)

• (v_go - v_fo ) = difference in gaseous and liquid specific volume at temperature T _o at inlet to PRV (m³/kg )

• (h_go - h_fo ) = difference in gaseous and liquid enthalpy at temperature T _o at inlet to PRV (J/kg)

  Equation (7) for exit quality, or vapour mass fraction at pipe section exit

(e.g. x _e = 0.3 ≡ 30% quality ≡ 30% vapour + 70% liquid by mass)

 where:

• h _fo = liquid enthalpy in tank at inlet to PRV (J/kg)

• h _fe = liquid enthalpy at back pressure at pipe section exit (J/kg)

• h _fg = latent heat of vaporization at back pressure at pipe section exit (J/kg)

• q = heat flux from fire exposure into vent pipe 108 kW/m²

• a = heated external surface area of vent pipe section (m² )

• W = mass flow rate in vent pipe section (kg/s)

  Equation (8), (9) for two-phase density (ρ) and specific volume (v)

 where:

• ρ_g = saturated vapour density at pipe section inlet or exit

• x = vapour fraction at pipe section inlet or exit