Page 113 - Electrical Installation in Hazardous Area

Calculation of release rates and extents 89

The ratio of specific heats (specific heat at constant pressure divided by the
specific heat at constant volume) has a value of around 1.4 or less for the
vast majority of flammable gases and vapours as shown by Table 4.1. If we
substitute the value 1.4 for 6 the mass release equation can be simplified. In
addition, the coefficient of discharge Cd has a maximum value of around 0.8
in ideal circumstances allowing further simplification and the final equation
becomes:
G = 0.006aP(M/t)’.’ kg/s (Equation 4.1)

This equation is, however, only valid if the upstream pressure is greater
than a specific multiple of the downstream pressure (atmospheric pressure
in our case) which multiple is called the critical pressure ratio. This ratio is
given by the following equation:

P/P, = [(6 + 1>/”’@-” (Equation 4.2)

where Pa = atmospheric pressure n/m2

Using the value of 1.4 for 6 the critical ratio is 1.9 and so, rounding
up, Equation4.1 can be assumed to be only valid when the absolute
upstream pressure exceeds 2 x 1@N/m2. Where this is not so the effects
of atmospheric pressure become significant and the mass release equation
becomes:
G = Cda[2~(P - Pa)]’.’ kg/s

where 0 = density of gas at atmospheric pressure and
release temperature

The density of the gas or vapour can be expressed in terms of the molec-
ular weight and the molar volume (22.4m3/kg Mole) and this gives a more
recognizable equation as follows:
G = 3.95a(M(P - 105/T)0.5} kg/s (Equation 4.3)

The results of Equations 4.1 and 4.3 can, if required, be converted into
volume release by use of the following equation:

Released volume (V) = V, G T/T,M m3/s
where V, = molar volume m3/kg Mole
To = melting point of ice (273 OK)
This equation simplifies to the following:

V = O.O82GT/M m3/s (Equation 4.4)