Calculation of Omega

Omega can be evaluated directly from the EOS for the Omega method (see equation 

This relationship makes use of properties at a pressure, PtI which is lower than that in the upstream vessel. It is suggested151 that Pt is taken to be 80 or 90% of P0 (90% if there is little friction) and that an isenthalpic flash routine (within, a computerised package for evaluating multi-component physical properties) is used to find the two-phase specific volume v, at Pt. Woodward161 gives examples of the use of this approach. 

It will not always be possible to use the more accurate definition given in equation (A8.4) above, for example in cases where the required physical property data would be difficult to generate. In such cases, the following alternative approximate definitions of Omega have been proposed[3,4,51. However, the additional condition of applicability (h) in A8.2 needs to be considered before their use. Omega can be calculated by any of equations (A8.5) to (A8.10) below, which are essentially equivalent. In these equations, Omega is evaluated entirely at the conditions in the upstream reactor.  

Note that for gassy systems, a number of terms in the above equations disappear and leaves  

Earlier descriptions of the Omega method13,41 defined Omega such that the first term in equations (A8.5)-(A8.10) was equivalent to ao rather than to This led to discrepancies for g 4 in calculating G for choked nozzle flow, compared with experimental results. The definitions of Omega given above151 overcome this problem. 

---