The homogeneous model for two-phase flow

The homogeneous flow model and the separated flow model may be used to estimate the pressure drop for the churn regime but the former is not recommended for use with annular flow. The separated flow model of Martinelli and Nelson (1948), and developments thereof, may be used for annular flow. 

The approaches adopted in the homogeneous model and the separated flow model are opposites in the former it is assumed that the two-phase flow can be treated as a hypothetical single-phase flow having some kind of average properties, while in the separated flow model it is assumed that distinct parts of the flow cross section can be assigned to the two phases, reflecting what occurs to a large extent in annular flow. 

By definition, the average density is the reciprocal of the average specific volume of the mixture, so that 

The momentum equation takes a simple form, which may be derived from the general form given in equations 7.9 by putting 

the three components of the total pressure gradient, friction, acceleration and the static head, are clear. 

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