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In two previous papers to this Society (1, 2)* an ‘alternative’ method was presented for the prediction of the unsteady gas flow behaviour through a reciprocating internal combustion engine. The computational procedures led further to the prediction of the overall performance characteristics of the power unit, be it operating on a two- or a four-stroke cycle. Correlation with measurements was given to illustrate its effectiveness and accuracy. In the ducts of such engines there are inevitably sectional changes of area which are either gradual or sudden. A tapered pipe is typical of a gradual area change whereas a throttle or a turbocharger nozzle represents a sudden area change. In those previous papers it was indicated that a fuller explanation, of the theoretical procedures required to predict accurately the unsteady gas flow in such duct sections would be given in a later paper to this Society; this is that necessary publication.