The work described in this thesis concerns the development of a vortex singularity flow model for the prediction of jet engine combustion chamber flows. In an attempt to understand the operation of the chamber dilution zone, a program was written which successfully predicted an irrotational three-dimensional jet in a crosswind. A novel approach for the inclusion of viscous effects was successfully tested by predicting flows in both a parallel and a stepped duct. The approach consists of a finite-difference solution of the Vorticity transport equation and an Integral Equation solution of the Poisson equation for stream function. The results obtained wixh this approach have shown general agreement with those of other investigators. Suggestions are made as to how the computer methods for the irrotational and rotational predictions could be improved. It was concluded that the Vorticity/lntegral method was a sound theoretical approach to predicting viscous flows, and could eventually be used to predict combustion chamber flows.