This thesis uses numerical techniques and analysis to study the development and interactions between multiple in-line slender air jets. Consideration is given to two-and three-dimensional flow regimes, but the emphasis is on the latter. The applications (and mechanisms) involved in high-speed machine sorting of small food items, such as grains of rice, are explained. The underpinning mathematics required to develop the mathematical model are stated. In Chapter 2 an analytical solution for the two-dimensional steady jet is demonstrated and used to provide a far-downstream asymptote for validation of the numerical scheme, for steady and unsteady jets. A numerical scheme is demonstrated to be versatile and reasonably accurate. Small-distance analysis complements the numerical scheme and limitations are discussed. A comprehensive small-time analysis is undertaken, results from which support later work on three-dimensional jets. Interference between inline jets is considered in Chapter 3, which applies methods previously used to study two-dimensional in-parallel wakes. The conclusions from this chapter support and help explain results in later chapters. The numerical scheme is extended to three-dimensional steady and unsteady jets. Issuing nozzles of various cross-sections are considered with the aim of obtaining pressure data for comparison with physical data. Small-distance analysis is again investigated, enabling a weakness in the numerical solution to be highlighted. Potential flow theory is used to model interference aspects of multiple in-line unsteady three-dimensional jets. The emphasis is placed on jets from nozzles of either circular or rectangular cross-section but, in fact, the analysis applies for any cross-section. The impact properties of a typical jet when it hits one of the particles such as a grain of rice being sorted are discussed briefly, and final comments are made.