In this thesis the following aspects have been investigated: (i) the numerical solutions for unsteady 2-dimensional, incompressible viscous fluid flows induced by a harmonically oscillating cascade, and (ii) the fluid flows in industrial cyclones and their separation efficiencies. In the first part of the thesis we deal with fluid flows induced by harmonically oscillating cascades of cylinders with different cross sectional shapes. Numerical solutions for large amplitude oscillations of a cascade of normal flat plates are obtained by using a finite-difference method and it is found that solutions are in good agreement with some related experimental results. For small amplitude oscillations a perturbation method, series truncation technique and finite-difference methods are used to obtain solutions for cascades of normal flat plates and square cylinders. By assuming that the streaming Reynolds number is 0(1) then the outer streaming flows for cascades of square cylinders, normal flat plates and circular cylinders are investigated numerically for the streaming Reynolds number Rs up to 70. Conformal mapping, grid generation and boundary element methods are used to deal with the different geometries in order to determine the outer potential flows. For small values of the streaming Reynolds number it is found experimentally that the flow remains symmetrical and the numerically predicted fluid flow is in good agreement with the experimental results. As the value of the streaming Reynolds number increases then it is found experimentally that the flow develops asymmetries and this occurs when 8