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This paper is concerned with the simulation of the flow in a flat, 'two-dimensional' laboratory centrifugal pump. The main concern of the study is the calculation of the flow-induced noise. The aim of the present paper is to develop a computationally simple and fast method which is capable of giving a useful estimate of the noise-generating 'background-flow'. A companion paper describes the hydroacoustic part of the analysis. In the numerical flow model of the pump, the inlet is modelled by a point source and the blades of the impeller are covered with vortex elements with discrete, bound vortices. The casing is covered with source panels. Vortices are shed from the trailing edges of the impeller blades and convected with the streaming fluid in order to satisfy Kelvin's theorem. After computation of the velocity field, the fluid forces acting on the impeller blades are calculated by application of the unsteady Bernoulli equation. Some case studies of pump flows are presented. The acoustic properties of these flows is the subject of the second part of the paper. r

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