For a centrifugal pump, the interaction between the leakage and the pressure profile in the side chambers is crucial to the performance and reliability of the pump. However, existing theoretical models for directly predicting the flow in the pump side chambers suffer from nonself closure, low accuracy, and slow convergence, and hardly any research presents such predictions for the adjustable-speed centrifugal pump. A pressure model for the simplified geometric configuration of the side chambers in turbomachinery, specifically the open rotor–stator cavity, is established by introducing Poncet's K formula. With the application of this theoretical model, as well as the consideration of the static pressure rises in the impeller and the pressure drops through seals and balance holes, a new one-dimensional (1D) pressure model is built and developed as a design tool for solving the flow in the pump side chambers. Compared with the pressure measurements on the casing wall of an adjustable-speed centrifugal pump, the predictions made by the new 1D pressure model indicate good accuracy and are better than the predictions made by the pressure model using the conventional constant K. It is found that the thrust acting on the shrouds varies almost linearly with the squared rotating speed, whereas the rotating speed hardly influences the volumetric efficiency. Since only the flow rate, rotating speed, and geometric parameters are required, the new 1D pressure model can be readily applied to other pumps, and it is preferred for good and fast prediction in the preliminary design stage.