In the actual operation of pumps, regulating the rotating speed of the pump based on the affinity law through variable speed drives is deemed as a prudent and convenient approach to mitigate energy loss. However, the multistage side channel pump is composed of one centrifugal impeller at the first stage and one or more side channel structures, the applicability of affinity law to this composite structure has not been confirmed. Three schemes with different suction angles of single-stage and one multistage side channel pump were investigated under different rotating speeds through numerical and experimental analysis. The findings elucidated that the single-stage side channel pumps exhibit a proportionate relationship to the affinity law, regardless of how the geometry varies. The numerical work was validated by the comparison between the simulated result and the tested result of the multistage side channel pump under two rotating speeds. Noticeably, the entire performance of the multistage side channel pump conforms to the affinity law, which has the same phenomenon as the single-stage side channel pump. The entropy production causing dissipation of turbulence flows in each stage exhibits a similar tendency as the overall head. As a result, the vortex distribution in average time and transient moment are almost analogous in the impeller of each stage under corresponding flow points. This briefly explains composite structures could be considered as pumps in series regardless of their composition. The outcome of this research could offer a theoretical basis for energy-saving methods of side channel pumps.