Multistage pumps are essential in emergency water supply, irrigation, and other systems undergoing unavoidable hydraulic transitions like pump startup and valve operations. These transitions cause rapid changes in impeller speed, flow rate, and pressure, destabilizing the internal flow field and impacting system reliability. To study transient flow characteristics, a numerical analysis of a three-stage pump was conducted, focusing on vortex identification, entropy production, and time–frequency pressure pulsation. Using the SST turbulence model, the simulation analyzed different start times and flow rate variations. Findings revealed that shorter startup times intensified transient effects, with the head increasing rapidly initially and then stabilizing. Vortex structures showed periodic development and dissipation. Entropy production rose with impeller speed, peaking higher with shorter startups. Blade passing frequency dominated pressure pulsations, with increased low-frequency pulsations as speed rose. During valve opening, flow stabilization accelerated with increasing flow rates, reducing amplitude and eliminating low-frequency components. This research aids the reliable operation of high-pressure pumping systems in energy storage.