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With the development of large-capacity hydro turbines, the hydraulic instability of bydro turbines has become one of the most important problems that affect the stable operation of the hydro-electric units. The hydraulic vibration and unstable operation of Francis hydro turbines are primarily caused by the unsteady pressure pulsations inside draft tubes.The forced rotating vortex core at the runner exit and the channel vortices inside Francis turbine runners are origins of the unsteady pressure pulsations when operating at partial load. This paper briefly analyzes the hydraulic instability of operation caused by the vortex core and channel vortices at partial load, then, presents a way to estimate the hydraulic stability by calculation of the flow behavior at the runner exit.The validity of estimation is examined by comparison with experimental data. This will be helpful to evaluate the altative design and predict the hydraulic stability for both the prototype and model hydro turbines.