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The transient process accompanied by extreme acceleration in the conical sections of hydraulic systems (e.g., draft tube, diffuser) can induce large cavitation bubbles both at the closed ends and in the bulk liquid. The collapses of the large cavitation bubbles can cause severe damage to the solid walls. We conduct experiments in the tubes with different conical-frustum shaped closed ends with the `tube-arrest' method and observe bubbles generated at these two locations. For the bubbles generated at the close end of the tube, we propose the onset criteria, consisting of two universal non-dimensional parameters $Ca_1$ and $Ca_2$, of large cavitation bubbles separating the water column. We investigate their dynamics including the collapse time and speed. The results indicate that the larger the conical angle, the faster the bubbles collapse. For the bubbles generated in the bulk liquid, we numerically study the collapse time, the jet characteristics and the pressure pulse at bubble collapse. We observe a much stronger jet and pressure pulse of bubbles in tubes, comparing with a bubble near an infinite plate. Our results can provide guidance in the design and safe operation of hydraulic machinery with complex geometries, considering the cavitation during the transient process.