We consider a point charge and Gaussian bunch of charged particles moving along the axis of a circular perfectly conducting pipe with uniform dielectric filling and open end. It is supposed that this semi-infinite waveguide is located in collinear infinite vacuum pipe with perfectly conducting walls and larger diameter. We deal with two cases corresponding to the open end of the inner waveguide with and without flange. Radiation produced by a charge or bunch flying from dielectric part to wide vacuum part is analyzed. We use modified residue-calculus technique and construct rigorous analytical theory describing scattered field in each sub-area of the structure. Cherenkov radiation generated in the dielectric waveguide and penetrating into the vacuum regions of the structure is of main interest throughout the present paper. We show that this part of radiation can be easily analyzed using the presented formalism. We also perform numerical simulation in CST PS code and verify the analytical results.