We present interesting features of transonic winds erupted from the gravitational potential well for a three-fluid system, comprising of thermal plasma, cosmic rays and self-excited Alfv'en waves. The analysis is carried out on the hydro-dynamical basis with a particular emphasis on cosmic-ray streaming instability and damping mechanism. Boundary conditions on the gravitational potential well helped to explore steady-state transonic wind solutions. A critical analysis on various mass outflow rate is also presented and the dependence of the critical or sonic point is studied for different sets of physical parameters. For the graphical appreciation of the numerical results different contour plots presented to analyse impacts of mass flow rates.