In this work steady–state flows of hydrodynamic plasma in cylindrical channel and in channel bounded by two coaxial surfaces are obtained. The plasma in channels is taken to be viscous electrically noncompressible two – component and quasineutral. The flows obtained are similar to famous Poiseuille’s and Couette’s flows. Modifications of hydrodynamic velocity’s profile, is shown, are due to ion – electron’s interaction when total current goes through three critical values. It leads to wall–adjacent flow and countermotion. As result, steady–state plasma flow’s parameters depend on the sign of total current. Critical values of total current and ion’s and electron’s wall viscous friction are calculated.

Mathematical modelling in actual problems of science and technics