Equations to determine the rate of change of the helicity in a dynamic liquid system are obtained. For the convenience of carrying out engineering calculations the equations are presented in dimensional and dimensionless forms. The conditions for critical transition to a helical character of a twisted flow and to the crisis-induced rearrangement of the flow velocity field due to the change in the flow vortex structure are considered. A new physical model of the vortex motion of a liquid is suggested. It allows one to explain a number of phenomena: the effect of spontaneous flow twisting in the collectors of tank-type nuclear reactors; the reason for the considerable increase in the nonuniformity of the radial distribution of pressure at the inlet into the active zone for liquid-metal heat-transfer agents as compared to the water one; the crisis-induced rearrangement of the flow velocity field with formation of large-scale vortex structures during flow in curvilinear channels and of spiral vortices on curvilinear surfaces.