We analyze the motion of viscous and incompressible liquids in the annular space of controllable hydraulic resistances with a cylindrical linear slide-valve. This theoretical study focuses on the turbulent and steady-state motion regimes. The hydraulic resistances mentioned above are the most frequent type of hydraulic resistances used in hydraulic actuators and automation systems. To study the liquids' motion in the controllable hydraulic resistances with a linear cylindrical slide-valve, the report proposes an original analytic method. This study can similarly be applied to any other type of hydraulic resistance. Another purpose of this study is to determine certain mathematical relationships useful to approach the theoretical functionality of hydraulic resistances with magnetic controllable fluids as incompressible fluids in the presence of a controllable magnetic field. In this report, we established general analytic equations to calculate (i) velocity and pressure distributions, (ii) average velocity, (iii) volume flow rate of the liquid, (iv) pressures difference, and (v) radial clearance.