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A magnetic fluid (MF) changes its surface shape in the magnetic field of a current-carrying wire while the current is changing. In the present paper, we propose to study a MF bridge which can open or close the channel formed by two cones and a cylinder by imposing the magnetic field of a wire. Numerical modelling of the bridge behavior for different values of MF volumes and currents in the wire is done for two cases: when the MF wets and does not wet surrounding solid boundaries. It is shown that the presence of limiting cones allows the MF to sustain the pressure drop which is much higher in case of non-wetting than in case of wetting. In case of wetting, the MF cannot sustain any pressure drop at low currents, but in case of non-wetting, the MF can do it even at zero current. It is found that in case of non-wetting, spasmodic and hysteresis phenomena are possible for some values of MF volumes and currents in the wire. The use of a MF in valves, dispensers and pumps is one of possible actuation methods. [ABSTRACT FROM AUTHOR]