A fluid discharging system having a pump and a discharging spray head having at least one nozzle through which fluid to be discharged exits is provided. The pump has a stator and a rotor which is attached in a chamber of the stator and can be rotated in relation to the stator about a rotational axis and axially along the axis. The axial displacement of the rotor in a first axial direction is configured such that it brings about pump filling operation. A fluid is drawn via an inlet into the stator chamber, and the axial displacement in an opposite second axial direction is configured such that it brings about discharging operation. The fluid in the chamber is expelled out of an outlet of the pump. The outlet of the pump is arranged in the rotor, and the discharging spray head is fluidically connected to the outlet of the pump.