A positive displacement pump (1) is equipped with a pump cylinder (2), a pump piston (7), a cylinder space (9), a pressure sensor (10), and a pressure channel (12). A main portion (13) of the pressure channel (12) extends parallel to a longitudinal axis (3) of the pump cylinder (2), for providing fluidic connection between the cylinder space (9) and the pressure sensor (10). In the improved alternative positive displacement pump (1), the main portion (13) of the pressure channel (12) is located inside of the pump cylinder (2) or pump piston (7) and extends, at least in a foremost position of the pump piston (7), from a cylinder bottom (5) beyond or to an opening (11,11′) in the cylinder wall (4) or pump piston (7).