Rotary engine fluid pump and method of pumping a fluid

Embodiments of the invention provide a rotary engine, the rotary engine comprising: a housing defining a working chamber of the engine; a rotor arranged to rotate within the working chamber, the rotor having a radially inner portion and a radially outer working surface, the radially inner portion comprising a pump portion, the pump portion being operable to pump a fluid through the radially inner portion as the rotor is rotated; and a fill member, the fill member being arranged to create a region of increased fluid pressure within a radially inner portion of the rotor as the rotor rotates thereby to pump fluid through the rotor.