PURPOSE: To obtain a pump with high total adiabatic efficiency by providing constitution such that inflow fluid to pressure-reduced space from a sinking part, caused by fitting a blade into the sinking part of a female rotor, is cooled by a cooling device and then introduced into an operating chamber in a male rotor side.

CONSTITUTION: A male rotor 1 having a sheet of blade 2, integrally rotated with a rotary hollow body 6 while brought into close contact with the peripheral surface of a fixed hollow body 4, and a female rotor 8 having a sinking part 10, to which the blade 2 of the male rotor 1 is fitted while sinking from an external peripheral surface, are housed in a casing rotatably in an opposite direction to each other. Fluid in an operating chamber 12, interposed by the blade 2 of the male rotor 1 and the female rotor 8, is delivered into the rotary hollow body through a delivery port 5, formed in the fixed hollow body 4, and an opening/closing port 7 formed in the rotary hollow body 6. Here, constitution is provided such that inflow fluid to pressure-reduced space 14 from the sinking part 10 is cooled by a cooling device 20 and then introduced into the operating chamber 12 in a side of the male rotor 1.