A bladeless conical radial rotary machine method and system are disclosed. Turbo-machinery and methods are disclosed for a bladeless conical radial rotary machine wherein fluid is directed axially within the pump body to produce an axial output. The rotor comprises a plurality of spaced apart conical elements. The fluid is smoothly directed to any number of subsequent boundary layer pumping stages which are axially positioned with respect to each other. The fluid is smoothly directed to any number of subsequent boundary layer pumping stages which are axially positioned with respect to each other. A coupling between pumping stages is disclosed.