A motorless mass flowmeter in accordance with one embodiment of the invention comprises a turbine subassembly, a drum, and an impeller. The drum is rigidly connected to the turbine subassembly such that the drum rotates in accompaniment to rotation of the turbine subassembly. The impeller is rotationally coupled to the drum by way of a spring that allows relative rotation against the bias of the spring. The turbine subassembly has jets and bypass valves. The turbine subassembly may be implemented in the form of a laminated bypass valve structure. The laminated bypass valve structure may include an entrance layer having entrance port(s), a closure layer having closure member(s), an exit layer defining exit passage(s), and an intermediary layer forming conduit(s) for guiding fluid from entrance port(s) to exit passage(s).