An analysis is first performed to determine the exposed frontal area and effective volume as a function of rotor angle for circular lobed helical screw turbines. It is shown that once the female to male lobe ratio is set, the entire design is determined with respect to the male rotor pitch radius. These volume and area functions are then used in an overall dynamic model of the turbine. The model includes inlet and exhaust dynamics, leakage throughout the turbine, and the thermodynamics within the lobes. “Start up” of the system can be tested which is particularly important in determining critical speeds. The principal intended use of the model is for comparative parametric studies.