This first part of a three-part paper describes the theoretical modelling of the behaviour of an oscillating circular piston positive displacement flowmeter (also known as the rotary piston flowmeter), by considering the principal forces acting on the piston. These include pressure forces, unsteady flow effects, inlet and outlet flow losses, retarding forces due to thin films and frictional effects. Effects which are too small to affect significantly the dynamic behaviour are not included nor are detailed discussions of liquid leakage. The numerical model lends itself to a time marching solution which applies the forces at each position and deduces the new position and velocities. Thus the local size of the various forces is calculated at each point in the motion for the precise position of the piston at that moment.

In the second part of the paper we set out the calculation process and then demonstrate the validity of our model by comparing it with experimental results. The approach used in this work should lend itself to the modelling of the behaviour of other positive displacement flowmeters.