A rotary pump in a housing which defines an annular chamber with an inlet and outlet port which are located on either side of a partition which extends across the chamber. A flexible annular diaphragm forms one side of the chamber and faces a wall on the housing which forms the second side of the chamber. The diaphragm is sealed at its innermost and outermost edges to the housing and has legs extending away azimuthally around and integral with the diaphragm. A swashplate is connected to the legs of the diaphragm such that in use, movement of the swashplate causes the diaphragm to press precessively against the wall of the housing to force fluid drawn in at the inlet on one side of the partition around the chamber and to expel the fluid at the outlet at the other side of the partition.