A pump comprises a housing (10) and a rotor (11) that rotates in the housing. The housing (10) has a fluid inlet (14) and a fluid outlet (15). The rotor (11) includes two shaped surface (21, 22; 50a, 50b, 50c) radially inwardly of the housing (10) and forming with the interior surface of the housing respective chambers (23, 24; 51a, 51b, 51c) for conveying fluid from the inlet (14) to the outlet (15) on rotation of the rotor (11). A seal (12; 56) is provided between the outlet (15) and the inlet to engage the shaped surfaces (23, 24; 50a, 50b, 50c)) to prevent the passage of fluid from the outlet (15) to the inlet (14) as each shaped surface (23, 24; 50a, 50b, 50c) travels from the outlet (15) to the inlet (14). The shape of the surfaces (21, 22; 50a, 50b, 50c) provides an optimised volume for the chambers (23, 24; 51a, 51b, 51c) and the seal (12; 56) is urged into contact with the rotor (11) by spring arrangements (13, 39, 41, 59) that provide an even force along the axial length of surfaces (21, 22).