A new model for calculation of the velocity field in a pump meridian is presented in this paper. It is a parameterized rotational flow model providing the pump designer with an option to simulate various flow conditions at the blade leading edge using a single parameter, which leads to different blade designs. Despite being rotational, this flow model does not allow for creation of helical swirl structures, a feature that is usually sought to be suppressed in a pump impeller. A condition for a flow pattern suitable for a pump hydraulic design is derived using curvilinear coordinates. The variation of the meridional velocity for different choices of the parameter is demonstrated, and the meridional flow field is compared against the turbulent flow. The resulting velocity field is easy to obtain and provides a unified approach to determine the distribution of the blade inlet angles along the leading edge for a range of design requirements.