A method and apparatus for estimating a flow rate of a phase of a multiphase fluid is disclosed. In the first method, nuclei in the fluid are polarized over two distances and a measured magnetization gives the relative fraction of two components of the fluid for a selected velocity. In the second method, nuclei in the fluid are polarized over a specified distance and measurements of the decay of spin echo signals is used to give the relative fraction of two components of the fluid for the selected velocity.