An electromagnetic flow meter for monitoring the flow of a conducting continuous phase of a multiphase fluid comprising: a flow tube comprising a non-electrically conducting body with a flow tube cross-section and a circumference; a means for generating a magnetic field (3a, 3b) across the flow tube cross-section so that a voltage is induced in the conducting fluid as it flows through the flow tube; an array of voltage detection electrodes arranged around the circumference of the flow tube configured to measure flow induced voltages at the boundary of the flow tube cross-section, the flow tube cross-section being divided into a plurality of pixel regions; and processing means for determining an axial velocity profile of the conducting continuous phase of the multiphase fluid by calculating the local axial velocity of the conducting fluid in each of the pixel regions, wherein the processing means is configured to calculate the local axial velocity of the conducting continuous phase of the multiphase fluid in each pixel region using the measured induced voltages and predetermined weight functions for each pixel region, characterized in that the electromagnetic flow meter further comprises a means for measuring a local concentration distribution of the conducting continuous phase of the multiphase fluid, and wherein the electromagnetic flow meter is further characterised in that: the processing means is configured to calculate the volumetric flow rate of the conducting continuous phase of the multiphase fluid using the local axial velocity of the conducting continuous phase of the multiphase fluid in each pixel region and the local concentration distribution of the conducting continuous phase of the multiphase fluid; the means for generating a magnetic field is configured to generate a non-uniform magnetic field across the flow tube cross-section; and the means for generating a magnetic field is further configured to successively generate multiple magnetic fields, each magnetic field having a different magnetic flux density distribution. a flow tube comprising a non-electrically conducting body with a flow tube cross-section and a circumference; a means for generating a magnetic field (3a, 3b) across the flow tube cross-section so that a voltage is induced in the conducting fluid as it flows through the flow tube; an array of voltage detection electrodes arranged around the circumference of the flow tube configured to measure flow induced voltages at the boundary of the flow tube cross-section, the flow tube cross-section being divided into a plurality of pixel regions; and processing means for determining an axial velocity profile of the conducting continuous phase of the multiphase fluid by calculating the local axial velocity of the conducting fluid in each of the pixel regions, wherein the processing means is configured to calculate the local axial velocity of the conducting continuous phase of the multiphase fluid in each pixel region using the measured induced voltages and predetermined weight functions for each pixel region, characterized in that the electromagnetic flow meter further comprises a means for measuring a local concentration distribution of the conducting continuous phase of the multiphase fluid, and wherein the electromagnetic flow meter is further characterised in that: the processing means is configured to calculate the volumetric flow rate of the conducting continuous phase of the multiphase fluid using the local axial velocity of the conducting continuous phase of the multiphase fluid in each pixel region and the local concentration distribution of the conducting continuous phase of the multiphase fluid; the means for generating a magnetic field is configured to generate a non-uniform magnetic field across the flow tube cross-section; and the means for generating a magnetic field is further configured to successively generate multiple magnetic fields, each magnetic field having a different magnetic flux density distribution. the processing means is configured to calculate the volumetric flow rate of the conducting continuous phase of the multiphase fluid using the local axial velocity of the conducting continuous phase of the multiphase fluid in each pixel region and the local concentration distribution of the conducting continuous phase of the multiphase fluid; the means for generating a magnetic field is configured to generate a non-uniform magnetic field across the flow tube cross-section; and the means for generating a magnetic field is further configured to successively generate multiple magnetic fields, each magnetic field having a different magnetic flux density distribution.