Methods and apparatus for measuring individual phase fractions and phase flow rates in a multiphase flow based on velocity of the flow, speed of sound through the fluid mixture, and the density of the fluid mixture are disclosed. Techniques presented herein are based on measuring frictional pressure drop across a flowmeter conduit, determining a surface roughness term for the conduit during initial flow tests or through other mechanical means, implementing a correction method to balance the momentum equation, and calculating the fluid mixture density using the measured pressure drop. The techniques may be applicable to measuring flow parameters in horizontally oriented conduits and, more generally, conduits of any orientation. The method for determining phase fractions or one or more flow rates of phase components of a fluid mixture flowing in a conduit comprises: measuring a bulk velocity and a speed of sound of the fluid mixture; determining a differential pressure between two points in the conduit; calculating a density of the fluid mixture as a function of the differential pressure, the bulk velocity, and a surface roughness parameter associated with the conduit; and calculating at least one of phase fractions or the one or more flow rates of the phase components of the fluid mixture, using the speed of sound, the bulk velocity, and the calculated density.
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