An apparatus 10 and method is provided that includes a spatial array of unsteady pressure sensors 15 18 placed at predetermined axial locations x.sub.1 x.sub.N disposed axially along a pipe 14 for measuring the velocity and volumetric flow rate of a single phase or multi-phase fluid 12 having a non-negligible axial Mach number flowing in the pipe 14. The pressure sensors 15 18 provide acoustic pressure signals P.sub.1(t) P.sub.N(t) to a signal processing unit 30 which determines the speed of sound propagating with and against the flow of the fluid 12 in the pipe 14 using acoustic spatial array signal processing techniques. The apparatus, responsive to the measured speed of sound propagating with and against the flow of the fluid, determines the velocity and the flow rate of the fluid propagating through the pipe.