A flow meter for measuring fluid flow of a flowing fluid in a conduit , the flow meter comprising: a plurality of transducers and a reflector engaged with the conduit; and a signal processor in electrical communication with the plurality of transducers , the signal processor configured to: cause the transducers to transmit acoustic signals through the flowing fluid and receive flow signals from the plurality of transducers or the reflectors based on the acoustic signals, wherein the plurality of transducers receive and produce: a measurement of flow rate; and an associated estimate of uncertainty due to changes that have affected accuracy of the flow rate based on the flow signals, wherein the flow rate is determined via ultrasonic communication between the transducers and the reflector located in a chordal plane; wherein the transducers form multiple transducer pairs positioned to form acoustic transmission paths that are co-located in two or more chordal planes, in each chordal plane the transducer pairs located in the chordal plane are positioned to form acoustic transmission paths that traverse at least once from one side of the plane to another side of the plane, if all paths are direct from one transducer to another transducer of a transducer pair, there is a minimum of three traverses in each chordal plane and if any paths employ a point of reflection, there is a minimum of four traverses such that in either case a sum of a number of paths and a number of traverses in each chordal plane is greater than or equal to six. a plurality of transducers and a reflector engaged with the conduit; and a signal processor in electrical communication with the plurality of transducers , the signal processor configured to: cause the transducers to transmit acoustic signals through the flowing fluid and receive flow signals from the plurality of transducers or the reflectors based on the acoustic signals, wherein the plurality of transducers receive and produce: a measurement of flow rate; and an associated estimate of uncertainty due to changes that have affected accuracy of the flow rate based on the flow signals, wherein the flow rate is determined via ultrasonic communication between the transducers and the reflector located in a chordal plane; cause the transducers to transmit acoustic signals through the flowing fluid and receive flow signals from the plurality of transducers or the reflectors based on the acoustic signals, wherein the plurality of transducers receive and produce: a measurement of flow rate; and an associated estimate of uncertainty due to changes that have affected accuracy of the flow rate based on the flow signals, wherein the flow rate is determined via ultrasonic communication between the transducers and the reflector located in a chordal plane; a measurement of flow rate; and an associated estimate of uncertainty due to changes that have affected accuracy of the flow rate based on the flow signals, wherein the flow rate is determined via ultrasonic communication between the transducers and the reflector located in a chordal plane; wherein the transducers form multiple transducer pairs positioned to form acoustic transmission paths that are co-located in two or more chordal planes, in each chordal plane the transducer pairs located in the chordal plane are positioned to form acoustic transmission paths that traverse at least once from one side of the plane to another side of the plane, if all paths are direct from one transducer to another transducer of a transducer pair, there is a minimum of three traverses in each chordal plane and if any paths employ a point of reflection, there is a minimum of four traverses such that in either case a sum of a number of paths and a number of traverses in each chordal plane is greater than or equal to six. <EOS>