The present invention relates in general to flowmeters and in particular to a new and useful flowmeter which is capable of measuring both mass and velocity, despite non-uniform flow and density profiles. 
The least complex acoustic (ultrasonic) flow meter uses a single pair of transducers in the flow to be measured, one upstream and one downstream.  These alternately send and receive.  The difference in transit time between the upstream direction and the downstream direction is related to the flow velocity.  One of the shortcomings of this technique is that the flow is not uniform across a pipe or conduit.  The single pair flowmeter requires a correction factor based on assumed flow distribution. 
Multiple pairs of transducers are used in some flowmeters to allow summation of flows over the individual paths.  This still requires assumptions about the flow profiles.  Elaborate numerical integration schemes are used to make corrections. 
These flowmeters give only velocity flow.  Mass flow may be computed knowing the flow pattern and the density of the fluid involved.  Problems arise, however, when the density is not uniform in space and/or time. 
Density is measured by several techniques, including signal attenuation (e.g. gamma, acoustic, or optical), capacitance, etc.  The attenuation and capacitance measurements are affected by uneven distributions. 
Mass flow can be measured by using a momentum/stress conversion, but this is difficult to implement since it requires a special curved conduit, and other measures. 
References which are pertinent in understanding the invention are U.S. Pat.  No.  4,109,523 to Teyssandier; U.S. Pat.  No.  4,024,760 to Estraea Jr., U.S. Pat.  No.  3,940,985 to Wyler; and U.S. Pat.  No.  3,778,614 to Hounsfield.  These patents all disclose flow measuring techniques which utilize various irradiated signals such as sound and electromagnetic signals. 
Other pertinent references are: Scudder, Henry J., "Introduction to Computer Aided Tomography", Proceedings of the IEEE, Volume 66, No.  6, June 1978.  Pages 628-637;Mersereau, R. M., "Digital Reconstruction of Multidimensional Signals from their Projections", Proceedings of the IEEE, Volume 62, No.  10, Oct. 1974.  Pages 1319-1338; and Raptis, et al., " Instrumentation for Process Control by Acoustic Techniques in Coal Conversion Plants", Proceedings of 1979 JACC, Pages 437-442.