Method and apparatus for determining fluid flow

Claim 1

A method for determining average fluid velocity across a reference plane of a fluid conveyance comprising the steps of selecting a plurality of functions f j (p,m k ), which each represent an approximation of the flow velocity profile P(p) of fluid traversing said reference plane, where p defines a position in said plane and each m k is a function of the Reynolds number; approximating the flow velocity profile by a linear combination of said functions, said combination being of the form ##EQU18## where each A j ,k is an unknown scalar constant and j and k are positive integers over which the summation is taken; measuring the time durations for acoustical sounds to travel upstream and downstream along each of a plurality of straight line paths, each path extending between an upstream wall position of said fluid conveyance and a downstream wall position of the conveyance, the number of known paths being not less than the multiplicative product of j and k; determining a measured average fluid flow velocity, vel. meas(i), for each path from the measured time durations; determining said unknown constants A j ,k by forming a system of simultaneous equations having the form ##EQU19## where PL i is the length of the i th path, P i defines the i th known path and P i is the line integral along the path P i , and solving said system of simultaneous equations for said A j ,k by evaluating said line integrals along said flow paths, substituting the known values for vel. meas(i) and PL i , and solving for the constants A j ,k ; determining average flow V across said plane by evaluating the equation ##EQU20## where PA is the area of the reference plane bounded by said conveyance and the integral is taken over the entire area of the reference plane bounded by the fluid conveyance.

Claim 2

A method for determining average fluid velocity across a reference plane of a fluid conveyance comprising the steps of selecting a plurality of functions f j (p,m k ), which each represent an approximation of the flow velocity profile P(p) of fluid traversing said reference plane, where p defines a position in said plane and each m k is a function of the Reynolds number; approximating the flow velocity profile by a linear combination of said functions, said combination being of the form ##EQU18## where each A j ,k is an unknown scalar constant and j and k are positive integers over which the summation is taken; measuring the time durations for acoustical sounds to travel upstream and downstream along each of a plurality of straight line paths, each path extending between an upstream wall position of said fluid conveyance and a downstream wall position of the conveyance, the number of known paths being not less than the multiplicative product of j and k; determining a measured average fluid flow velocity, vel. meas(i), for each path from the measured time durations; determining said unknown constants A j ,k by forming a system of simultaneous equations having the form ##EQU19## where PL i is the length of the i th path, P i defines the i th known path and P i is the line integral along the path P i , and solving said system of simultaneous equations for said A j ,k by evaluating said line integrals along said flow paths, substituting the known values for vel. meas(i) and PL i , and solving for the constants A j ,k ; determining average flow V across said plane by evaluating the equation ##EQU20## where PA is the area of the reference plane bounded by said conveyance and the integral is taken over the entire area of the reference plane bounded by the fluid conveyance.

Claim 9

An apparatus for determining average fluid flow velocity across a reference plane of a fluid conveyance comprising a plurality of transducer pairs, each transducer being positioned in the boundary walls of said fluid conveyance for emitting and for receiving acoustical signals, and each transducer pair spanning a longitudinal section of said conveyance, a synchronizing control element for selectively operating said transducer pairs for producing generated acoustical signals for each said transducer in a predetermined sequence and for receiving said acoustical signals with the transducer associated with the transmitting transducer, means for repeatedly measuring an upstream and a downstream transit time duration for each transducer associated pair and determining, from the upstream and downstream acoustic signal transit time durations for each transducer pair, a measure of average fluid flow velocity, vel. meas(i), for each straight line path associated with and extending between each of said associated transducer pairs, means responsive to said measuring and determining means for solving a system of simultaneous equations having the general form ##EQU24## for the A j ,k, where A j ,k are unknown scalar constants, PL i is the path length of the i th path between the i th pair of transducers, f j (p,m k ) represents a plurality of approximations of the flow velocity profile of fluid traversing said member where p is position in the reference plane, and m k is a function of the Reynolds number of the fluid, and the integral is a line integral taken along the i th straight line path, and means response to said solving means for evaluating an equation of the form ##EQU25## where V is the average velocity across the reference plane normal to the fluid flow path, A is the cross-sectional area of the conveyance, and the integral is taken across the area of the conveyance, whereby the average fluid flow velocity across the reference plane is determined.

Claim 10

An apparatus for determining average fluid flow velocity across a reference plane of a fluid conveyance comprising a plurality of transducer pairs, each transducer being positioned in the boundary walls of said fluid conveyance for emitting and for receiving acoustical signals, and each transducer pair spanning a longitudinal section of said conveyance, a synchronizing control element for selectively operating said transducer pairs for producing generated acoustical signals for each said transducer in a predetermined sequence and for receiving said acoustical signals with the transducer associated with the transmitting transducer, means for repeatedly measuring an upstream and a downstream transit time duration for each transducer associated pair and determining, from the upstream and downstream acoustic signal transit time durations for each transducer pair, a measure of average fluid flow velocity, vel. meas(i), for each straight line path associated with and extending between each of said associated transducer pairs, means responsive to said measuring and determining means for solving a system of simultaneous equations having the general form ##EQU24## for the A j ,k, where A j ,k are unknown scalar constants, PL i is the path length of the i th path between the i th pair of transducers, f j (p,m k ) represents a plurality of approximations of the flow velocity profile of fluid traversing said member where p is position in the reference plane, and m k is a function of the Reynolds number of the fluid, and the integral is a line integral taken along the i th straight line path, and means response to said solving means for evaluating an equation of the form ##EQU25## where V is the average velocity across the reference plane normal to the fluid flow path, A is the cross-sectional area of the conveyance, and the integral is taken across the area of the conveyance, whereby the average fluid flow velocity across the reference plane is determined.