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The active fluid volume in an electromagnetic flowmeter is taken as a finite circular cylinder. The magnetic potential and virtual-current potential in this volume are expanded in Fourier series in the variables theta (polar angle) and z (axial coordinate). Any magnetic field and virtual current is thus represented by the matrices anm and bpq respectively (being the coefficients in the double-Fourier series). Expressions for the matrix elements for a four-pole electromagnet and for one or two pairs of point electrodes are derived. A method is given for obtaining the matrix elements representing a magnetic field in terms of values of the normal component of the flux density over a cylinder coaxial with the tube. The axisymmetric weight function (and hence the fully developed flow sensitivity) can be derived by evaluating a double sum involving the elements anm and bpq and the coefficients Wnm(r) which are independent of magnetic field and virtual current. Calculations of the weight function and sensitivity have been made and examples of results given.

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