The theory of induced voltage electromagnetic flowmeters

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Abstract
The performance of an electromagnetic flowmeter head is assessed in terms of a weight vector W such that the output voltage ∝ ∫ v. Wdτ, where v is the velocity and τ the flowmeter volume. The condition curl W = 0 with W → 0 at ∞ is shown to be necessary and sufficient for the velocity to depend only on the flow rate and not on the flow pattern. A class of such ‘ideal’ meters is described. It is shown that meters with point electrodes can never be ideal but may, with considerable complication of the magnetic field, be made immune to asymmetric velocity-profile variations if the flow is rectilinear.