Induction flow-measurement theory for poorly conducting fluids

Abstract

The equations governing the electrodynamics of moving media are solved to give a general expression for the induced electromotive force in an electromagnetic flowmeter for poorly conducting fluids with dielectric and magnetic properties. The expression is a generalization of one already known for conducting fluids. Conditions of validity are given. Nomenclature B magnetic induction c speed of light in vacuum c' speed of light in stationary fluid D displacement current E electric field H magnetic field i = V- 1 j combined current density and displacement currents J current density = ( μ σ + K | v / l + i ω | ) / ( μ σ + ε μ | v / l + i ω | ) K = ε μ − ε 0 μ 0 l characteristic length M magnetization P polarization R ratio of order of magnitude of nonlinear component of signal to linear component of signal Rm magnetic Reynolds number U electric potential v characteristic velocity v fluid velocity W weight vector 8 skin depth e permittivity of fluid (or other material) e0 permittivity of vacuum p permeability of fluid (or other material) p 0 permeability of vacuum p charge density <t conductivity of fluid (or other material) (j) magnetic potential S electromotive force in detection coil (external electric field flowmeter) suffix 0 indicates fields when fluid Velocity is zero everywhere suffix s indicates fields associated with static charge embedded in fluid suffix r indicates ‘virtual’ fields ~ of the same order of magnitude as < less than or of the same order of magnitude as