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INDUCED POTENTIAL FOR AN ARBITRARY VELOCITY PROFILE
INDUCED POTENTIAL FOR FULLY DEVELOPED VELOCITY PROFILE
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adjustable parameters applied magnetic field approximate solution average fluid velocity average velocity axial symmetry basic equations becomes infinite boundary conditions center velocity computed conductive pipe wall convergence critical Reynolds number Cylindrical coordinate density dimensionless distortion factor distortion from axial effect of velocity electrical conductivity electrodes entry length equation 15a equations 8a error exact series solution flow measurement flowmeter sensitivity fluid conductivity ratio given by equation Green's function Hartmann number increases induced magnetic field infinite series inner radii ratio liquid metal applications Magnetohydrodynamic meter modified Bessel functions nonconductive pipe wall Numerical results obtained output potential percent Pipe outer-to pipe outer-to-inner radii pipe wall thickness PRINCIPLE AND RITZ Ratio of pipe RESULTS FROM VARIATIONAL Ritz technique Shercliff refs stationary point stationary value tion trial functions VARIATIONAL PRINCIPLE variational solution velocity and induced velocity profile distortion wall is conductive wall is nonconductive wall region wall to fluid weighting factor