Magnetohydrodynamics — Hartmann Flow Push a liquid metal (or plasma) down a duct that sits in a magnetic field pointing across it. The moving conductor generates electric currents; those currents, crossed with the field, produce a drag that fights the flow hardest where it moves fastest. The parabola of ordinary pipe flow gets ironed flat, with the whole velocity change squeezed into paper-thin layers at the walls. The journey: add the Lorentz force J×B to the momentum balance and Ohm’s law for a moving conductor; one number, the Hartmann number Ha = B a √(σ/μ), sets everything. The wall layers thin as 1/Ha; turn the field along the flow and the braking vanishes.