We present results of a numerical analysis of Hartmann's historical experiments on flows of mercury in pipes and ducts under the influence of magnetic fields. The computed critical parameters for the laminar-turbulent transition as well as the friction coefficients are in excellent agreement with Hartmann's data. The simulations provide a first detailed view of the flow structures that are experimentally inaccessible. Novel flow regimes with localized turbulent spots near the sidewalls parallel to the magnetic field and otherwise laminar flow are discovered. We finally suggest how these predictions can be tested in a transparent fluid using optical flow measurement.