We look at the problem of unsteady magnetohydrodynamic flow of an electrically conducting, laminar, incompressible, Newtonian, viscous fluid through a tube exposed to screen electrodes placed centrally in the flow field and at the two ends of the tube. The governing differential equations which comprise such effects as the electric field, the magnetic and flow fields are non-dimensionalized and solved numerically. The rotational electromagnetic forces arising from the combined influences of both the magnetic and the flow fields, are not balanced by the fluids pressure gradient forces and impact on the hydrodynamics of the fluid flow significantly. Graphical representation of numerical results for the steady state flow and electromagnetic fields are discussed. For cases involving no net flow through the tube, symmetric flow is observed for the symmetrical geometric configuration. This is however not the case for through flow, where the flow decelerates as it moves towards the centrally placed electrodes. A comprehensive parametric study is conducted to show the influence of certain dimensionless variables on the flow and magnetic fields, and in all cases they help to confirm both the numerical formulation and the overriding physics.