A novel Lagrangian formulation is proposed for self‐consistent fluid mechanics problems, like magnetohydrodynamics, in which the force field is to be determined along with the velocity field. A key feature of the formulation is that the momentum balance and continuity equations are exactly satisfied locally, even in numerical applications. This is accomplished by choosing a Lagrangian representation for the velocity field and using the momentum balance equation to cmpute the force field pointwise in terms of the Lagrangian mapping function. The formulation is illustrated for one‐dimensional electrohydrodynamics, in which case the mass continuity and momentum balance equations are coupled to the Poisson equation. The formulation may be suitable for describing phenomena like the formation of convective cells, boundary layers, or discontinuities in a natural way.