Electrohydrodynamic jetting is an industrial practice. In this work, a finite element variational multiscale formulation is developed to stabilise the numerical solution of the electrohydrodynamic flow problem. Particularly, the spatial approximation is delat with, which may suffer instabilities arising from equal interpolation spaces for unknown velocity and pressure, and convection dominant type of flows. This approach grants accurate and stable numerical descriptions of the coupled flows modelled by transport equations. Future work is intended to validate the model: the electric current must be estimated with experimental measurements.