Problems of viscous drag reduction and boundary layer control have been and continue to be objectives of research for their economic impact and the enhancement of the flight characteristics of flying vehicles. Corona discharge is a new technique in this regard;The study of this technique requires consideration of the electrostatics and fluid mechanics. In order to effectively evaluate the technique with minimum complications, the geometry chosen was a dc positive corona discharge on a flat plate of zero thickness at zero angle of attack with the fluid flow as steady state, two-dimensional, incompressible viscous one. Five coupled partial differential equations govern this model requiring the simultaneous solution of these equations. A finite difference method has been employed to approximate these equations through an appropriate scheme for each equation. A clustered grid is used in the vertical direction to handle the high velocity gradient inside the boundary layer. The insufficient boundary conditions necessary for the numerical solution of Poisson's equation is compensated by making the numerical model find the appropriate computational domain which leads to a unique solution. Stability conditions of the five-point scheme approximating Poisson's equation has been determined computationally;Results obtained using the numerical model are presented. As a result of this research the corona discharge near a surface of finite conductivity is now better understood as an electrostatic phenomena. The corona discharge between wire-to-wire electrodes occurs if the electric potential difference between the electrodes is raised to a value higher than the corona onset voltage. The corona current is proportional to the potential difference between the electrodes and inversely proportional to the corona wire diameter. At the same time it does not significantly respond to the gap length between the electrodes until the corona wire diameter becomes large, then it varies inversely as the gap length;The corona discharge can be applied to reduce drag on bodies when the Reynolds number is relatively small. The drag reduction achieved by corona discharge inside a boundary layer is a function of many parameters. The drag reduction is proportional to both the electric potential difference and the gap length between the two electrodes and inversely proportional to the free stream velocity. It is also proportional to the location of the corona electrodes as measured from the plate leading edge and inversely proportional to the corona wire diameter. The increased effect of corona discharge at low flow speeds confirms its ability to significantly enhance the cooling rate of a hot body by boosting the convection of the flow around that body. The quantitative analysis of electrostatic cooling is the natural extension of this study.