A procedure for solving the Navier-Stokes equations for the steady, one-dimensional flow of a binary water-based lubricant within an infinite breadth hydrodynamic journal bearing is described. The method uses the Newton-Raphson iterative technique to obtain the interface layer in the flooded clearance along the bearing. The implementation of the Simpson rule of integration technique into the equation set allows pressures, drags and the load carrying capacities to be predicted for a range of viscosity ratios.