Reynolds' equation is separable into two single variable differential equations for the case of a hydrodynamic bearing with its lubrication film curved in one direction. One of the equations is not, in general, soluble analytically. A simple numerical solution of this equation is described. The solution depends only on the shape of the lubrication film and not on the ratio b/l where b is the pad breadth and l is its length. This means that a sequence of bearing parameters for a set of values of b/l can be calculated rapidly from the single numerical solution of the differential equation.