Coathanger dies are effective in delivering uniform flow of a polymer melt; however, when the fluid flow index varies from the design values, the flow is not uniform. Although mechanisms such as die lip adjustments have been effective tools for adjusting flow profiles, the issue of a variable flow index has not been fully addressed at the design stage. An analytical solution, based on the assumptions present in the 1-D design equation, has been developed for the flow distribution in a coathanger manifold. This solution determines the flow distribution for a power-law fluid with a flow index n* in a manifold designed for a separate flow index n. From this solution, a uniformity index and a critical design angle are defined. The critical design angle is the angle at which the local derivative of the uniformity index with respect to n* approaches a maximum (for n* < n) or a minimum (for n* > n) as a function of the design angle. The critical design angle is independent of n and is presented as a function of the manifold aspect ratio.