Propagating wave fronts resulting from autocatalytic chemical reactions have been the focus of much recent research. For the most part, the hydrodynamics resulting from such reactions has been neglected. In this work, a relation is derived for the normal speed of a propagating wave front as a function of the local curvature when fluid motion is allowed. This "eikonal" equation is a generalization of one which was derived in the absence of fluid flow. It is also shown that small variations in the fluid density due to the chemical reaction do not change the form of the relation. © 1993 The American Physical Society.