A configuration of a plane interface between two stratified layers is appropriate for two-phase systems which are dominated by gravity, as is the case for large scale air-water systems under earth gravitation. However, for a general two-fluid system, the basic in situ configuration is stratified layers with a curved interface. The prescription of the characteristic interface curvature is required in order to initiate the solution of the dow problem and the associated transport phenomena. Energy considerations are employed to predict the interface configuration. The effect of the fluid physical properties, in situ hold up, tube dimension, wall adhesion and gravitation on the characteristic interface curvature are explored. The prediction of interface curvature provides the closure relation required for a complete solution of stratified flows with curved interfaces for a variety of two-fluid systems.