Two-dimensional instead of three-dimensional computational fluid dynamic solutions of flow problems are quite often used in industry to facilitate short design turn-around times with varying degrees of success. A simple and robust approach for improving the accuracy of two-dimensional computational fluid dynamics solutions for problems involving internal flow passages in industrial applications is presented. The technique utilizes an approximation to the shearing stresses that act in the fully three-dimensional case but are ignored in the traditional two-dimensional approximation. Although the technique does not fully account for all the three-dimensional effects in such flows, it gives a reasonable estimate of the operation of devices with internal flows, even those involving transients. The usefulness and accuracy of the method are demonstrated through the application of the method to predict the performance of a supersonic fluidic oscillator for industrial design purposes. This brief provides industrial designers with a simple and robust tool for improving the accuracy of their computational fluid dynamic simulations.