This paper proposes a novel orifice flow model for non-Newtonian fluids. The orifice model is developed for sharp orifices with small apertures (orifice to pipe diameter ratio: 0.04 ≤ β ≤ 0.16) for which predictive models are not present in the literature. The orifice flow experiment is conducted with three different orifices and three different fluids. From the experimental data, a correlation is developed that relates Euler number to Reynolds number and orifice diameter ratio. It also accounts for elastic effects of the fluid on orifice flow by including Weissenberg number in the model. The developed model predicts the experimental data within reasonable accuracy.