Recent experimental work has shown that when the mean velocity profile upstream of an orifice plate has a deficit on the centerline and higher velocities at the outer edges of the pipe, the pressure drop across the orifice is greater than if the flow upstream is “fully developed.” It is proposed that this increase in ΔP is directly correlated with the radial distribution of momentum upstream of the orifice plate. In an effort to investigate how the upstream flow condition affects the pressure distribution along the pipe wall and to determine if the hypothesis is correct, Creare.X Inc.’s FLUENT numerical analysis program was used to simulate the effects. Two β ratios (0.50 and 0.75) have been considered with various mean velocity inlet profiles. Inlet profiles include the 1/6th, 1/7th, 1/8th, 1/9th and 1/10th power law, uniform flow, and two linear distributions. The results indicate that there is a correlation between the second and third-order moments of momentum and the value of the discharge coefficient. This empirical correlation, after being fully verified by experimental data, can be used to estimate the change in the coefficient of discharge given the inlet velocity profile.