The effects of cylindrical orifice length and diameter on the flow rate of three commonly used pharmaceutical direct compression diluents (lactose, dibasic calcium phosphate dihydrate and pregelatinised starch) were investigated, besides the powder particle characteristics (particle size, aspect ratio, roundness and convexity) and the packing properties (true, bulk and tapped density). Flow rate was determined for three different sieve fractions through a series of miniature tableting dies of different orifice diameter (0.4, 0.3 and 0.2 cm) and thickness (1.5, 1.0 and 0.5 cm). It was found that flow rate decreased with the increase of the orifice length for the small diameter (0.2 cm) but for the large diameter (0.4 cm) was increased with the orifice length (die thickness). Flow rate changes with the orifice length are attributed to the flow regime (transitional arch formation) and possible alterations in the position of the free flowing zone caused by pressure gradients arising from the flow of self-entrained air, both above the entrance in the die orifice and across it. Modelling by the conventional Jones-Pilpel non-linear equation and by two machine learning algorithms (lazy learning, LL, and feed-forward back-propagation, FBP) was applied and predictive performance of the fitted models was compared. It was found that both FBP and LL algorithms have significantly higher predictive performance than the Jones-Pilpel non-linear equation, because they account both dimensions of the cylindrical die opening (diameter and length). The automatic relevance determination for FBP revealed that orifice length is the third most influential variable after the orifice diameter and particle size, followed by the bulk density, the difference between bulk and tapped densities and the particle convexity.