The experimental work presented in this paper has shown that the how rates of coarse materials through conical hoppers conform to the models of Beverloo et al. (1961. Chem. Engng Sci. 15, 260) and Base and Tanaka (1959, The Engineer (London) 208, 465), with the mass flow rate being proportional to D-5/2 where D is the orifice diameter. Significantly lower dow rates were found for fine particles, though the mass flow rates were still found to be proportional to D-5/2, but with the constant of proportionality being a function of particle diameter. This is ascribed to the presence of interstitial pressure gradients set up as the material dilates on approaching the orifice. Direct measurements of these pressure profiles have been made, but precise numerical agreement with the values required to cause the reduced flow rate was not found. This was attributed to pressure variation across the hopper. The pressure gradients were, however, found to be independent of orifice diameter and inversely proportional to the square of the particle diameter. A correlation has been proposed in which the mass flow rate is proportional to D-5/2 multiplied by a factor which is a linear function of particle diameter squared. Of the measured flow rates 93% lie within +/- 20% of this correlation.