Hoppers are one of the most popular devices implemented to allow precise flow control mechanism when dispensing granulate materials from silos and other containers. Despite its ubiquity in many industrial processes, the effect that hopper geometry has on the flow rate is still poorly understood. In this work, we study the influence of the hopper angle on the main two variables that determine the flow rate: the solid-fraction and the velocities of the particles. To this end, we use a quasi-two-dimensional system which allows a precise characterization of the profiles of these variables at the orifice. Using these experimental results, we compute the flow-density vector and obtain the resulting expression for the volumetric flow rate. Finally, we compare this expression with an equation introduced back in 1961 by RL Brown.