Gravity-driven particle flow through outlets with inclined angles and outlets with off-centred positions is investigated numerically by discrete element simulations. The measured particle discharge rates are well fitted by Beverloo's law, demonstrating a fairly linear relationship with orifice size to a power 3/2. The impacts of the hopper angle and the eccentric position of the outlet on the particle velocity and orifice volume fraction distribution are systematically investigated. The particle velocity and volume fraction distributions for different hopper angles are found to exhibit self-similar features that are well described by a mixed parabolic and power law with fractional exponents. The coefficients involved in determining the particle velocity and volume fraction distribution have clear physical significance. In the case of hopper angles in the range of 55° - 90°, the values of these determining coefficients are quite similar at each angle, leading to identical discharge rates of particles. The predicted mass flow rate derived from the velocity and volume fraction curves is found to be in satisfactory agreement with that obtained in the experimental works of Mendez et al. (2021) and Darias et al. (2020). Regarding the hopper with an eccentrical outlet, an asymmetry behavior appears. Moreover, the outlet directly at a wall generates a significantly higher flow rate than other locations. In the end, an extension of the self-similarity laws is proposed to allow the prediction of granular discharge for the rectangular hopper, from the centred to the border outlet case.