Employing the kinematic model proposed by Nedderman and Tuzun and the boundary conditions for granular media in a two-dimensional flat-bottomed hopper with eccentric and centric discharge, two boundary-value problems were constructed. The heights of the stagnant zone for two kinds of granular materials after hopper eccentric and centric discharge were experimentally measured. We postulated that the kinematic constant would be proportional to the height of the stagnant zone. Employing experimental results and the Newton-Raphson method, the kinematic constants under eccentric discharge were obtained. The profiles of the horizontal and vertical velocity components for eccentric as well as centric discharge were then calculated. The theoretical predictions obtained using the kinematic model qualitatively agree with experimental results obtained using a simple image analysis.