Dynamical Study of Granular Flow through a Two-Dimensional Hopper

The mass flow rate of a granular flow through an aperture under gravity is a long-standing challenge issue in physical science. We show that for steady flow field close to laminar flow, the dynamical equations together with the continue equation and Mohr-circle description of the stress are closed, and hence solvable. In a case of streamline guided by the two-dimensional hopper, we obtain a consistent condition and use it to determine the stress and the velocity distribution. Our result indicates that 3/2 power scaling behavior is recovered with a coefficient C(\mu,\alpha) being a function of frictional coefficient and the hopper angle. It is found that the predicted coefficient C(\mu,\alpha) is compatible with previous studies.