A numerical study of dynamics in thin hopper flow and granular jet
Wang Meng-Ke1, 2, Yang Guang-Hui1, 2, Zhang Sheng1, 2, Cai Han-Jie1, 2, Lin Ping1, 2, †, Chen Liang-Wen1, 2, Yang Lei1, 2
       

The time-averaged profile of vz for D = 5d, 10d, 20d, 30d at two heights z1 = 2d and z2 = 5d. The fit lines using kinematic model for heights z1 = 2d and z2 = 5d are also shown. The vertical black dashed line is drawn for visual clarity.