This will show actual particles flowing from a larger width channel, through a tapered throat and then to a smaller width channel. The initial particle density (particles per unit area) is the same in all three sections of the channel. The flow will be such that the particle density does not change. This behavior corresponds to the flow of an incompressible fluid. To keep the particle density constant, the flow rate in the tapered section has to speed up in the `x` direction as well as adopting a converging speed in the `y` direction. If the starting channel half width is `w_1` and its length is `L_1` and the ending half width is `w_2` and the length of the tapered secion is `L_t` then the speeds in the x and y directions are:
`w=w_1-(w_1-w_2)(x-L_1)/L_t`
`v_x=w/w_1 v_1`
`v_y=-(w_1-w_2)/L_t (y/w) v_x `