Fig. 1. (a) Schematic of the setup; (b) photograph of the permeable side wall of the silo; (c) the experimental devices used when the inclination is less than 45 degrees; (d) the experimental devices used when the inclination is greater than 45 degrees; (e) schematic of the wedge-shaped orifice D.

Fig. 2. Typical data of M(t) at D = 14 mm, ;the lower left and upper right insets are the data of 40−80 s and 80−120 s extracted from the main graph, both of which show good linearity. Both flow rates calculated from these two insets are 6.53 g/s, indicating that the flow is very stable.

Fig. 3. (a) The variation of flow rateQ with the inclination cosine at different orifices D, where the solid line is a linear fit; (b) variation of the normalized flow rate with , where is the rate at , and the solid line is the fitted result of equation (3); (c) the relationship between the critical angle of flow ceasing and the ratio d/D, where the solid line and are results of linear fitting.

Fig. 4. (a) Results of fitting the data in Figure 3 using the Beverloo formula (1) and (2), the inset is the change of with Dat different inclination, and the solid line is a linear fit; (b) and (c) variations of the parameters and with , and solid lines are results of fits by using equation (2). The inset in (c) is the change of with .

Fig. 5. (a) and (b): Beverloo parameters and of GOF in water (solid squares) and in air (hollow circles) as a function of ; (c)−(f): the changes of GOF flow rateQwith Din water and in air when , respectively, and the inset is the change of with D. The experimental data in air comes from ref. [16].

Fig. 6. Ratio of (a) Beverloo coefficient and (b) GOF flow rate Q in water and in air (from Ref. [16])