Fig. 1. Experimental arrangement of sand jets in air Fig. 2. Pictures of sand jet fronts for d,=31.1 mm with time interval of 8 ms Fig. 4. Mean velocities of sand jets at the nozzle The observations on the front speed of the sand jets are shown in Fig. 5(a). The front velocity U increases continuously with the length of the jet front from the initial section L in all experiments. tively small compared with the size of the nozzle and the wall of the hopper is not very steep. Our result is close to the value estimated from 0.74 gd, and the error is within 10%. For the sand jets from the 19.2-mm nozzle, the obtained V, is increased by 15.6%. This difference is due to the attached short pipe in the 19.2-mm nozzle as reported by Rao and Nott (2008) that the flow rate of granular material from a hopper can be increased by the use of an extended pipe. Fig. 5. (a) Frontal velocities of sand jets from different nozzles; (b) variation of (U-U5)/8 with L Fig. 6. Comparison of steady and frontal velocities of a sand jet (d,=63.8 mm) Fig. 7. (a) Variations of steady sand jet diameters; (b) dimensionless diameters along the steady sand jets Fig. 9. Waves observed along sand jets with time interval of 4 ms Fig. 8. Concentration variations along the steady sand jets Fig. 10. Wave speed and wavelength along two steady jets
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