58 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS wilere, (1) k/2 is the width of the empty annulus or "statistical empty space" at the orifice, (2) D is the orifice diameter, (3) p the bulk density, (4) Q the flow rate, and (5) [i the included half angle of the flow channel. The predictions of Brown's equation have been compared with experi- mental data obtained in this laboratory for three materials, 1-3 mm gravel, Figure 2600-- 2400 2200 2000 1800 1600 1400 ,,... 40C 20C 0 0 Experimental points ß PainIs, calculated from Brown s equalion e Points coincide The scatter of the calculated / points is caused by slight differenc,• in the orifice sizes used / / ß/152 mm orifice (nominal) • o I , •" 76 mm orifice(nominal} 38mm orifice (nominal} 0 1.0 •-0 3.0 4.0 5-0 Tangent of the complement of the hopper angle Comparison of the experimental and the flow rates computed from Bro•vn's equation for 1-3 mm gravel.

TIlE FLOXV OF PARTICULATE MATERIALS FROM HOPPERS 59 66 pm sand and 55 pm calcite. The sand and gravel were free flowing but the calcite was moderately cohesive. The hoppers used were fitted with cones of 45 ø, 65 ø, 75 ø and 80 ø to the horizontal with a flat plate for the 0 ø angle. Orifice diameters of 38, 76 and 152 mm were used at each cone angle. Comparison of the flow rates with those calculated from Brown's equation, for the gravel and sand are shown in Figs. 2 and 3 respectively. It can be seen that the agreement is good in the case of the gravel but poor for the 220O 2000 Experimental points Points calculated from Brown's equation 180( -- 160( -- -- / . / ,/ The scatter of the calculated points is caused by slight differences in the orifice sizes used 152 mm orifice (nominal) 800 -- 600 -- 400-- 200 -- 0-- I I ¸ i.o Tangent of the complement of the hopper angle Fi.gure 3. Comparison of the experimental and the flow rates computed from Brown's equation for 66 gm sand. sand. The break in the curve for the gravel occurred at the angle at which mass flow occurred until it reaches this angle the material can be con-