conditions. Three sizes of sand were used each with three different 

 amplitudes of oscillation. Thus 27 runs were made altogether. The 

 size range used was 



#14 < D < #10 mesh 



#10 < D < # 8 mesh 



# 8 < D < #6 mesh 



_3 

 The average value of D for each of these ranges were 5.5.1 x 10 feet, 



-3 -3 



7.15 x 10 feet and 9.25 x 10 feet, respectively. As a matter of 



fact, these were exactly the same sizes used in the measurement of the 

 velocity and phase shift distribution. The size of the sample in each 

 run was measured volumetrically . No distinction was made as to whether 

 the material in the tray came over the right or left edge. Each run was 

 repeated a number of times and the measured quantities were averaged out. 

 The bulk volume of the sample was converted into dry weight by multi- 

 plication through a coefficient determined experimentally. 



Since the width of the flume was equal to 1 foot, the dry weight 

 of the sample when divided by the period and the number of oscillations 

 completed during the testing time gave the value of q„ . Next equation 

 (4-26) was used to determine $. This equation is of the form 



. % r~pf~ - 3/2 



Y s V g(Ps-Pf) 



D 



p s qg 2/? 



For given values of — the ratio -=- is proportional to D ". Herein 



Pf * 



s B 3 /2 



— was equal to 2.63 which means that -=- = 1190 D . The graphical 



Pf $ ° * 



representation of this equation shown in Figure 9 was used to calculate 

 $ from measured values of q g . 



On the other hand Y was calculated from equation (4-10) which is 



Y = Ps - Pf _£l 



P f u 2 



_ 2 _2 



In fact, the amplitude |u| was used instead of u because what we were 



really interested in was the value of | Y | . A pair of values of the 



parameters $ and Y were thus obtained for each run. These values were 



next plotted against each other as shown in Figure 8. Although there 



is considerable scatter, it seems that the experimental points can be 



reasonably represented by the empirical curve drawn through them. We 



may claim therefore that this curve expresses the functional relationship 



C-2 



