However, the data of Scott (1954), within scatter, are fairly con- 

 sistent with equation (10), and the data of Inman (1957) in Figure 5(f) 

 show increased scatter when plotted against Ua/v . On the basis of 

 theory and some observations, Shulyak (1969) found that 



X = C(U + Ui)T Cii) 



where C and Ui are functions of grain and fluid properties. The presence 

 of Ui makes this expression incompatible with equations (9) and (10) . 



e. Disappearance of Ripples . Observers agree that, as a, or U, 

 or both increase, bed forms reach a maximum height and then decline and 

 eventually disappear in a slurry, a condition Dingier (1975) calls "sheet 

 flow." At the onset of this condition, (j) = i^^. Kennedy and Falcon (1965), 

 using Inman 's (1957) data, find this disappearance at a/D - 8,000 

 (UT/D - 50,000), while Carstens, Neilson, and Altinbilek (1969) find 

 a/D = 1,700. Earlier, Carstens (1966) described the growth and decline 

 of bed forms in terms of (f)V2 rather than a/D, with maximum size at 

 (j)-^/^ = 6.5 and disappearance at (j)^/^ = <^^^/'^ - 13.0. In any case, 

 the tunnel in Carstens' studies was restricted to a single period (3.56 

 seconds), so possible separate effects of c|) and a/D could not easily 

 be distinguished. Mogridge and Kamphuis (1972) observe that bed forms 

 decrease and disappear with increasing a/D, but seem to imply that T 

 (with X2) is here held constant, so that U increases with a. In 

 Figure 4, as <^ increases n/D decreases and can reasonably be extrapolated 

 to zero. Manohar (1955) (with Figure 23 in his report) provides a crite- 

 rion for the disappearance of bed forms which can be written 



((,1/2^1/5 = 20.9 



For each grain material (value of r) , Manohar (1955) obtained U3 by 

 averaging all observations, each at a given value of a, and thereby 

 obscured any dependence of ((ig on a/D. With all observations plotted, 

 the data (in Manohar 's Table 9) show U^ clearly increasing with a for 

 eight grain materials, with scatter obscuring the trend in the single 

 remaining case of the lightest plastic. For glass beads and quartz 

 sand (2.5 < Pg/p < 2.65), the data are closely approximated by 



)^l/2 = 20.2 r"l/'+ + 0.33xl0~3 rl/2(a/D) . (12) 



24 



