The shape of the immersed body determines significantly the drag 

 resistance of the fluid at Reynolds numbers much higher than those at 

 which Stokes' relationship is valid. At Reynolds numbers greater than 

 50 the drag coefficients for discs and spheres diverge noticeably in 

 Schiller's diagram. Rubey (1933) and Zegrzda (1934) were among the first 

 to recognize the effect of particle shape on drag resistance. The manner 

 in which shape affects settling velocity can be expressed in terms of 

 drag coefficient and Reynolds number (Wadell, 1934; Rouse, 1950; Albertson, 

 1953; Schulz, et al. , 1954; Prandtl and Tietjens, 1957; Zeigler and Gill, 

 1959; Briggs et al., 1962). 



Wadell (1933) was the first to define shape rigidly and he did so in 

 terms of a sphere, since it has a higher settling velocity for a given 

 volume than any solid of any other shape. Wadell (1934) pointed out that 

 irregularly shaped solids do not have diameters in the geometric sense and 

 that any computations using diameters must deal with spheres or relate 

 some measurable property of the particle to a sphere. One such basic 

 relationship is the nominal diameter, which is the diameter of a sphere 

 having the same volume as the particle. 



Several geometric shape expressions have been proposed involving a 

 ratio of the triaxial dimensions of a particle: a = long axis; b = inter- 

 mediate axis; and c = short axis (Briggs, et al., 1962). Krumbein (1942) 

 suggested the following expression, which his investigations showed was 

 related to sphericity as defined by Wadell: 



n = 3 v(b/a) (c/b) (5) 



Corey (1949) suggested a simplified shape parameter which he called the 

 shape factor (S.F.): 



S.F. = £ 



Uh)h (6) 



where all axes were mutually perpendicular. Corey selected the expression 

 c/ab^ for his shape factor because he and others found that the particles 

 usually oriented themselves in the fluid so that they presented the 

 greatest resistance to the passing fluid, thus having the maximum projected 

 area, as discussed by Wadell (1934) and Krumbein (1942), oriented normal 

 to the path of motion. For this reason, Schulz, et al. (1954) considered 

 Corey's shape factor a logical dimensionless shape parameter expressing 

 the relative flatness of the particle. Corey found difficulty drawing 

 lines of constant shape factor in a C D - R e diagram using the triaxial 

 measurements in the equations for Cp and R e and concluded that the nominal 

 diameter should be used for the characteristic length and a.rea in the C D 

 and R e parameters. 



