The coefficient of resistance as a function of Reynolds number for solids of various shapes

Abstract The purpose of the present article is twofold. First it is an attempt to show the usefulness of the degree of true sphericity as an expression for shape of rock particles. Second it is intended as a background for a new, analytical, sedimentographic method to be given in a forthcoming paper. Any radical variation in shape influences the numerical value of the degree of true sphericity and affects the size of the surface area, the size of the largest cross-sectional area and the degree of circularity of a great number of cross-sections of a solid. These factors determine to a large extent the settling velocity of that solid. The resistance of wholly submerged bodies, as a theoretical foundation for determining the coefficient of resistance as a function of Reynolds number for solids of different degree of sphericity, is discussed. The influence of the degree of circularity on the resistance is then shown by graphs constructed on the basis of available data. Formulae for calculating the coefficient of resistance and Reynolds number are introduced and their practical value demonstrated by graphic illustrations. The sedimentological significance and usefulness of the results are discussed.

[1]  G. Kirchhoff,et al.  Zur Theorie freier Flüssigkeitsstrahlen. , 1869 .

[2]  T. Kármán,et al.  Ueber den Mechanismus des Widerstandes, den ein bewegter Körper in einer Flüssigkeit erfährt , 1911 .

[3]  T. Bromwich,et al.  Motion of a Sphere in a Viscous Fluid , 1929, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  H. Green.  The effect of non-uniformity and particle shape on “average particle size” , 1927 .

[5]  Mechanik der Flüssigen und Gasförmigen Körper , 1927 .

[6]  H. Wadell,et al.  Sphericity and Roundness of Rock Particles , 1933, The Journal of Geology.

[7]  J. Owens.  Experiments on the Settlement of Solids in Water , 1911 .

[8]  Osborne Reynolds,et al.  XXIX. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels , 1883, Philosophical Transactions of the Royal Society of London.

[9]  Geo.W. Keely,et al.  On the resistance of fluids , 1835 .

[10]  C. Wieselsberger,et al.  Ergebnisse der aerodynamischen Versuchsanstalt zu Göttingen , 1921 .

[11]  O. Miyagi.  X. The motion of an air bubble rising in water , 1925 .

[12]  H. Wadell.  Volume, Shape, and Roundness of Rock Particles , 1932, The Journal of Geology.

[13]  Lord Rayleigh F.R.S..  LIII. On the resistance of fluids , 1876 .

[14]  J. A. H. Murray.  New English dictionary. , 1887 .

[15]  F. C. Johansen,et al.  On the Flow of Air behind an Inclined Flat Plate of Infinite Span , 1927 .

[16]  J. Maxwell,et al.  Theory of Heat , 1892 .

[17]  H. D. Arnold.  LXXIV. Limitations imposed by slip and inertia terms upon Stoke's law for the motion of spheres through liquids , 1911 .

[18]  E. Cox.  A method of assigning numerical and percentage values to the degree of roundness of sand grains , 1927 .

[19]  F. Schulze.  Anleitung zur Untersuchung der Ackererden auf ihre wichtigsten physikalischen Eigenschaften und Bestandtheile , 1849 .

[20]  T. Hatch.  Determination of “average particle size” from the screen-analysis of non-uniform particulate substances , 1933 .

[21]  H. Green.  A photomicrographic method for the determination of particle size of paint and rubber pigments , 1921 .

[22]  C H Toy,et al.  A NEW ENGLISH DICTIONARY. , 1886, Science.