* W = fall velocity
" D = diameter of sediment particle
" g = gravitational acceleration
* P = kinematic viscosity of fluid
% specific weight of sediment
% y = specific weight of fluid
The following assumptions were made in the derivation of Stokes' Law: 1) Inertia forces are neglected (highly viscous flow) 2) Spherical grains were assumed
3) No slip between the fluid and the surface of the particle 4) The particle falls in an infinite and calm fluid These assumptions limit the usefulness of the fall velocity equation. Since inertia forces are omitted, the equation will only predict the fall velocity correctly if the Reynold's Number, P,< < 1. Furthermore, most sand grains are not completely spherical. In addition, the last assumption is seldom found in real situations. Although Stokes' fall velocity equation does have limitations, for our purposes it gives a reasonable prediction of the fall velocity.
In order to solve the fall velocity equation, the sediment sizes for the prototype and model are required. The sand obtained for the model consisted of a mean diameter of 0.18 mm. A grain size distribution graph showing the median grain size for the model is seen in Figure 3.4. The prototype sediment size was 0.4 mm. This size was chosen because it is a typical size found in the field. In Leatherman (1979), the median grain size for Assateague Island, Maryland was approximately 0.3 mmn and the median grain size for Nauset Spit, Massachusetts was approximately 0.4 mm. Applying these values to the fall velocity equation, the values for WP and W. are 0.51 ft/sec (0. 16 mlsec) and 0. 13 ft/sec (0.04 m/sec), respectively. For similitude