> velocities cannot be justified with 
peed suitable equipment development. 
pO 7he necessary cost-effectiveness 
‘ analysis for pneumatic systems has 
v not yet been completed, but prelim- 
inary estimates indicate that the 
elimination of high cost labor and 
loading equipment by use of such a 
system probably can always be 
justified. 
SS Sea-bottom excavation presents 
<— a uniquely simple case for the use of 
Figure 53. Forces acting on a dense, water for spoil removal. The dense 
falling particle in a vertically | Water is a part of the environmental 
moving stream of fluid. system and it is therefore available in 
the amounts needed. A brief research 
of the engineering literature uncovered no theoretical treatment of particle 
transport by water—and probably for an excellent reason. Referring to 
Figure 53, an irregular particle of undisclosed dimensions is falling in the 
conveying medium of density p and viscosity wu. If allowed to fall for a 
considerable distance, the particle will achieve a steady state velocity V, 
after which it no longer will accelerate. The equations describing the 
terminal velocity are simple and well known: 
Ww 
Wii aC ArO V2 (17) 
and VV ON, (18) 
where W = weight of the falling particle 
Pm = density of the falling particle 
Vv = volume of the falling particle 
A = projected frontal area of the falling particle 
Cy = an experimental drag coefficient, a function of shape and 
Reynolds number 
While it would be fairly easy to classify common soils, rocks, etc., 
according to their probable drag coefficient, etc., the excercise would be of 
questionable value for two reasons. First, equipment would be typically 
designed to handle the worst case, and this can easily be determined by 
66 
