According to Reynolds' Similarity Law, the flow pattern around the drag 

 coefficients on two similar bodies (identical in shape but dissimilar in size) moving 

 through a body of water are similar if their Reynolds numbers, Rg, are identical: 



R = y^ = ^ (D-3) 



e H V 



where V is the velocity of the body relative to the water, p is the density of the 

 water, ^i is Its absolute viscosity, U Is its kinematic viscosity {\i/p), and d is a 

 characterizing dimension of the body. 



Hence it is possible to determine the appropriate Cp for a body moving through 

 water from the results of experiments performed on an identically shaped body of a 

 different scale and possibly in a different fluid, provided the Reynolds numbers are 

 equal. 



The kinematic viscosity of sea water at normal temperatures and pressures is 

 on the order of 1.5 x 10"^ square feet per second. If a load to be lowered to the 

 deep ocean has a typical dimension of 15 feet, and moves at a velocity on the order 

 of 1 foot per second, the Reynolds number, R , equals 10°. It appears that relatively 

 little information is available from the literature on the variation of coefficients of 

 drag at Reynolds numbers greater than 10^ to 10'. Figure D-1 with inserts show the 

 variation of Cq with R for spheres and cylinders respectively, and summarizes some, 

 though by no means all, existing data on the coefficients of drag applicable to bodies 

 of different shapes. 



Although objects to be dropped or lowered to the deep ocean floor may not be 

 spherical or cylindrical, a brief Investigation of the dynamics of a sphere Is illu- 

 minating. Consider a body held stationary In water and which is then allowed to 

 fall freely. During the initial motions, the velocity is small and the body will 

 accelerate under its own weight minus a buoyancy force due to the weight of water 

 displaced, the drag force being negligible at this stage. This net vertical force acts 

 on the mass of the body plus a certain fraction of its mass which is included to 

 account for the water contained in the body, if any, and an effective mass of water 

 to which accelerations are imparted due to the motion of the body. The latter terms 

 are usually called the "apparent added mass"; the total mass (body mass and apparent 

 added mass) being termed the "virtual mass." Values of the apparent added mass vary 

 from 40% to 150% of the mass of the body. 



As the velocity Increases from zero, the drag force opposing the motion becomes 

 significant, and at a particular time t = t] this force is given by 



Fd = s(i''Vi')5 (°-^> 



70 



