308 Bulletin, Scripps Institution of Oceanography 
is adopted in the presentation here. Thus, with W in pounds per cubic feet, g in 
feet per second squared (32.2), A in square feet, and U in feet per second, the 
value of F from equation (19) will be in pounds. For sea water, W is about 64 
pounds per cubie foot, so that W/2g is just about unity, thus simplifying the 
expression for the drag force as follows: 
F = CpAU? 
The drag coefficient Cp depends upon the shape and the roughness of the object 
and on the Reynolds number Re, associated with the flow. The Reynolds number 
is defined by 
Re=UD/v 
where D is the effective diameter of the object and v is the kinematic viscosity of 
the fluid. For water at 70°F, v is about 10° square feet per second. Consequently, 
the following expression for Re is valid for problems dealing with flow of water 
around obstacles: 
Re=10°UD 
If the submerged object is a circular cylinder or a sphere, then the effective 
diameter is the actual diameter. The values of drag coefficients for smooth circular 
cylinders of large length-to-diameter ratio, with the axis perpendicular to the 
flow, are presented in table 5, prepared from data in Rouse (1946). The ranges 
of Reynolds numbers represented are those encountered in most engineering 
TABLE 5 
Drac ConFFIcIENTSs 
Reynolds number (Re) Drag coefficient (Cp) 
nH OVI Holy! AU) ord eey cnctenmie ba ceeieta Bisceds etiun e/eicee emer OLR CIO 1.0 
LOMO; 2 PG ILO ARC ee paar eran eaten Reis Ming eae 1.2 
arrerithanton LO nmr marr rere renner eer laces 0.33 
problems. The values have been obtained from laboratory studies under condi- 
tions of steady (unaccelerated) flow. 
The results of these laboratory experiments indicate that there exists a critical 
value of Reynolds number above which the regime of disturbed flow around the 
object is changed abruptly, leading to a decrease of Cp. Not much information is 
available for roughened cylinders; however, the indications are that (a) for lower- 
than-critical Re the value of Cp is essentially unchanged; (6b) for higher-than- 
critical Re the value of Cp is larger than that for a smooth surface; and (c) the 
value of the critical Re is somewhat reduced. A brief series of tests which we con- 
ducted indicate that the drag of twisted wires is somewhat less at higher Reynolds 
numbers, possibly because of spoiling. 
The value of Cp for a long flat plate of width D is about 2.0 (or about 6 times 
the value of Cp for a cylinder at high Reynolds numbers), and apparently has no 
critical value of Re in the range 3 x 10° to 10°. 
STEPS IN THE GRAPHIC SOLUTION OF A DEEP-MoorING CONFIGURATION 
Step 1. Measure or assume velocity distribution 
Step 2. Caleulate V? 
