1178 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



Vcos a xCopd ' 



where H is the hydrodynamic constant. Also, we define the Reynolds 

 number for flow normal to the cable in the usual way ; 



,j dV sin a /,->. 



V being the kinematic viscosity of water. For smooth cable we now as- 

 sume that the drag coefficient Cd depends on Nr in the same way as for 

 flow around a smooth cylinder of infinite length. Experimental data for 

 this relationship, namely, 



Co = Cn{Nu) (58) 



are available in the hterature and have been collated by Eisner. 



For a given velocity T^, (56) through (58) represent three equations 

 for the unkno\\Tis a, Co , and Nr . In general, the solution of these equa- 

 tions depends on V, thus contradicting the assumption made in Section 

 3.2 that Cd , and therefore H, are constants independent of T'. However, 

 for sufficiently large T'^ we can expect the resulting a to be small so that 

 \/cos a ;^ 1 . In this case (56) and (57) combine to give 



Cn = ?^^., (59) 



■■' Nr'' 



which together with (58) yields two equations for Cd and Nr that are 

 indeed independent of V. In laying, V will normally be large enough for 

 this approxhnation to hold. 



Equations (58) and (59) are in turn easily solved graphically by find- 

 ing the intersection on log-log paper of the curves, Cd versus Nr , 

 that these equations represent. Since p and p are properties only of the 

 water, we see that Cd is a function only of the product wd of the unit 

 weight of the cable times its diameter. In Fig. 31 we have plotted the 

 resulting values of Cd for wd ranghig from 10"^ to 10 pounds. For this 

 computation we have assumed sea water at 32°F with an assumed density 

 of 1.994 slugs per cubic foot and a kinematic viscosity of 2.006 X 10 

 ft^/sec. 



For other than large values of V, (56) through (58) can be readily 

 solved if one interchanges the roles of a and V, that is, if one considers a 

 as given and V as unknown. Equations (56) and (57) can again be com- 

 bined in this case to give 



