187 



identically repeated every twelve lunar (or other component) hours, 

 the values of C2 and S2 may be derived from the equations 



Qc2={ho-h6) cos 0+{hi-h^) cos 30° + . . .+ {h-hn) cos 150° (56^) 



Qs2=(ho-h) sin 0+(/ii-A7) sin 30°+. . .+ (h-hn) sin 150° (57^) 



The mean tide elevation of the primary entrance tides should be the 

 mean of the elevations computed from the representative tides at the 

 two entrances. 



COMPUTATION OF PRIMARY TIDES AND CURRENTS IN 

 A CONNECTING CANAL 



361. A general mathematical analysis of the tides and currents in 

 a long canal appears impossible if the friction term in the general 

 equation of motion is taken as a reversing function which varies with 

 the square of the current velocity. A general solution when the 

 frictional resistance is assumed to vary with the first power of the 

 velocity is given by Maurice Levy in "Legons sur la Theorie des 

 Marees" (Gauthier-Villars, 1898); and its application to the Cape 

 Cod Canal is presented in a paper by William Barclay Parsons con- 

 tained in the Transactions of the American Society of Civil Engineers, 

 volume LXXXII (1918), pages 1-157. The equations developed by 

 this analysis are lengthy and unwieldy, and the established coefficients 

 of frictional flow are not applicable thereto. Another method for 

 determining the tides and currents is presented by Col. Earl I. Brown, 

 Corps of Engineers, United States Army, in a paper on the Trans- 

 actions of the American Society of Civil Engineers, volume 96 (1932), 

 pages 753 et seq. The solution therein presented proposes that the 

 currents at high water be determined from the mean depth of the 

 canal at high water, and the currents at low water from the mean 

 depth at low water. 



362. A better method is to compute the primary currents and 

 tides from established frictional coefficients, by a process of successive 

 approximations, on a line of procedure somewhat similar to that 

 applied in computations of steady flow. The canal is divided into 

 subsections so short that the variation in the velocity of the current 

 because of channel storage is not material in any subsection. The 

 primary currents in the subsections, and the primary tides at the 

 ends of the subsections, must satisfy the two conditions: 



(a) The fluctuations of the current in each subsection must 

 conform to the fluctuations of the surface head set up by the 

 tides at the ends of the subsection. 



(b) The currents in the subsections must also conform to the 

 storage and release of water from subsection to subsection 

 because of the rise and fall of the tides. 



192750 — 40 13 



