188 



The computations are started by determining the tides which 

 would be produced if the instantaneous profiles were straight Imes. 

 The primary current in the subsection at the middle of the canal is 

 then computed from the surface head established by these tides, and 

 the currents in the other subsections determined therefrom by com- 

 puting the increments in the velocity due to tidal storage between the 

 successive subsections. The surface heads corresponding to these 

 currents are next computed and adjusted to the total head through 

 the canal. These subsection heads establish corrected primary tides, 

 and corrected instantaneous profiles, more nearly conforming to the 

 true profiles than the straight lines initially assumed. The primary 

 current in the middle subsection is then recomputed from the adjusted 

 surface head in this subsection, and corresponding currents in the 

 other sections from the storage and release of water with the corrected 

 tidal fluctuations. The process is repeated until the further corrections 

 become negligible. 



363. It may be noted that the computations are started by taking 

 the instantaneous profiles as straight lines, and the current at the 

 middle of the canal as unaffected by channel storage. As shown in 

 paragraph 331 both of these conditions would be approximately 

 realized in as long a canal as is likely to be undertaken, if frictional 

 resistance were neglected. An examination of the recorded instan- 

 taneous profiles in actual canals shows that they do not, in fact, 

 depart widely from straight lines. The procedure will be found 

 applicable to any case likely to be encountered. 



364. Coordinate components of the primary tides and currents. — 

 The equation of the primary tide at any station on the canal is in 

 the form : 



y=A cos {at-\-a) 



The speed, a, at all stations is that selected for 

 the primary entrance tides, but the initial phase, 

 a, dift'ers from station to station. To carry out 

 the computations outluied in the preceding 

 paragraphs, these tides are resolved into com- 

 ponents with common initial phases. As is 

 apparent from figure 59, the primary tide at a 

 given point may be resolved into two com- 

 ponents; the Y component with an amplitude 

 of A cos a and an initial phase of 0°, and the 

 X component with an amplitude of A sin a, 



and an initial phase of 90°. 



The equation of the primary surface head in a subsection of the 



canal is similarly 



hs=H cos {at-\-H°) 



FiGUKE 59. — Coordinate com- 

 ponents ol the tide. 



