194 



stantially straight lines. The corresponding heads are then recom- 

 puted and the process repeated until a satisfactory concordance of the 

 currents and heads is attained. 



375. First example. — The computations of the primary tides and 

 currents in a canal of uniform dimensions will be illustrated by apply- 

 ing the procedure outlined in the preceding paragraphs to a canal 

 200,000 feet (37.8 miles) in length, and of uniform cross section, with 

 a bottom depth of 40 feet at mean tide, a bottom width of 250 feet, and 

 side slopes of 1 on 3)^ (fig. 60). 



^> < soo' 



Figure 60. — Cross section of assumed canal. 



The representative tide at the initial end of the canal has an ampli- 

 tude of 4 feet and the speed of the M2 component (28°. 98 per mean 

 solar hour, or 30° per mean lunar hour). The representative tide at 

 the other entrance has an amplitude of 2 feet, and the same speed. 

 Its high water occurs 2 lunar hours, or 60°, before that at the 

 initial entrance. Taking the origin of time at high water at the 

 initial entrance, the equation of the tide at this entrance is then 

 2/=4 cos m2^ and at the other entrance, y = 2 cos (m2^ + 60°). 



The area of the cross section of the water prism at mean tide is 

 15,000 square feet and the surface width is 500 feet, giving a mean 

 depth of 30 feet at mean tide. The hydraulic radius at mean tide is 

 also taken as 30 feet, as the refinement of computing the wetted 

 perimeter is superfluous in view of the uncertainty in the Chezy 

 coefficient. The Chezy coefficient at mean tide is taken as 120. 



376. Division into subsections. — The canal will be divided into a 

 middle subsection and two subsections on either side, total of 5 sub- 

 sections, each 40,000 feet in length, as shown in figure 61. 



I , 1 , I 



111' 

 , 1 I \ I 1 1 1 1 1 , 



O 20 40 60 80 100 \eO \40 \eO 180 500 



FiGUBE 61. — Division of canal irto subsections. 



A canal of uniform, dimensions should always be divided into an 

 odd number of sections each of the same length; but shorter sub- 

 sections are required in a shallower canal. The ends and midpoints 

 of the subsections are conveniently indicated by station numbering, 

 as shown in the figure, the stations being taken as 1,000 feet in length. 

 In the present exam.ple the velocity station at the middle of the 

 canal is at station 100, and the velocity stations of the other sub- 

 sections at stations 20, 60, 140, and 180. The storage stations 



