220 



canal to the velocity station, of the products of the surface areas, 

 U, between the successive velocity stations, at mean tide, and 

 a A sin {at-\-a), the rate of increase of the tide at the storage stations 

 niidway between the velocity stations. 



Designating the area of any typical cross section of the canal as 

 Mo, and placing, as in equations (281) and (282): 



Mo/M=m 



aUIMo=I 



equation (293) may be written: 



B sin (at-\-^)=m'ZlA sin {at+a) 

 whence: 



(B/m) sin ^=^IA sin a (294) 



{B/m) cos ^=i:IA cos a. (295) 



If the canal is of uniform dimensions, and the subsections of equal 

 length, Mo=M, l/m=l, and I=aAx/D. 



The component currents in the subsections are computed from 

 equations (294) and (295), and the resulting surface heads from 

 equations (288), (289), and (290). 



423. Example. — The computations may be illustrated by applying 

 them to a closed canal of uniform cross section, 60,000 feet (11 miles) 

 in length, with a mean depth of 16 feet at midtide, when the tidal 



fluctuation in the entrance has a 



■60 50 40 30 20 10 5 O 



range of 6 feet, and the speed of 

 the M2 component, 0.0001405 

 radians per second. The origin 



FiGUEE 75.-Storage and velocity stations (stations ^^ distances is at the head of the 



of 1,000 feet). 



canal, and the origin of time at 

 a high water at the entrance. The canal will be divided into three 

 subsections, each 20,000 feet in length, as shown in figure 75. 



Station is at the head of the canal. The velocity stations, at the 

 middle of the subsections, are at stations 10, 30, and 50. The storage 

 stations are at stations 5, 20, and 40. As the currents near the head of 

 the canal are extremely smah, the surface head in the quarter section 

 between stations and 5 is always negligible, and the components of 

 the tide at station 5 may be taken as those at station 0. 



424. Coefficients. — An appropriate value of Chezy coefficient, C, is 

 100. The storage coefficient, /, at ah storage stations, except for the 

 half section at the head of the canal, is: 



7=aA.r/jO=0.0001405X20,000/16 = 0.176. 



For the half section at the head of the canal, 7=0.088. 



Since the canal is of uniform dimensions, to=1. The coefficients 

 for the determination of the subsection heads (par. 373) are: 



