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328. Example oj jridionless tides and currents in a long connecting 

 canal. — The characteristics of frictionless flow in a connecting- canal 

 whose length is less than one-half of the wave length of the tidal 

 components, may be exemplified by the tides and currents that would 

 be produced in a canal 200,000 feet (37.8 miles) in length, of uniform 

 width, and with a mean depth of 30 feet, by the M2 component of the 

 tide, if its range at the initial entrance is 8 feet, and at the other en- 

 trance 4 feet, high water at the latter being 2 lunar hours, or 60°, 

 earlier than at the former. Taking the origin of time at an instant 

 of high water at the initial entrance, the given data are: 



A=4 feet; 0:0= 0; ^i = 2 feet; ai = 60°; 

 Z=200,000 feet; Z>=30 feet; c=-^gD=3im; 

 a=m2=0°.00805 per second; 7=m2i:/c=51°.83 = 51°50'. 



The computation of the amplitudes and phases of the tide and cur- 

 rent at the entrances to the canal {x=0 and x—L) and at its quarter 

 and mid points («=}^X, )^Z, and %L) is summarized in the following 

 tabulation: 



The equations of the tides and currents then are: 

 At the initial end: 



2/ =4 cos vci2t 



?;=2.99 sin (m2^-49°39') 



At the first quarter point: 



2/ = 3.51 cos (m2^+8°5') 

 ?;=3.59 sin (m2<-38°15') 



At the middle: 



2/=2.94 cos (m2i+19°6') 

 ?;=4.10 sin (m2/-30°) 



At the third quarter point: 



2/=2.38 cos (m2i+35°300 

 ?;=4.48 sin (m2i-23°22') 



