Chapter VII 



FRICTIONLESS FLOW IN A LONG CANAL OF 

 UNIFORM DIMENSIONS 



Paragraphs 

 Equations of a component of the tide and current in a canal if fiow were 



frictionless 316-324 



Application to connecting canal 325-329 



Instantaneous profiles and wave lengths 326-327 



Tides and currents at middle of a connecting canaL^ 330-331 



Special cases , 332-333 



Meeting of tides 334 



Closed canals 335-337 



Progressive, retrogressive, and stationary waves 338-345 



Critical lengths . 346-347 



Nodes in a closed canal 348 



Shallow water components 349 



Seiches 350 



316. Frictional resistance to flow must, in fact, be considerable in 

 the deepest artificial channel that can be conceived of, if the currents 

 are sufficient to be of any consequence; but the inclusion of frictional 

 resistance imposes insuperable limitations on a general analysis of 

 the flow in a long tidal canal. An analysis of the tides and currents 

 that would be created by frictionless flow in a long canal of uniform 

 cross section, while not affording a quantitive determination of the 

 tides and currents in an actual canal, develops certain general char- 

 acteristics of the flow in such canals, and affords a background for the 

 procedure, explained in the next chapter, for computing the actual 

 tides and currents. In this analysis of frictionless flow, the currents 

 are considered to be so moderate that the velocity head term of the 

 general equation of motion also may be dropped ; and the channel so 

 deep with respect to the tidal range that the variations in the mean 

 depth of the channel, as the tide rises and falls, may be disregarded. 



317. The tide at any station in long tidal canal, whether connecting 

 or closed, may be presumed to be the resultant of semidiurnal and 

 diurnal harmonic components of the speeds established in chapter II. 

 The height of the tide above mean sea level at the time /, at a station 

 distant x from the origin of distances, is then: 



y=M2 cos (m2«!-hQ:i) + §2 cos (82^+0:2) + • • • (190) 



(157) 



