200 



387. Effect offridional resistance. — The effect of frictional resistance 

 upon the primary tides and currents in the canal selected for the first 

 example is shown by a comparison between the results of the preced- 

 ing computations and of those derived in Par. 328, Chapter VII, for 

 frictionless flow in the same canal with the same entrance tides. The 

 origins of time and distance are the same in the two cases. Angles are 

 written to the nearest 10 minutes of arc. 



As is to be expected, frictional resistance reduces considerably the 

 amplitude of the currents. Its effect upon the timing of the currents 

 is even more marked. When frictional resistance is neglected, the 

 strength of the positive current at the initial entrance was found to 

 be (90°+49°40')/28°.98 = 4.82 solar hours after high water, while 

 when frictional resistance is considered, the strength of the positive 

 current is (90°— 47°20')/28°.98 = 1.47 hours after high water. 

 Frictional resistance advances therefore the strength of the current 

 at the initial entrance by 3)f hours. At the other entrance, it ad- 

 vances the current by Iji hours. 



In the present example, the amplitude of the tide at the middle of 

 the channel is but little affected by frictional resistance, but the rela- 

 tive phases of the tide at this station show that the time of high water 

 is altered by nearly half an hour. 



388. Relation between channel storage and the lyrimary currents and 

 discharges at the entrances to a canaL — The primary discharge at an 

 entrance to the canal is derived immediately by multiplying the cur- 

 rent velocity by the area of the cross section at mean tide. Obviously, 

 the difference in the discharges at the two entrances at any moment 

 must be equal to the rate of storage or release of water in the tidal 

 prism of the canal at that moment. 



In the present example, the area of the cross section at both 

 entrances is 15,000 square feet. The entrance velocities and dis- 

 charges and the rates of filling and emptying of the canal during 

 successive tidal cycles are shown diagrammatically in figure 64. 



389. The discharge at the initial entrance, station 0, is an inflow 

 into the canal when positive, and an outflow when negative; wliile 

 at the further entrance, station 200, it is an outflow when positive 

 and an inflow when negative. During the time interval marked AB 



