128 



256. "Hydraulic" or "frictional" flow. — The first of the preceding 

 examples (fig. 38) shows that if the head in a tidal channel is sufficient 

 to produce strong currents, and the channel is not of great depth, the 

 lag of the current with respect to the head is small, and the current at 

 any instant is substantially the same as that which would be produced 

 by the instantaneous head were the flow steady. The flow under 

 these conditions is often termed "hydraulic." A better name is 

 "frictional tidal flow." Currents of this character are found in the 

 East River, N. Y., and in other tidal straits of moderate depths which 

 .are subject to a considerable tidal head. 



If the lag is small, the value of -ycos<^ in equation (155) is close to 

 unity, and the amplitude, B, of the velocity varies from day to day 

 as the square root of the amplitude, S, of the slope, and hence as the 

 square root of the amplitude of the head, H, during the tidal cycle. 

 : Since the tides at the ends of a tidal strait keep in general step as their 

 amplitudes change from day to day with the changing declinations 

 and distances of the moon, the daily variation in H is nearly propor- 

 tional to the daily variation in the tidal range. Wlien therefore the 

 flow in a strait is largely frictional, or "hydraulic," the "strength 

 of the current" in each section of the channel varies from day to day 

 approximately as the square root of the tidal range. 



257. Fridionless tidal flow. — The lag of the current increases as the 

 slopes in the channel and the current velocities decrease. It increases 

 also as the depth of the channel and the coefficient C increase. As 

 shown in the last example (fig. 40), the lag becomes very large in deep 

 channels with small slopes. Most of the potential energy due to the 

 head in the channel is then taken up in the acceleration and decelera- 

 tion of the current and little in overcoming frictional resistance. The 

 flow under these conditions is sometimes termed "tidal," as distin- 

 guished from the "hydraulic" flow determined principally by fric- 

 tional resistance. A better name is "frictionless flow." 



258. In a section of channel which is so deep, or in which the cur- 

 rents are so weak, that the flow is nearly frictionless, is nearly 90°. 

 A small error in taking off its value from table IX would then produce 

 a large error in the computation of the amplitude, B, from equation 

 (160). When is large, the value of B is better derived from equa- 

 tion (156): 



B={g/a)S sin 



For tidal fluctuations having the speed of the M2 component, and 

 for ^=32.16, the value of g/a is 228,900; and its logarithm is 5.35958. 



