TIDAL CURRENTS 



Chapter V 

 RELATION OF CURRENT TO SURFACE SLOPE 



Paragraphs 



General equation of tidal motion 216-223 



Friction term for harmonically varying current 224-226 



Surface, velocity, acceleration and friction heads 227-233 



Entrance and recovery heads 234-235 



Contraction heads 236 



Currents due to harmonically varying head 237-253 



Lag of tidal currents 254-255 



"Hydraulic" or f rictional flow 256 



Frictionless flow 257-258 



Distortions of primary current 260-277 



Actual velocity curves 278-282 



Limitations on computation of current from surface heads 284r-286 



Relation of current to surface head and slope when flow is frictionless __ 287-290 

 Component currents 29 1-294 



216. General equation j or varying flow in a channel. — The velocity 

 of the current in a tidal channel is continuously increasing or decreas- 

 ing, and the direction of the flow is periodically reversed. To become 

 applicable to tidal flow, the famihar equations for steady flow must 

 therefore be elaborated to account for the work done in the accelera- 

 tion and deceleration of the current. The most casual consideration 

 of tidal flow shows, however, that in a channel whose width and 

 depth are small in comparison with the length, the lateral and vertical 

 movements of the water may be neglected, as they are in the equations 

 for steady flow. Similarly, in the derivation of the equations for tidal 

 flow, the velocity at a given instant may be taken as of the same 

 value throughout a cross section of the channel perpendicular to the 

 channel axis. 



217. Units. — In the ensuing development and application of the 

 equations for tidal flow, the time, t, will be expressed in seconds, unless 

 otherwise stated; lengths, heads, and other dimensions in feet; veloci- 

 ties in feet per second and acceleration in feet per second per second. 

 Conforming to these units, the speeds of the harmonic components 

 (par. 49) are derived in radians (or degrees) per second; but in the 

 application of the formulas, it ordinarily will be more convenient to 

 convert these speeds into degrees per hour. 



(109) 



