120 



Taking station 180+30 as the initial station: 



A, cos «i = 3.18 cos 61°10' = 1.534 A^ sin a,^d.l8 sin 61°10' = 2.786 

 Ao cos ao=3.74 cos 58°34' = 1.950 A sin o;o=3.74 sin 58°34' = 3.191 



HcosH^=-Al6 HsmH'=--A05 



tan iJ«=0.405/0.416 = 0.9736 



The corresponding angle, from a table of natural tangents, is 

 44°14'. Since the sine and cosine are both negative, FP hes in the 

 third quadrant, and is: 



and 



H''=180°-i-4:4:°U'=224:°14:' 



H=OAlQlcos 44°i4' = 0.58 



The equation of the surface head in the section between the two 

 stations is therefore: 



hs=0.58 cos (m2f+224°140 



24 1 . Generating radi us of head. — The rela- 

 tion between the generating radii of the 

 curves representing the tidal heights at 

 the two ends of the channel and that of the 

 head in the channel is shown m figure 37, 

 in which CPo=x4o is the generating radius 

 of the tide at the initial end, CPi=Ai that 

 at the other end of the channel, CP2=PoPi 

 is the generating radius of the curve showing 

 the surface head. 

 242. Equation of primary current. — As will later be made apparent, 

 the currents produced by a simple harmonic fluctuation of the surface 

 head in a short section of the channel depart somewhat from a simple 

 harmonic fluctuation. These distortions of the current are due to 

 the form of the velocity head term, {vjg)'dvj(ix, in the general equation 

 of motion, to the minor components of the friction term produced by a 

 harmonically varying current (par. 226) and to the variation in the 

 hydraulic radius and Chezy coefficient with the rise and fall of the 

 tide. Under usual conditions of tidal flow the velocity head in a 

 short section of a channel is relatively so small that the velocity head 

 term may be omitted. The other disturbing elements may be treated 



Figure 37. ^Relation ot head to tides. 



