133 



The values of Av are computed from the successive vahies of v. 

 As the best approximation, A5 will be taken as the increase, 8—80, in 

 the preceding interval. Equation (165) then becomes: 



ha=bAv-^b{8-8o) (168) 



269. The friction head, hf, is, from equation (130): 



hf=±l{v+8y/C'r 



in which C and r vary with the stage of the tide. A diagra.m may ber 

 prepared showing the values of: 



F=llC'r (169) 



corresponding to the stages of the tide. 



The expression for the friction head may be written: 



h^=±F(v+8y 

 = ±Fv'±2Fv8±F8' (170> 



Since 5 is a comparatively small correction, at least a first approxi- 

 mation may be derived by dropping its square and neglecting any 

 effect that it may have upon the algebraic sign of the corrected veloc- 

 ity, i;+ 5; giving: 



hf=±Fv'+28{±v)F (171) 



in wliich the positive sign is to be applied when v is positive, and the 

 negative sign when negative. Obviously, therefore, the factor (±y) 

 is always positive. Representing the numerical value of v, on the 

 given half hour, asz;, equation (171) becomes: 



hj=±Fv-+28Fv (172) 



270. The velocity head, hv, remains to be considered. The deriva- 

 tion of the tidal currents in a short section of channel was predicated 

 on the assumption that the section is so short that at any instant the 

 variation of the velocity between the ends of section is immaterial. 

 Under this assumption the velocity head would disappear. "While the 

 derivation remains valid even though there be a sufficient difference 

 between the velocities at the ends of the section to produce some veloc- 

 ity head, yet in the ordinary case it is too small to be worth computing. 

 It may be included in the computations by determining the velocities 

 at the ends of the section at the successive intervals of time. For tliis 

 purpose the change in the discharge between the ends of the section 

 because of the storage and release of water with the rise and fall of the 

 tide, as developed in subsequent chapters, must be taken into consider- 



