116 



The elevation of the water surface at the initial end of the section at 

 the time t will be designated y^, at the other end at the same instant, 

 2/1; the velocity at the initial end, Vq, and the velocity at the other end, 



229. In the first term of equation (126) the slope, by/dx, may be 

 <jonsidered the average slope through the section. This term is then 

 the difference, yi—yo, between the elevations of the water surface at 

 the ends of the section: it will be called the surface head and desig- 

 nated hs- Then 



h,^lby/bjr.=y,-yo (127) 



It may be noted that the surface head is positive when the water is 

 sloping upward in the positive direction along the channel, and nega- 

 tive when sloping downward. 



230. The second term of equation (126), (v/g)bv/dx is the change in 

 v^/2g between the ends of the section, and is therefore the velocity 

 head, h^, giving: 



h,=l{vlg)bvlbx=vlJ2g-vlJ2g (128) 



It may be noted that the velocity head is positive when the velocity 

 is increasing numerically in the positive direction, and negative when 

 the velocity is numerically decreasing in that direction. 



231. The third term of the equation may be called the acceleration 

 head, and designated ha, giving 



ha={l/g)c>v/dt (129) 



In which dv/bt is the acceleration of the average velocity through the 

 section. 



The acceleration head is positive when the average velocity through 

 the section is increasing algebraically with respect to time. 



232. The fourth term is the friction head, hf, giving: 



h^=±lvyC'r (130) 



in which v may be taken as the average velocity through the section 

 at the given instant, C is the Chezy coefficient applicable to the sec- 

 tion, and r the hydraulic radius. The friction head has the same 

 sign as the velocity. 



233. Substituting the symbols for the various heads in equation 

 (126): 



hs+K+ha+hf=0 (131) 



In this equation, hs, K, and hf have the same significance as in 

 steady flow, except that hs and hf, as well as h„ may be negative. 

 The acceleration head is the additional term which must be included 



