117 



in tidal flow. It is readily evaluated when the rate of change in the 

 velocity is known. Thus if the velocity is algebraically decreasing 

 at a given time at the rate of 0.003 feet per second per second in a 

 section of channel 10,000 feet in length, the acceleration head is 

 -10,000X0.003/32. 16=-0.93 feet. 



"234. Entrance and recovery heads. — In steady flow, the head due to 

 the increase in velocity at the entrance to a contracted section of a 

 channel is termed the entrance head. Its commonly accepted 

 value is: 



h=^mW-v,')l2g (132) 



In this equation Vq is the velocity in the approach to the contrac- 

 tion, ^1 the velocity in the contracted section, and w a coefficient to 

 account for the increased turbulence at the contraction. The entrance 

 head is then the change in v^!2g at the entrance, times a suitable 

 coefficient. If the velocity in the contracted section is not large, m is 

 often taken as unity. 



At the outlet of the contracted section, the decrease in the kinetic 

 energy of the flowing water gives rise to a recovery of head whose 

 value is given by the same formula by taking z'o as the velocity in 

 the contracted section, and i\ the velocity in the expanded channel. 

 The recovery head is then also the change, in the positive direction, 

 of v^l2g^ times a suitable coefficient. Since, however, the recovery of 

 energy is never complete, the value of m for the recovery head is 

 always less than unity, and frequently is taken as 0.5. 



235. In reversing tidal flow each end of a contracted section of 

 channel is alternately the entrance and the outlet. At the initial end 

 the flow is into the contracted section when the velocity is positive, 

 and out when the velocity is negative; but since the numerical value 

 of the velocity remains the greater in the contracted section, the 

 change in v^l^g at the entrance is positive, whichever the direction of 

 the flow. At the other end the flow is out of the contracted section 

 when the velocity is positive, and into the section when negative; 

 but the change (in the positive direction) of v^l2g is always negative. 

 At both ends, therefore, the change (in the positive direction) of 

 v^l2g represents an entrance head when it has the same sign as the 

 velocity, and a recovery head, to which a reducing factor should be 

 applied, when it is of opposite sign to the velocity. On an expanded 

 section of the channel, the contrary condition obviously exists. 



236. Contraction heads. — At a sudden local contraction in a section 

 of channel that otherwise may be taken as uniform, such as at a bridge, 

 the increased turbulence resulting from the increase and decrease of 

 the current produces a net head, of the same nature as an increase in 

 the friction head. Such a contraction head may be introduced in 

 •computations of tidal flow by determining, from the applicable for- 



