470 APPLIED MECHANICS 
H is a maximum when v “6 af ae = 14'8 feet per second. 
Maximum value of H=14:8(57:58 —0-0875 x 14°8?) = 568. 
H is zero when v=0, and when 
0 Sat 600 
= af Pee = 25:6 feet per second. S00 1A PK 
Efficiency per cent. 8 400 Dae: és 
flv? St tet & 
=100(1- )= 1000-1520, Es00Lp4 KH 
T2p,gd Ee rk : ; 
The horse-power and the effici: SAY am 
ency per cent. are shown plotted on _—'00 Nh) 20 
a velocity base in Fig. 765. In 9 
mH Pe x 
hydraulic mains the velocity of the 4 8 12 6 20 4 
water seldom exceeds 5 feet per Velocity Bie per Second.) 
second, and in the example just 1G. 765, 
considered the efficiency at this velocity is 96°2 per cent. 
410. Flow of Water in Channels.—When water flows in an open — 
channel, or when it flows in a pipe or closed channel without filling the 
pipe or channel, the water will have a free surface, and the hydraulic 
gradient will be the longitudinal slope of the free surface, and, since in 
most cases the depth of the water will be uniform in the direction of flow, 
the hydraulic gradient will be the same as the longitudinal slope of the 
channel. 
Reasoning as in Art. 404 on the loss of head due to friction in a pipe, — 
2 
it follows that for a channel (Fig. 766) the loss of head h’=f - é . me and 
v= 4 *4,/ ied =c ,/mi, whichis the Chézy formula. 
It must be kept in mind that the coefficient 
of friction f and the coefficient c, which is a 
function of jf, depends on the roughness of the 
surface of the channel, and also on the form and 
slope of the channel. 
411. Bazin’s Channel Formula.—The eminent French hydraulic 
engineer Bazin examined the results of a very large number of experiments 
on the flow of water in channels of varied forms and dimensions, and in ~ 
1897 he published a formula based on these results. 
TOR6. CR a 
The Bazin channel formula is » = y /miy 
Pit 
. Jm 
where y is a coefficient depending on the roughness of the channel. The — 
unit of length in the formula is the foot. 
The formula may be written v=c ,/mi, where ¢ is the quantity in the — 
large bracket above. 
