THE FLOW OF WATER IN IRRIGATION CHANNELS. 5 
d N , then the area at that particular cross section is ex- 
pressed as follows : 
. 2d„- 1+ d 1 A (5) 
AT /dO + 2d, + 2d, 
a = Nx( x 
Note that the end soundings are given but one-half the weight 
assigned to the interior soundings, for the reason that their influence, 
in considering the average, extends over but half the distance covered 
by the interior soundings. A similar reasoning applies to the two fol- 
io whig formulas. 
Assuming the reach of canal tested to be divided into M equal 
sections and the areas a , a x , a 2 , a M found as by formula 5, 
then the mean area of the water cross section throughout the reach 
is as follows : 
. _ a0 + 2a 1 + 2a 2 + 2a M _ t + a M , 
A- 2M ~ ~~ {b) 
The lengths of the wetted perimeters at a , a l7 a 2 , etc., are found 
either by computation or by plotting each cross section on a large 
scale and measuring the length by scale of the line of contact between 
the water and the containing channel. Letting p , p 1; p 2 , p M 
be the lengths of the various wetted perimeters for the corresponding 
, a M , then 
_pO + 2 P l + 2p 2 + . . . . . . 2p M _ 1 + p 
and, by definition 
r ~~ 2M u; 
R=p (8) 
Thus the field data for the determination of the term R in formula 
8 consist of soundings or their equivalent with attendant horizontal 
measurements to determine the mean values of A and P throughout 
the reach tested. 
The hydraulic grade is taken as the slope of the water surface in 
the reach of canal tested, corrected for any appreciable change in the 
mean velocity of the water at the . two ends of the reach. If the 
cross sections develop the fact that the mean velocity at the upper 
end of the reach is less than that at the lower end, then the difference 
between the velocity heads necessary to create the velocities at the 
two ends of the reach must be deducted from the actual fall of the 
water surface in the reach tested. If the velocity at the lower end is 
less than that at the upper end, then the lost velocity head, in addi- 
tion to the surface fall, has been used to overcome the retarding 
influences. 
