THE FLOW OF WATER IN IRRIGATION CHANNELS. 5 



du, then the area at that particular cross section is ex- 

 pressed as follows : 



= ^j,,/ d0 + 2d, + 2d3 2d^_, + dA 



(5) 



Note that the end soundings are given but one-haK the weight 

 assigned to the ulterior soundmgs, 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- 

 lowing formulas. 



Assuming the reach of canal tested to be divided into M equal 



sections and the areas a^, a^, aj, a^ found as by formula 5, 



then the mean area of the water cross section throughout the reach 

 is as follows : 



^_ a0 + 2ai + 2a2+ 2s.^^^ + a^ 



A- ■ 2M ^^^ 



The lengths of the wetted perimeters at a^, a^, aj, 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 Po? Pi; P2; Pm 



be the lengths of the various wetted perimeters for the corresponduig 

 areas a^, a^, ay, then 



^ p0 + 2p, + 2p3+ 2py_, + p^ 



r- 2M ^'' 



and, by definition 



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 hydrauhc 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 hc!ads ruicessary to create the velocities at the 

 two ends of the reach must bo 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 th(5 surface fall, lias been used to ovcrcojne the retardhig 

 influences. 



