The document summarizes the design of an irrigation channel using Lacey's theory. It is given that the discharge is 50 cumecs and the silt factor is 1.0. The calculations determine that the velocity is 0.842 m/sec, the hydraulic radius is 1.774 m, and the perimeter is 33.59 m. Assuming a trapezoidal cross-section with 1/2 side slopes, the area is calculated to be 59.38 m^2. Solving the equations gives the depth as 1.968 m and the bottom width as 29.34 m. The calculated slope is 1/6409.

1. Q.2) Design an irrigation channel using Lacey’s theory for the
discharge of 50 cumecs and silt factor 1.0, assuming suitable data.
Sol. Given Q=50 cumecs, f=1.0
Now V=[Qf2/140](1/6) = [50 × 12/140](1/6)
=.842m/sec
R = 5V2/2f =1.774m
P = 4.75√Q = 4.75√50
=33.59 m ……………..(1)
Assuming a trapezoildal section with side slopes ½:1,
perimeter p = B + √5 D
Area of cross section
A = BD + D2/2
A = Q/V = 50/.842 = 59.38m2
BD + 0.5D2 = 59.38 ………………….(2)
B + 2.24D = 33.59
B = 33.59 – 2.24 D
Substituting this value of B in eq.(2)
(33.59 – 2.24D)D + .5D2 = 59.38
Or D = 1.968m & B = 29.34m
Slope S = f5/3/3340 Q1/6
= 15/3/3340 × 501/6
S = 1/6409 Ans.