Question

Design a canal having a trapezoidal cross section to carry a design discharge of

irrigation water of 900 cfs. The slope of the canal is to be 0.002. The canal is to be

lined with concrete, and it is to have the best hydraulic section for the design

flow. Adopt a Manning’s roughness coefficient ? for lined canals under (troweled concrete) ? = 0.012.

Answer 1

Ans) We know,

Q = (A / n)

where, Q = Discharge = 900 cfs

n = Manning roughness coefficient for concrete = 0.012

A = Cross sectional area of channel =

R = Hydraulic depth

   S = Bed slope = 0.002

Also, R = Area / Wetted perimeter

For trapezoidal channel, A = BD + m

where, B= Bottom width

D = Depth of water in channel

m = Side slope m :1 , assume m = 2

=> A = BD + 2

Wetted perimeter (P) = B + 2D = B + 2 D

=> Wetted perimeter (P) = B + 4.472 D

=> R = A / P = (BD + 2 ) /  (B + 4.472 D)

For most economical trapezoidal channel, top width is twice of side wall length

=> B + 2mD = 2 (D)

=> B + 4D = 2 D

=> B + 4 D = 4.472 D

=> B = 0.472 D

=> A = BD + m = (0.472 + 2) = 2.472

Therefore, R = 2.472 / (0.472D + 4.472D)= 0.5 D

Putting values in Manning formula,

=> 900 = (2.472 / 0.012)

=> 900 = 206 x 0.63 x 0.0447

=> 5.8 = 900

=> = 155.17

=> D = 6.63 ft

=> B = 0.472 D = 0.472 x 6.63 = 3.13 ft

Hence,

Bottom width of canal (B) = 3.13 ft

Top width of canal = B + 2mD = 3.13 + 2(2)(6.63) = 29.65 ft

Flow depth (D) = 6.63 ft, provide 1 ft freeboard so depth of channel = 7.63 ft  

Side slope (m :1 ) = 2 : 1

Side wall length = D = 14.82 ft