Question

A trapezoidal channel with side slopes 1:1 has to be designed to convey 10 m^3/sec at a velocity of 2 m/sec, so that the amount of concrete lining for the bed and sides is the minimum.

a) calculate the area of lining required for one meter length of the canal.

b) if manning's roughness coefficient n = 0.015 , calculate the bed slope of the canal

Answer 1

Lolution Data: 0-10 m/s v=am/s Area Discharge Q = 105m² velocity v 2 -- 1 A : 5m² for most economical trapezoidal section, Half of top klidth = one q the sloping side (ie) brand donati For, n=1, the condition becomes, brand- dr n +1 N=1 b+Qd = dr2 = 1.414d. A = (b +nd) d = (0.828 d + 1xd) A = 1:828 d² But, A = 5 m² 5= 1.828 d² d=1-654 m b=0.8280 = 0.828* 1.654 = 1.369m]

Area of lining requined for one meter length of canal = (sletted perimeter) & (length of canal P= 1.369+ (2x1654), 7+1 = 6:04#m Area of uning = 6:047*1 = 16.044m² 6 xle have Iveco mi Here, m=A I P P=209) + Baxa) +b (3xdk2 + b p-P312 x 164) + 1.369 P = 5.189 m : m = A = 51 = 0.964 P 5.189 = . from , v=cumi 2=0.00 964 xi Aquaring on both sides, A = (²x0.9641

²i= A 0.964 i Bed slope, i- 0.9646² dlhere, es chezy's con stent.