51 An open channel has a width of 5 m and drops at the rate

51. An open channel has a width of 5 m and drops at the rate of l m/100 m. Assume a roughness coefficient, n, of 0.015. If the depth of the water is 3 m, the flow rate in the channel is most nearly

Solution

Though they have not mentioned type of channel section, as they have given only width and depth of channel we assume it as rectangular section.

Given

Depth y=3m

Width b=5m

Slope s= 1/100

Roughness coeff n=0.015

Therefore ,Channel section area A=dxb=5x3=15 sqm

Wetted perimeter P= 2x5 + 3= 13 m

Hydraulic radius R=A/P =15/13

Flow rate Q=(A/n)xR^(2/3) xS

=(15/0.015)x(15/13)^(2/3) x(1/100)

=110 cum/sec.