Answer:
Q = 3.42 m³/s
Explanation:
given,
depth of the rectangular channel, y = 2 m
width of the channel, B = 3 m
slope of the channel, = 1 in 700
manning's coefficient, n = 0.06
discharge through the channel
[tex]Q = \dfrac{1}{n}AR^{2/3}\sqrt{S}[/tex]
R is the hydraulic radius.
hydraulic radius is the ratio of area of the channel to wetted perimeter.
A = B y = 3 x 2 =6 m²
P = B + 2 y = 3 + 2 x 2 = 7 m
[tex]R = \dfrac{6}{7}= 0.857 m[/tex]
now,
[tex]Q = \dfrac{1}{0.06}\times 6 \times 0.857^{2/3}\sqrt{\dfrac{1}{700}}[/tex]
Q = 3.42 m³/s
hence, the discharge through the channel is equal to 3.42 m³/s