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Solution
Answer: B) 5.7 ft
Refer to PE Civil Reference Handbook Section 6.4.5 for steady uniform flow.
Manning's Equation:
\[Q=\frac{1.486}{n} A R_{h}^{2/3} S^{1/2}\\\]
where:
\(\text{Q= discharge rate} (ft^3/sec) = 2000\ cfs\)
\(S = \text{channel slope} = 0.02\)
\(n = \text{manning roughness coefficient}\)
\(A = \text{channel cross-sectional area}\)
Determine manning roughness coefficient based on excavated rock-cut:
\[n = 0.035\]
Area:
\[A=(b+zy)y , b\ is\ unknown\ , z = 2 , y = 7\ ft\]\[A=(b+2\times7)\times7 = 7b+98\ ft^2\\\]
Hydraulic Radius:
\[R_h= (b+zy) y/[b+2y(1+Z^2)^{1/2}]\]
\[R_h=(b+2\times7) \times7/ [b+2\times7\times (1+2^2) ^{1/2}]\\\]
\[Try\ b = 5, get\ Q = 1897\ CFS\]
\[Try\ b = 6, get\ Q = 2030\ CFS\]
\[Try\ b = 5.7, get\ Q = 1990\ CFS\]
\[\to b = 5.7 ft\]
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