A rectangular concrete channel is $3.00\text{ m}$ wide and carries water $1.50\text{ m}$ deep. The friction slope is $S_f=0.00100$ and Manning $n=0.0150$. Determine the uniform discharge.

A $4.00\text{ m}$ wide rectangular channel must carry $10.0\text{ m}^3/\text{s}$ with $n=0.0150$ and $S_f=0.000800$. Determine the normal depth and verify the result.

A trapezoidal channel has bottom width $b=2.00\text{ m}$, side slope $m=1.50$, depth $y=1.20\text{ m}$, $n=0.0250$, and $S_f=0.00150$. Determine discharge.

A rectangular channel is $5.00\text{ m}$ wide and $1.00\text{ m}$ deep and must carry $12.0\text{ m}^3/\text{s}$. Use Manning $n=0.0180$. Determine the required friction slope.

A channel section has $A=4.00\text{ m}^2$, $R=0.800\text{ m}$, measured discharge $Q=8.00\text{ m}^3/\text{s}$, and energy slope $S_f=0.00160$. Estimate the effective Manning coefficient represented by the observation.

Determine the hydraulically efficient rectangular dimensions for a required flow area of $12.0\text{ m}^2$.

A hydraulically efficient trapezoidal channel must have area $20.0\text{ m}^2$ and side slopes $1\text{H}:1\text{V}$. Determine depth and bottom width.

A circular conduit has diameter $D=1.20\text{ m}$, $n=0.0130$, and $S_f=0.00200$. Determine the half-full discharge and compare it with the nominal full-flow gravity discharge using Manning's equation.

For the same $1.20\text{ m}$ conduit, evaluate Manning discharge at $y/D=0.940$ using $n=0.0130$ and $S_f=0.00200$, then compare it with the nominal full-flow discharge.

A main-channel subsection has $A_1=20.0\text{ m}^2$, $R_1=1.50\text{ m}$, and $n_1=0.0300$. An adjacent floodplain subsection has $A_2=30.0\text{ m}^2$, $R_2=0.500\text{ m}$, and $n_2=0.0600$. The common energy slope is $S_f=0.00100$. Estimate total discharge by summing conveyances.