Problem 1: Manning Discharge in a Rectangular Channel

A rectangular concrete channel is $3.0\text{ m}$ wide and carries water $1.5\text{ m}$ deep. The slope is $0.001$ and Manning $n=0.015$. Determine discharge.

Problem 2: Normal Depth in a Rectangular Channel

A $4.0\text{ m}$ wide rectangular channel carries $10\text{ m}^3/\text{s}$. Use $n=0.015$ and slope $S=0.0008$. Determine normal depth.

Problem 3: Manning Discharge in a Trapezoidal Channel

A trapezoidal channel has bottom width $2.0\text{ m}$, side slope $1.5\text{H}:1\text{V}$, depth $1.2\text{ m}$, slope $0.0015$, and $n=0.025$. Determine discharge.

Problem 4: Most Efficient Rectangular Section

Determine the dimensions of the hydraulically efficient rectangular section with flow area $12\text{ m}^2$.

Problem 5: Most Efficient Trapezoidal Section

A hydraulically efficient trapezoidal channel must have area $20\text{ m}^2$ and side slopes $1\text{H}:1\text{V}$. Determine depth and bottom width.

Problem 6: Half-Full Circular Conduit

A circular conduit of diameter $1.2\text{ m}$ flows half full under gravity. Use $n=0.013$ and slope $0.002$. Determine area, hydraulic radius, and discharge.

Problem 7: Compound-Section Conveyance

A main channel subsection has $A_1=20\text{ m}^2$, $R_1=1.5\text{ m}$, and $n_1=0.030$. An adjacent floodplain subsection has $A_2=30\text{ m}^2$, $R_2=0.50\text{ m}$, and $n_2=0.060$. If the common energy slope is $0.001$, estimate total discharge by summing conveyances.

Problem 8: Required Channel Slope

A rectangular channel is $5.0\text{ m}$ wide and $1.0\text{ m}$ deep and must carry $12\text{ m}^3/\text{s}$. Use $n=0.018$. Determine the required uniform-flow slope.