Open Channel Flow: Uniform Flow

Open channel flow implies flow in a channel with a free surface exposed to atmospheric pressure. Examples include rivers, canals, and sewers.

Geometric Elements

• Depth of Flow ($y$): Vertical distance from bottom to free surface.
• Wetted Perimeter ($P$): Length of the channel cross-section in contact with water.
• Hydraulic Radius ($R$): Ratio of Area to Wetted Perimeter. $R = \frac{A}{P}$

Uniform Flow Formulas

Chezy Formula

$V = C \sqrt{RS}$

• $C$ = Chezy coefficient (related to roughness)
• $S$ = Slope of the energy line (channel bottom slope for uniform flow)

Manning Formula

The most widely used empirical formula.

$V = \frac{1}{n} R^{2/3} S^{1/2} \quad (\text{SI Units})$

• $n$ = Manning's roughness coefficient.
• For English units, use $1.486/n$.

Discharge ($Q$): $Q = AV = \frac{1}{n} A R^{2/3} S^{1/2}$

Most Efficient Hydraulic Section

The cross-section that conveys the maximum discharge for a given area and slope (i.e., minimum wetted perimeter).

• Rectangular: Width = 2 $\times$ Depth ($b = 2y$).
• Trapezoidal: Half-hexagon (Sides slope 60°).

Solved Problems