General Characteristics of Open-Channel Flow

Open-channel flow refers to the movement of fluid with a free surface exposed to the atmosphere, typically occurring in natural or man-made channels such as rivers, streams, and canals. Here are the key characteristics and concepts related to open-channel flow:

Presence of a Free Surface

• Free Surface: The flow has a surface exposed to the atmosphere, distinguishing it from pipe flow where the fluid is enclosed.

Influence of Gravity

• Gravity: The primary driving force for the flow, causing the fluid to move downhill along the channel.

Flow Classification

• Uniform Flow: The depth of flow remains constant along the channel length. This occurs when the channel slope, roughness, and cross-section are consistent.
• Gradually Varied Flow (GVF): The depth of flow changes gradually along the channel due to changes in channel slope, roughness, or discharge.
• Rapidly Varied Flow (RVF): The depth of flow changes abruptly, often due to obstacles or sudden changes in channel geometry.

Channel Geometry

• Cross-Sectional Shape: Natural channels can have irregular shapes, while man-made channels are often designed with specific shapes such as trapezoidal, rectangular, or parabolic.
• Hydraulic Radius (R_h): Defined as the cross-sectional area of flow divided by the wetted perimeter. It is a key parameter in flow calculations.

Flow Regimes

• Subcritical Flow: Occurs when the flow velocity is less than the wave velocity. It is characterized by a tranquil flow and is influenced by downstream conditions.
• Supercritical Flow: Occurs when the flow velocity is greater than the wave velocity. It is characterized by rapid, turbulent flow and is influenced by upstream conditions.
• Critical Flow: The flow velocity is equal to the wave velocity. It represents the transition between subcritical and supercritical flow.

Energy Considerations

• Specific Energy: The total energy per unit weight of fluid relative to the channel bottom. It includes the potential energy (due to depth) and kinetic energy (due to velocity).
• Energy Losses: Due to friction and turbulence, energy losses occur as the fluid flows along the channel. These losses are often quantified using the Manning equation or the Chezy equation.

Hydraulic Jump

• Hydraulic Jump: A phenomenon where supercritical flow transitions to subcritical flow, resulting in a sudden rise in water level and significant energy dissipation.

Manning's Equation

Manning's Equation: Used to calculate the velocity of flow in an open channel. It is given by:

$$V = \frac{1}{n} R_h^{2/3} S^{1/2}$$

Where:

• V: Flow velocity
• n: Manning roughness coefficient
• R_h: Hydraulic radius
• S: Slope of the energy grade line

Example: Open-Channel Flow in a Trapezoidal Channel

When analyzing open-channel flow in a trapezoidal channel, the following steps are typically followed:

1. Determine the Channel Geometry: Measure the bottom width, side slopes, and depth of flow.
2. Calculate the Hydraulic Radius: Use the cross-sectional area and wetted perimeter to find the hydraulic radius.
3. Apply Manning's Equation: Calculate the flow velocity and discharge using the Manning equation.
4. Analyze Flow Regime: Determine whether the flow is subcritical, supercritical, or critical based on the Froude number.