Open Channel Flow

Why it matters

Open channel flow is essential in civil engineering for the design and analysis of channels, canals, and drainage systems. Understanding this flow helps in efficient water resource management, flood control, and irrigation planning.

Key ideas

• Open Channel Flow: This refers to the flow of liquid with a free surface exposed to atmospheric pressure, such as rivers, canals, and sewers.
• Types of Flow: Classified based on the flow depth variation:
  • Uniform Flow: The flow depth remains constant along the channel length.
  • Non-uniform Flow: The flow depth changes along the channel length, further divided into gradually varied flow and rapidly varied flow.
• Flow Regimes: Determined by the Froude number (Fr):
  • Subcritical Flow: Fr < 1, wave speed is greater than flow velocity.
  • Critical Flow: Fr = 1, wave speed equals flow velocity.
  • Supercritical Flow: Fr > 1, flow velocity is greater than wave speed.
• Channel Shapes: Common shapes include rectangular, trapezoidal, and circular, each affecting flow characteristics.
• Energy and Momentum Principles: Used to analyze flow behavior and design channels.

Formulas

• Q = A·V
  • Q: Discharge (m³/s)
  • A: Cross-sectional area (m²)
  • V: Velocity (m/s)
• Fr = V / (g·D)^(0.5)
  • Fr: Froude number (dimensionless)
  • V: Velocity (m/s)
  • g: Acceleration due to gravity (9.81 m/s²)
  • D: Hydraulic depth A/T (m), where T is free-surface top width; distinguish hydraulic radius A/P
• For a small-slope channel with hydrostatic pressure and kinetic-energy coefficient approximated as 1: E = y + V²/(2·g)
  • E: Specific energy (m)
  • y: Flow depth (m)
  • V: Velocity (m/s)
  • g: Acceleration due to gravity (9.81 m/s²)

Worked example

Given: A rectangular channel with a width of 3 m carries water at a depth of 2 m and a velocity of 1.5 m/s. Calculate the discharge and Froude number.

1. Calculate the cross-sectional area (A):
   • A = width × depth = 3 m × 2 m = 6 m²
2. Calculate the discharge (Q):
   • Q = A·V = 6 m² × 1.5 m/s = 9 m³/s
3. Calculate the hydraulic depth (D):
   • D = A / width = 6 m² / 3 m = 2 m
4. Calculate the Froude number (Fr):
   • Fr = V / (g·D)^(0.5) = 1.5 m/s / (9.81 m/s² × 2 m)^(0.5) ≈ 0.34

Final Answer: Discharge is 9 m³/s and Froude number is 0.34.

Common mistakes

• Confusing hydraulic depth with flow depth.
• Incorrectly calculating the cross-sectional area for non-rectangular channels.
• Misapplying the Froude number formula, especially the square root operation.

For GATE CE

Questions often involve calculating discharge, flow velocity, and Froude number for different channel shapes. Practice problems on uniform and non-uniform flow, and understanding flow regimes.

Quick check

1. What is the Froude number for critical flow?
2. How does the flow depth vary in uniform flow?
3. What is the unit of discharge?

Answers: 1. 1, 2. It remains constant, 3. m³/s