Open Channel Flow Notes

Open Channel Flow Basics

  • Universitat Politècnica de Catalunya Hydraulics Course
    • Professors: Soledad Estrella Toral & Ernest Blade
  • Key Concepts Covered:
    • Characteristics of open channel flow vs. pipe flow
    • Types of channels
    • Velocity distribution in a cross-section
    • Pressure distribution in a cross-section
    • Effects of slope on pressure distribution

Characteristics of Open Channel Flow vs. Pipe Flow

  • Hydraulic Variables:
    • Definition of hydraulic variables differs between pipe flow and open channel flow.
    • Key variables include hydraulic head (9;H9), velocities (v), and pressure terms.
  • Energy Considerations:
    • Energy line and piezometric concepts are essential in analyzing flow behavior.

Types of Channels

  • Artificial Channels:
    • Created by human intervention: e.g., channels, collectors, spillways.
  • Natural Channels:
    • Formed naturally: e.g., rivers, streams, estuaries.

Types of Flow in Channels

  • Steady Flow

    • Water depths (y) and velocities (v) are constant over time.
    • Uniform Flow: Steady condition with constant depth and velocity throughout the channel.
    • Varied Flow: Water depths and velocities change, but the change is smooth or abrupt.
    • Gradually Varied Flow:
      • Smooth changes with moderate curvature along the channel.
    • Rapidly Varied Flow:
      • Sharp changes in depth and velocity over short distances.

  • Unsteady Flow

    • Water depths and velocities change with time.
    • Unsteady Uniform Flow: Rare condition where velocity and depth are uniform but time-variant.
    • Unsteady Varied Flow: Similar classification as steady varied flow but changes with time.

Velocity Distribution in Cross-Sections

  • Velocity Variation:
    • Velocity is zero at the channel boundaries, increasing to a maximum at depths between 5-25% of surface levels.
  • Factors Influencing Velocity Distribution:
    • Channel geometry
    • Surface roughness
    • Alignment of the channel layout

Pressure Distribution in Open Channels

  • Hydrostatic Pressure Condition:
    • Pressure increases with the depth below the free surface:
      P =
      ho_w imes h
    • Hydrostatic nature implies parallel flow with minimal changes in velocity.
  • Aberrations:
    • Significant curvature leads to non-hydrostatic pressure distribution due to centrifugal effects in curvilinear flow.
  • Hydrostatic vs. Non-Hydrostatic Pressure:
    • Convex Flow: Pressure < Hydrostatic Pressure
    • Concave Flow: Pressure > Hydrostatic Pressure

Effects of Slope on Pressure Distribution

  • As slope increases, projections of pressure distribution need to account for hydraulic effects.
  • Commonly, for slopes greater than 6 degrees, the static pressure slope can be neglected.
  • Critical Angles:
    • Flow characteristics change significantly at angles around 6 degrees.

Uniform Steady Flow in Open Channels

  • Equations of Motion
    • Characterized by constant discharge (Q), water depths, and velocities (v) along the channel.
    • Conditions for prismatic channels are required.
    • Resistance due to boundary friction balances the fluid's weight.

Chézy and Manning Formulas for Flow Resistance

  • Chézy Formula:
    • Describes frictional resistance in open channels with variables including velocity, area, and channel bed condition.
  • Manning Formula:
    • n = rac{k}{R^{2/3}}
    • Important for calculating flow regime and estimating water depth in channels.

Specific Energy Analysis

  • Concept of Specific Energy (E):
    • Defined as energy per unit weight of fluid above a reference level.
    • Relationship between water depth, flow rate, and specific energy helps assess critical and subcritical flows.
  • Critical Flow:
    • Characterized by a specific energy state that gives minimum energy for flow.

This helps in understanding transitions between flow regimes in channels.

Hydraulic Jump and Flow Transitions

  • Hydraulic Jump:
    • Occurs when flow changes from supercritical to subcritical, characterized by energy dissipation and change in depth.
  • Types of Jumps:
    • Vary by the Froude number: undular, weak, steady, and strong jumps, each affecting energy loss differently.

Calculating Flow Surface Profiles

  • Gradually Varied Flow:
    • Governed by the backwater equation, which requires specific boundary conditions based on flow type.
    • The conditions vary according to upstream and downstream flow states.
  • Local Losses & Rapidly Varied Flow:
    • These changes often occur in short reaches due to abrupt geometry changes leading to complex flow characteristics.

Applications and Control Sections

  • Control Sections:
    • Gauge discharge and measure flow depth at critical points within the channel.
    • Utilized in weirs, spillways for hydrological measurements.