12.1 Classification of Open Channel Flows

Open channel flows are categorized based on flow characteristics and behavior. Understanding these classifications is crucial for analyzing and designing hydraulic structures, predicting flow patterns, and managing water resources effectively.

From laminar to turbulent, steady to unsteady, and subcritical to supercritical, each flow type has unique properties. The Froude number and specific energy concepts are key tools for engineers to assess and control open channel flows in various applications.

Classification of Open Channel Flows

Laminar vs turbulent flow

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• Laminar flow in open channels occurs at low Reynolds numbers ($Re < 500$) where fluid particles move in parallel layers without mixing resulting in a parabolic velocity distribution across the channel (rare in practical applications)
• Turbulent flow in open channels occurs at high Reynolds numbers ($Re > 2000$) where fluid particles exhibit irregular motion and mixing leading to a more uniform velocity distribution across the channel (most common in open channel flows)

Classification of open channel flows

• Steady flow maintains constant flow properties (depth, velocity) and discharge at a given location over time
• Unsteady flow experiences varying flow properties over time at a given location (flood waves, tidal flows, dam-break flows)
• Uniform flow maintains constant flow properties along the channel length when slope, roughness, and cross-section remain unchanged
• Non-uniform flow experiences varying flow properties along the channel length
  • Gradually varied flow (GVF) exhibits gradual changes in flow properties over a long distance (backwater curves, drawdown curves)
  • Rapidly varied flow (RVF) exhibits abrupt changes in flow properties over a short distance (hydraulic jumps, drops, falls)

Types of critical flows

• Froude number ($Fr = \frac{V}{\sqrt{gD}}$) classifies open channel flows based on the ratio of inertial to gravity forces ($V$ = average velocity, $g$ = gravitational acceleration, $D$ = hydraulic depth)
• Subcritical flow ($Fr < 1$) occurs when gravity forces dominate inertial forces resulting in slower flow velocity than wave propagation speed (mild slopes, deep and slow-moving flows)
• Critical flow ($Fr = 1$) occurs when gravity and inertial forces are balanced resulting in flow velocity equaling wave propagation speed (minimum specific energy for a given discharge)
• Supercritical flow ($Fr > 1$) occurs when inertial forces dominate gravity forces resulting in faster flow velocity than wave propagation speed (steep slopes, shallow and fast-moving flows)

Specific energy in channels

• Specific energy ($E = y + \frac{V^2}{2g}$) represents the energy per unit weight of fluid at a given channel section ($y$ = flow depth, $\frac{V^2}{2g}$ = velocity head)
• Specific energy diagram plots specific energy against flow depth for a given discharge with minimum specific energy occurring at critical depth ($y_c$)
• Applications of specific energy include determining flow transition between subcritical and supercritical states, analyzing hydraulic jump formation, and designing channel contractions and expansions to minimize energy losses