CELE Hydraulics & Fluid Mechanics — Flow in Open ChannelsConcept Map

Concept

Uniform Flow & Manning's Equation

Sub Concepts

• Manning roughness coefficient (n)
• Hydraulic radius (R = A/P)
• Wetted perimeter (P)
• Flow area (A)
• Bed slope (S)
• Mean velocity (v)
• Discharge (Q = Av)

Relationship To Central

Foundational principle for steady, constant-depth flow analysis in channels

Concept

Channel Geometry & Hydraulic Properties

Sub Concepts

• Rectangular channels
• Trapezoidal channels
• Circular channels
• Most efficient (best hydraulic) section
• Cross-sectional area
• Geometric constraints

Relationship To Central

Physical characteristics that define flow capacity and efficiency

Concept

Specific Energy & Flow Classification

Sub Concepts

• Specific energy (E = y + v²/2g)
• Potential energy component (depth y)
• Kinetic energy component (v²/2g)
• Energy gradient
• Reference datum (channel bottom)

Relationship To Central

Energy-based approach to understanding flow behavior and transitions

Concept

Froude Number & Flow Regimes

Sub Concepts

• Froude number (Fr = v/√(gy))
• Subcritical flow (Fr < 1, tranquil)
• Critical flow (Fr = 1)
• Supercritical flow (Fr > 1, rapid)
• Hydraulic depth (A/T)

Relationship To Central

Dimensionless criterion for classifying flow behavior

Concept

Critical Flow Conditions

Sub Concepts

• Critical depth (yc)
• Unit discharge (q = Q/b)
• Minimum specific energy (E_min = 3yc/2)
• Critical velocity (vc)
• Critical slope (Sc)

Relationship To Central

Boundary between subcritical and supercritical regimes; minimum energy state

Concept

Hydraulic Jump

Sub Concepts

• Conjugate (sequent) depths
• Initial depth (y₁)
• Sequent depth (y₂)
• Energy loss (ΔE)
• Jump length
• Froude number requirement

Relationship To Central

Abrupt transition mechanism dissipating energy from supercritical to subcritical flow

Concept

Design & Application

Sub Concepts

• Channel design for efficiency
• Manning coefficient selection
• Capacity calculations
• Slope requirements
• Lining considerations
• Philippine drainage standards (NSCP 2015)

Relationship To Central

Practical implementation of open-channel flow theory in engineering projects

To

Hydraulic Radius

From

Manning's Equation

Strength

strong

Relationship

Manning equation requires R = A/P; hydraulic radius is the geometric parameter determining velocity for given slope and roughness

To

Discharge

From

Uniform Flow

Strength

strong

Relationship

Uniform flow analysis yields velocity via Manning; discharge is then calculated as Q = A × v

To

Most Efficient Section

From

Channel Geometry

Strength

strong

Relationship

Most efficient sections are geometric configurations (b = 2y for rectangular) that minimize wetted perimeter for given area, maximizing discharge

To

Critical Flow

From

Specific Energy

Strength

strong

Relationship

Critical flow occurs at minimum specific energy; for rectangular channels, E_min = 1.5y_c where y_c is critical depth

To

Flow Classification

From

Froude Number

Strength

strong

Relationship

Froude number directly classifies flow regime: Fr < 1 subcritical, Fr = 1 critical, Fr > 1 supercritical

To

Unit Discharge

From

Critical Depth

Strength

strong

Relationship

Critical depth y_c is computed from unit discharge q = Q/b; formula: y_c = (q²/g)^1/3 for rectangular channels

To

Hydraulic Jump

From

Supercritical Flow

Strength

strong

Relationship

Hydraulic jump is the mechanism by which supercritical flow transitions abruptly to subcritical flow, dissipating excess kinetic energy

To

Energy Loss

From

Hydraulic Jump

Strength

strong

Relationship

Hydraulic jump causes significant energy dissipation through turbulence; loss is ΔE = (y₂ − y₁)³ / 4y₁y₂

To

Sequent Depth Ratio

From

Conjugate Depths

Strength

strong

Relationship

Sequent (conjugate) depth ratio y₂/y₁ = 0.5(√(1 + 8Fr₁²) − 1) relates upstream and downstream depths in a hydraulic jump

To

Velocity

From

Manning Roughness Coefficient

Strength

strong

Relationship

Manning coefficient n inversely affects velocity; higher n (rougher surface) reduces velocity for same slope and radius

To

Velocity

From

Bed Slope

Strength

strong

Relationship

Velocity is proportional to S^0.5 in Manning equation; steeper slopes produce higher velocities

To

Specific Energy

From

Depth

Strength

strong

Relationship

Specific energy increases with depth (potential component) but decreases as velocity increases; creates E-y curve with minimum at critical depth

To

Froude Number

From

Velocity

Strength

strong

Relationship

Froude number is ratio of inertial to gravitational forces; Fr = v / √(gy); higher velocity increases Fr

To

Hydraulic Radius

From

Wetted Perimeter

Strength

moderate

Relationship

Hydraulic radius R = A/P; minimizing wetted perimeter for given area maximizes R and hence discharge capacity

To

Manning Roughness Coefficient

From

Channel Geometry

Strength

moderate

Relationship

Manning n varies with channel lining material and shape; design must select n appropriate to geometric choice

To

Design Applications

From

Critical Flow

Strength

moderate

Relationship

Critical depth is a design control point for spillways, channel transitions, and flow measuring devices; ensures stable transitions

To

Stilling Basin Design

From

Hydraulic Jump

Strength

moderate

Relationship

Stilling basins are designed to contain and stabilize hydraulic jumps, protecting downstream structures from erosion

To

Upstream Control

From

Subcritical Flow

Strength

moderate

Relationship

Subcritical flow allows disturbances (waves) to propagate upstream; flow is controlled by upstream boundary conditions (gates, weirs)

To

Downstream Control

From

Supercritical Flow

Strength

moderate

Relationship

Supercritical flow cannot transmit information upstream; flow is controlled by downstream boundary conditions (obstacle, slope change)

To

Design Optimization

From

Most Efficient Section

Strength

moderate

Relationship

Most efficient section minimizes construction cost by achieving required discharge with minimum channel area and earthwork