CELE Hydraulics & Fluid Mechanics — Fundamentals of Fluid FlowConcept Map

Concept

Conservation of Mass (Continuity Equation)

Sub Concepts

• Volume Flow Rate Q
• Cross-sectional Area A
• Velocity v
• Diameter Relationship D₁/D₂
• Incompressible Flow Assumption

Relationship To Central

Core principle governing flow rates and velocity changes

Concept

Conservation of Energy (Bernoulli Equation)

Sub Concepts

• Pressure Head p/γ
• Velocity Head v²/2g
• Elevation Head z
• Energy Grade Line (EGL)
• Hydraulic Grade Line (HGL)
• Head Loss hL
• Pump Head hA
• Turbine Head hE

Relationship To Central

Core principle relating pressure, velocity, and elevation

Concept

Conservation of Momentum

Sub Concepts

• Momentum Rate ρQ(v₂-v₁)
• Force on Control Volume
• Pipe Bends
• Nozzles
• Vanes and Deflectors

Relationship To Central

Core principle for force analysis in flowing systems

Concept

Power in Flowing Systems

Sub Concepts

• Power Formula P = γQH
• Pump Power Input
• Turbine Power Output
• Efficiency η
• Head H

Relationship To Central

Application of energy principles to hydraulic machinery

Concept

Head Loss Mechanisms

Sub Concepts

• Friction Loss hf
• Minor Losses (Fittings)
• Entrance/Exit Losses
• Pipe Roughness
• Reynolds Number

Relationship To Central

Critical component of practical energy equation applications

Concept

Flow Analysis Tools

Sub Concepts

• Energy Grade Line (EGL)
• Hydraulic Grade Line (HGL)
• Total Head Concept
• Graphical Energy Analysis

Relationship To Central

Methods and diagrams for visualizing energy behavior

To

Conservation of Energy

From

Conservation of Mass

Strength

strong

Relationship

Continuity provides v₂ needed for velocity head term in Bernoulli equation

To

Conservation of Momentum

From

Conservation of Mass

Strength

strong

Relationship

Flow rate Q = Av appears in momentum equation as ρQ(v₂-v₁)

To

Power in Flowing Systems

From

Conservation of Energy

Strength

strong

Relationship

Power P = γQH calculated from total head H derived from energy equation

To

Conservation of Energy

From

Head Loss Mechanisms

Strength

strong

Relationship

Head loss hL is subtracted from energy equation to account for real fluid friction

To

Hydraulic Grade Line

From

Energy Grade Line

Strength

strong

Relationship

HGL = EGL minus velocity head v²/2g at each point

To

Conservation of Energy

From

Pump Head hA

Strength

strong

Relationship

Added to LHS of energy equation to increase total head

To

Conservation of Energy

From

Turbine Head hE

Strength

strong

Relationship

Subtracted from LHS of energy equation to extract available energy

To

Power in Flowing Systems

From

Efficiency η

Strength

moderate

Relationship

Divides pump input power; multiplies turbine output power

To

Head Loss Mechanisms

From

Reynolds Number

Strength

moderate

Relationship

Determines friction factor which governs friction loss calculations

To

Pipe Bends and Nozzles

From

Conservation of Momentum

Strength

strong

Relationship

Momentum equation ΣF = ρQ(v₂-v₁) directly calculates forces on deflectors

To

Pressure Head p/γ

From

Velocity Head v²/2g

Strength

strong

Relationship

Trade-off in Bernoulli: increased velocity causes pressure decrease

To

Conservation of Energy

From

Elevation Head z

Strength

moderate

Relationship

Gravitational potential energy component of total head

To

Energy Grade Line

From

Flow Analysis Tools

Strength

moderate

Relationship

EGL graphically represents energy distribution along pipe system

To

Hydraulic Grade Line

From

Flow Analysis Tools

Strength

moderate

Relationship

HGL shows piezometric head (pressure + elevation) without kinetic energy

To

Conservation of Momentum

From

Control Volume Analysis

Strength

strong

Relationship

Momentum equation derived by applying Newton's second law to control volume