CELE Hydraulics & Fluid Mechanics — Buoyancy and FlotationConcept Map

Concept

Archimedes' Principle

Sub Concepts

• Buoyant Force Formula: FB = γ_fluid × V_displaced
• Fully Submerged Bodies
• Partially Submerged Bodies
• Weight of Displaced Fluid

Relationship To Central

Foundational law governing all buoyant forces

Concept

Flotation Condition & Equilibrium

Sub Concepts

• Force Balance: FB = Weight
• Draft Calculation: d = V_displaced / A
• Specific Gravity Comparison (s < 1 floats)
• Displacement Volume for Floating Bodies

Relationship To Central

Determines whether bodies float or sink

Concept

Stability of Floating Bodies

Sub Concepts

• Center of Buoyancy (B)
• Center of Gravity (G)
• Metacenter (M)
• Metacentric Height: GM = BM - BG
• Stable, Unstable, and Neutral Equilibrium
• Righting Moment

Relationship To Central

Critical for safe design of marine structures

Concept

Waterline Plane Properties

Sub Concepts

• Second Moment of Inertia (I)
• Plan Area (A) of Floating Body
• Axis of Rotation (pitch vs. roll)
• BM = I / V_displaced Relationship

Relationship To Central

Essential for calculating metacentric height

Concept

Applications in Civil Engineering

Sub Concepts

• Barge and Pontoon Design
• Caisson and Cofferdam Flotation
• Ship Stability Analysis
• Apparent Weight Calculations
• Floating Structures in Philippine Rivers

Relationship To Central

Practical use in design and analysis

Concept

Common Pitfalls & Board-Exam Mistakes

Sub Concepts

• Using Total Volume Instead of Displaced Volume
• Confusing Waterline-Plane I with Body I
• Sign Errors in BG Calculations
• Incorrect Fluid Specific Weight (seawater ≠ freshwater)

Relationship To Central

Critical awareness for examination success

To

Buoyant Force Formula

From

Archimedes' Principle

Strength

strong

Relationship

FB = γ_fluid × V_displaced is the mathematical statement of Archimedes' Principle

To

Flotation Condition

From

Buoyant Force Formula

Strength

strong

Relationship

Body floats when FB equals its weight, leading to equilibrium at draft d

To

Floating or Sinking

From

Specific Gravity

Strength

strong

Relationship

Bodies with s < 1 float; s > 1 sink; determines whether flotation occurs

To

Displaced Volume

From

Draft Calculation

Strength

strong

Relationship

d = V_displaced / A; draft depends directly on how much volume must displace for equilibrium

To

Stability Analysis

From

Center of Buoyancy

Strength

strong

Relationship

B is one of three critical centers (B, G, M); its position determines GM calculation

To

Stability Analysis

From

Center of Gravity

Strength

strong

Relationship

G is one of three critical centers; distance from B (as BG) is key to stability

To

Stability Criteria

From

Metacenter

Strength

strong

Relationship

Position of M relative to G determines if body is stable (M above G) or unstable (M below G)

To

Righting Moment

From

Metacentric Height (GM)

Strength

strong

Relationship

Larger GM produces larger righting moment RM = W × GM × sin(θ), improving stability

To

Metacentric Height

From

Second Moment of Inertia (I)

Strength

strong

Relationship

BM = I / V_displaced; wider beams (larger I) increase metacentric height, improving stability

To

Second Moment of Inertia

From

Waterline Plane Properties

Strength

strong

Relationship

I is calculated from the waterline-plane area geometry; axis of rotation determines which I to use

To

Civil Engineering Applications

From

Stability Analysis

Strength

strong

Relationship

Barges, pontoons, and caissons must satisfy GM > 0 for safe design; stability governs safe operations

To

Ship Design Requirements

From

Righting Moment

Strength

moderate

Relationship

Larger righting moment ensures vessels can recover from wave-induced heel; critical for maritime safety

To

Archimedes' Principle

From

Volume Confusion Pitfall

Strength

moderate

Relationship

Common mistake: using total body volume instead of displaced volume; Archimedes' applies only to displaced fluid

To

Waterline Plane Properties

From

Moment of Inertia Error

Strength

moderate

Relationship

Pitfall: confusing body I with waterline-plane I; must use I of waterline area for BM calculation

To

Buoyant Force Calculation

From

Fluid Specific Weight

Strength

moderate

Relationship

Using wrong γ (seawater vs. freshwater) leads to incorrect FB and equilibrium conditions

To

Floating Body Equilibrium

From

Force Balance Condition

Strength

strong

Relationship

At equilibrium, FB = W; determines the draft and how much the body sinks into the fluid

To

Engineering Design Margins

From

Stable Equilibrium

Strength

moderate

Relationship

Sufficient GM ensures structure resists tipping; larger GM allows design for higher loads or rougher conditions