PhysicsChapter 6: Fluid Mechanics
Ships and Submarines
Explanation level
Overview
The textbook gives ships and submarines as connected applications of Archimedes' principle. They are combined here because both depend on controlling displaced water, buoyant force, weight and average density.
Learning Outcomes
- Explain why a heavy steel ship floats.
- Describe buoyancy, stability and structural reliability in ship design.
- Explain the action of submarine ballast tanks.
- Relate average density to rising, sinking and neutral buoyancy.
- Apply Archimedes' principle to floating vessels.
Intermediate Level
How Ships Float
A ship settles into water until it displaces a volume whose weight equals the ship's total weight. Its hollow hull makes the ship's average density smaller than the density of solid steel and allows a large displaced volume without excessive mass.
When to use: Ship floating without vertical acceleration.
When to use: Find the water volume displaced by a floating ship.
Ship Engineering
| Design requirement | How it is achieved | Purpose |
|---|---|---|
| Buoyancy | Wide hollow hull displaces enough water | Provides upward force equal to weight |
| Stability | Low weight distribution, ballast tanks and stable hull shape | Resists overturning |
| Structural reliability | Strong, light materials such as steel and aluminium | Withstands pressure, loads, stresses and vibration |
Adding cargo increases ship weight. The ship sinks slightly deeper until the larger displaced volume produces an equally larger upthrust. Safe loading limits prevent the deck from sitting too low in the water.
How Submarines Dive and Rise
A submarine has ballast tanks that can take in seawater or expel it. Filling the tanks increases mass and average density with little change in external volume. When weight exceeds upthrust, the submarine sinks.
To rise, compressed air forces seawater out of the ballast tanks. Mass and average density decrease. Upthrust then exceeds weight, so the submarine accelerates upward.
| Condition | Force comparison | Result |
|---|---|---|
| Ballast tanks flood | W > F_b | Submarine sinks |
| Neutral buoyancy | W = Fb | Submarine remains at constant depth |
| Water expelled | W < F_b | Submarine rises |
| Floating at surface | W = Fb for the immersed part | Vertical equilibrium |
Average Density View
- Average vessel density below fluid density favours rising or floating.
- Average vessel density equal to fluid density gives neutral buoyancy when fully immersed.
- Average vessel density above fluid density gives sinking.
Solved Numerical Examples
Example 1: Displacement of a Ship
A ship has mass 2.0 × 10⁶ kg. Find the volume of seawater displaced while it floats. Use ρ_seawater = 1025 kg m⁻³.
- m = 2.0 × 10⁶ kg
- ρ = 1025 kg m⁻³
Floating: ρgVd = mg
Cancel g
Vd = mρ
Vd = 2.0 × 10⁶1025
Final answer: Vd ≈ 1.95 × 10³ m³
Example 2: Submarine Force Balance
A submerged submarine experiences 8.0 × 10⁶ N upthrust and weighs 8.3 × 10⁶ N after flooding its tanks. Find the resultant vertical force.
- Fb = 8.0 × 10⁶ N upward
- W = 8.3 × 10⁶ N downward
Fnet = Fb - W
Fnet = 8.0 × 10⁶ - 8.3 × 10⁶
Final answer: Fnet = -3.0 × 10⁵ N, or 3.0 × 10⁵ N downward
Real-Life Applications
- Cargo loading changes the depth to which a ship sits in water.
- Plimsoll marks show safe loading depths.
- Ballast improves stability in ships and controls depth in submarines.
- Life boats and pontoons use hollow volumes to increase displacement.
- Underwater vehicles use buoyancy-control systems for depth control.
Common Mistakes
- Saying steel must sink without considering the hollow hull and average density.
- Assuming a floating ship displaces its own volume instead of enough water to match its weight.
- Saying ballast tanks change the submarine's outer volume greatly.
- Confusing stability with buoyancy.
- Assuming neutral buoyancy means no forces act.
Short-Question Preparation
Q. Why does a heavy steel ship float?
A. Its hollow hull gives a large displaced volume and low average density. It sinks only until the weight of displaced water, and therefore upthrust, equals its weight.
Q. How is ship stability improved?
A. Weight is kept low, ballast tanks are used and the hull is shaped to resist overturning.
Q. How does a submarine sink?
A. It admits seawater into ballast tanks, increasing weight and average density until weight exceeds upthrust.
Q. How does a submarine rise?
A. Compressed air expels ballast water, reducing weight until upthrust exceeds weight.
Long-Question Preparation
Q. Explain how ships float and submarines control depth.
A. 1. State Archimedes' principle. 2. For a floating ship, Fb = ρgVd = W. 3. Explain that a hollow hull increases displacement and lowers average density. 4. Describe buoyancy, stability and structural reliability. 5. A submarine changes mass using ballast tanks. 6. Flooded tanks give W > Fb, so it sinks. 7. Neutral buoyancy gives W = Fb. 8. Expelling water gives W < F_b, so it rises.
Sticky Notes
- Floating ship: Fb = W.
- Hollow hull → large displacement.
- Low ballast improves stability.
- Flood tanks → mass increases → sink.
- Expel water → mass decreases → rise.
- Neutral buoyancy: W = F_b while fully immersed.
60-Second Revision
- Ship: hull supplies displacement.
- Submarine: ballast changes mass.
- Rise when F_b > W.
- Sink when F_b < W.
- Equilibrium when Fb = W.
Summary
Ships use hull shape to displace enough water for upthrust to balance weight, while ballast and structure provide stability and strength. Submarines change ballast water, mass and average density to sink, maintain depth or rise.
Ask-the-Tutor Modes
- Explain why steel ships float.
- Compare buoyancy and stability.
- Explain ballast tanks step by step.
- Help with a displacement numerical.
- Check my force-direction reasoning.
- Test me with an MCQ.
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Exam preparation
Exam Focus
Important points
- Ship flotation
- Buoyancy-stability-reliability
- Ballast tanks
- Average density
- Force comparisons
Common mistakes
- Use average vessel density.
- Floating means Fb = W.
- Ballast mainly changes submarine mass.
- Buoyancy and stability are different design requirements.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Ships and Submarines
Sticky Notes · Quick Revision
Floating ship
ρwater gVd = Wship
In words Displaced-water weight equals ship weight.
Ship design
- Buoyancy provides flotation.
- Stability resists overturning.
- Structural reliability withstands loads.
Ballast control
- Flood tanks → weight increases → sink.
- Expel water → weight decreases → rise.
Exam warning
- Use average density of the hollow vessel.
- Neutral buoyancy means balanced forces, not no forces.
Ready to test yourself?
You've completed the learning section.
- 8 concept questions
- Easy → Medium → Hard
- Explanation after each answer
Exam Practice
Important Short Question
Q1. Why does a steel ship float?
Important Short Question
Q2. Name three ship-design requirements.
Conceptual Question
Q3. How does a submarine sink?
Long Question Preparation
Q4. Explain flotation of ships and operation of submarines.
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