Naval Arch 02 - Pressure and Buoyancy

Summary

In this lecture on hydrostatics, Laura Alfred explores the fundamental concepts of pressure and buoyancy. She explains how hydrostatic pressure increases linearly with depth and acts on objects in all directions, and introduces Archimedes' principle, showing that the buoyant force on an object equals the weight of the fluid it displaces. Using examples from ships and blocks, she illustrates how buoyancy depends on submerged volume and water density. The lecture also covers static equilibrium, emphasizing the alignment of a ship's center of gravity and center of buoyancy, and sets the stage for the next topic: stability and how vessels respond to tipping.

Takeaways

• 💧 Hydrostatic pressure is defined as Pz = ρgh, where pressure increases linearly with depth.
• 🌊 Pressure acts on objects in all directions, but the resulting force is normal to the surface it contacts.
• ⚖️ Archimedes' principle states that the buoyant force on an object equals the weight of the fluid displaced.
• 🛶 The buoyant force depends directly on the submerged volume of the object.
• 🚢 Ships experience buoyant forces proportional to their underwater volume, regardless of hull complexity.
• 🌐 Water density varies (saltwater vs freshwater), affecting buoyant force and ship draft.
• ⚓ Static equilibrium requires two conditions: total forces equal zero and sum of moments equal zero.
• 📍 The center of gravity (G) and center of buoyancy (B) must be vertically aligned for equilibrium.
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• 📏 Tipping causes misalignment of G and B, generating moments that disturb equilibrium.
• 🔄 Static equilibrium alone doesn't ensure stability; stability concerns whether the ship returns upright after tipping.
• 📐 Port and starboard symmetry is assumed for ships when analyzing equilibrium and buoyancy.
• 📝 Designers must account for changes in water density to ensure safe ship draft and equilibrium.

Q & A

What is hydrostatic pressure and how is it calculated?

Hydrostatic pressure is the pressure exerted by a fluid at rest. It is calculated using the formula P = ρgh, where ρ is the fluid density, g is the acceleration due to gravity, and h is the depth below the fluid's free surface.

Why is hydrostatic pressure considered a scalar quantity?

Hydrostatic pressure is a scalar because it has magnitude but no inherent direction. Directionality only arises when the pressure acts on a surface, producing a force normal to that surface.

What does Archimedes’ principle state regarding buoyancy?

Archimedes’ principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object, calculated as F_b = ρ g V_displaced.

How does the underwater volume of an object affect its buoyant force?

The buoyant force increases with the submerged volume. A fully submerged object experiences the maximum buoyant force, while partially submerged objects experience less.

Why does water density affect a ship’s buoyancy and draft?

Water density affects buoyancy because the buoyant force depends on the fluid's density. Saltwater is denser than freshwater, so a ship moving from saltwater to freshwater will experience reduced buoyant force, increasing its draft.

What are the two conditions for static equilibrium of a floating ship?

The two conditions are: 1) Force equilibrium – the total buoyant force equals the ship's weight. 2) Moment equilibrium – the sum of moments is zero, which occurs when the center of gravity (G) and the center of buoyancy (B) are vertically aligned.

How are the center of gravity (G) and center of buoyancy (B) defined?

The center of gravity (G) is the point through which the ship's weight acts, while the center of buoyancy (B) is the centroid of the displaced fluid where the buoyant force is considered to act.

What happens if a ship is tipped and G and B are no longer vertically aligned?

If G and B are misaligned, a moment is generated that can rotate the ship. The ship will either return to equilibrium if stable or continue tipping if unstable.

Why is port and starboard symmetry important for ship equilibrium?

Port and starboard symmetry ensures that the centers of gravity and buoyancy align along the centerline of the ship, maintaining stable equilibrium when floating.

What additional concept is needed beyond static equilibrium to ensure a ship’s safety?

Beyond static equilibrium, the concept of stability is needed to determine whether a ship will return upright after being tilted or if it may capsize. Stability analysis considers how the ship reacts to small disturbances.

How is buoyancy visually illustrated for objects and ships in the lecture?

The lecture uses examples of blocks and ships showing that the buoyant force corresponds to the volume submerged in water. Fully submerged objects or underwater ship volumes have the greatest buoyant force, and partially submerged objects have less.

Why does the lecture mention designing ships for both saltwater and freshwater?

Because the density of water affects buoyancy, ships transitioning between saltwater and freshwater need to be designed to handle changes in draft caused solely by the change in water density.