Hydrostatics and Buoyancy Principles

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Questions and Answers

What type of force does hydrostatic pressure exert on surfaces in contact with a fluid?

  • Centripetal force
  • Perpendicular force (correct)
  • Frictional force
  • Tangential force

According to Archimedes' principle, how is the buoyant force on a submerged object determined?

  • It is equal to the weight of the fluid displaced by the object. (correct)
  • It depends on the density of the object alone.
  • It is equal to the volume of the object.
  • It is equal to the weight of the object.

What conditions allow an object to float in a fluid?

  • It is hollow and filled with air.
  • It has the same density as the fluid.
  • It is less dense than the fluid. (correct)
  • It is denser than the fluid.

Where does the buoyant force act on a submerged or floating body?

<p>At the center of buoyancy (C)</p> Signup and view all the answers

What happens to an object that has the same density as the fluid it is in?

<p>It floats freely at any depth. (A)</p> Signup and view all the answers

The center of buoyancy is defined as which of the following?

<p>The centroid of the displaced fluid volume. (A)</p> Signup and view all the answers

What will occur if an object is denser than the fluid it is immersed in?

<p>It will sink. (A)</p> Signup and view all the answers

Which engineering applications primarily utilize the principles of buoyancy?

<p>Ships and submarines (C)</p> Signup and view all the answers

What determines the stability of a floating body?

<p>The relationship between its center of buoyancy and center of gravity (D)</p> Signup and view all the answers

What does a positive metacentric height (GM > 0) indicate about a floating body?

<p>The body is in stable equilibrium (B)</p> Signup and view all the answers

Which condition must be met for a fully submerged body to achieve equilibrium?

<p>The buoyant force must equal the weight of the body (C)</p> Signup and view all the answers

What happens to a floating body if its center of buoyancy is vertically below its center of gravity?

<p>It will tip further away from its original position (D)</p> Signup and view all the answers

The metacenter is defined as what?

<p>The point where the line of action of the buoyant force intersects the vertical axis when tilted (A)</p> Signup and view all the answers

In which condition is a floating body said to be in neutral equilibrium?

<p>The metacenter coincides with the center of gravity (B)</p> Signup and view all the answers

Which of the following applications relies on the principles of buoyancy?

<p>Hydrometers (C)</p> Signup and view all the answers

To maintain stability, ship design must focus on which of the following relationships?

<p>Center of buoyancy positioned relative to the center of gravity (D)</p> Signup and view all the answers

What is a characteristic of unstable equilibrium for floating bodies?

<p>The metacenter is below the center of gravity (C)</p> Signup and view all the answers

What type of equilibrium does a body demonstrate when the buoyant force creates no tendency to return after being tilted?

<p>Neutral Equilibrium (B)</p> Signup and view all the answers

Which of the following is NOT a condition for equilibrium of floating bodies?

<p>Center of buoyancy must be fixed at the waterline (D)</p> Signup and view all the answers

How can submarines control their center of buoyancy?

<p>By using ballast tanks (C)</p> Signup and view all the answers

Which of the following statements about vertical force balance for floating bodies is true?

<p>The weight of the body must equal the buoyant force (B)</p> Signup and view all the answers

In a scenario where a floating body is tilted and does not return to equilibrium, which state of equilibrium is likely present?

<p>Unstable Equilibrium (D)</p> Signup and view all the answers

Flashcards

Hydrostatic Pressure Force

The force exerted by a stationary fluid on a surface, acting perpendicular to the surface.

Buoyancy

The upward force exerted by a fluid on an object immersed in it.

Archimedes' Principle

The buoyant force on an object is equal to the weight of the fluid displaced by the object.

Center of Buoyancy

The centroid of the fluid volume displaced by a submerged or floating object.

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Object less dense than fluid

The buoyant force is greater than the object's weight, causing it to float.

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Object denser than fluid

The buoyant force is less than the object's weight, causing it to sink.

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Neutral Buoyancy

The buoyant force equals the object's weight; object stays at a constant position in the fluid.

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Fluid Statics

The study of fluids at rest.

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Center of Buoyancy Calculation for Complex Shapes

For objects with complex shapes, the center of buoyancy is found by integrating position vectors over the submerged volume. This considers the distribution of displaced fluid and creates a more precise point representing the overall buoyancy force.

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Center of Buoyancy vs. Center of Gravity

The center of buoyancy is the point where the buoyant force acts upward, while the center of gravity is where the object's weight acts downward. Their positions are crucial for stability.

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Stable Equilibrium of a Floating Body

A floating body is in stable equilibrium when its center of buoyancy is vertically above the center of gravity. Tilting creates a righting moment, restoring the body to its original position.

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Unstable Equilibrium of a Floating Body

A floating body is in unstable equilibrium when its center of buoyancy is vertically below the center of gravity. Tilting creates an overturning moment, causing the body to tip further.

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Neutral Equilibrium of a Floating Body

A floating body is in neutral equilibrium when its center of buoyancy and center of gravity are at the same vertical level. It remains in its new position after tilting.

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Metacenter (M)

The metacenter is the point where the line of action of the buoyant force intersects the vertical axis of a floating body when it is tilted.

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Metacentric Height (GM)

The metacentric height is the distance between the center of gravity (G) and the metacenter (M) of a floating body. It's a key measure of stability.

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Positive Metacentric Height

A floating body with a positive metacentric height (GM > 0) is in stable equilibrium. The body will return to its original position after being tilted.

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Negative Metacentric Height

A floating body with a negative metacentric height (GM < 0) is in unstable equilibrium. The body will tip over after being tilted.

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Zero Metacentric Height

A floating body with a zero metacentric height (GM = 0) is in neutral equilibrium. It will remain in its new position after being tilted.

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Equilibrium of Submerged Bodies: Vertical Force Balance

A submerged body is in equilibrium if the buoyant force equals its weight. This ensures that the body neither rises nor sinks due to vertical forces.

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Equilibrium of Submerged Bodies: Horizontal Force Balance

A submerged body is in equilibrium if there are no net horizontal forces acting on it. This means the body is at rest in all horizontal directions.

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Equilibrium of Submerged Bodies: Moment Balance

A submerged body is in equilibrium if the center of buoyancy and the center of gravity are vertically aligned. If not, a moment is generated causing rotation until equilibrium is restored.

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Equilibrium of Floating Bodies: Vertical Force Balance

A floating body is in equilibrium if the buoyant force equals its weight. This means it displaces a volume of fluid whose weight equals its own weight.

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Equilibrium of Floating Bodies: Stability

The stability of a floating body, determined by the relationship between its center of gravity and center of buoyancy, is influenced by the metacenter and metacentric height.

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Study Notes

Hydrostatic Pressure Force

  • Hydrostatic pressure force is the force exerted by a stationary fluid, acting perpendicular to any surface it contacts.
  • It's crucial for understanding how fluids exert force in various engineering applications.

Buoyancy and Floatation

  • Buoyancy is the upward force exerted by a fluid on an immersed object.
  • Archimedes' principle: An object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.
  • Conditions of buoyancy:
    • Object less dense than fluid: Floats (buoyant force > weight).
    • Object denser than fluid: Sinks (buoyant force < weight).
    • Object same density as fluid: Remains neutrally buoyant.
  • Center of buoyancy: The centroid of the displaced fluid volume; the point where the buoyant force acts.
  • Relationship between center of buoyancy (B) and center of gravity (G): Critical for stability.
  • Stability (floating bodies):
    • Stable equilibrium: B is above G (righting moment).
    • Unstable equilibrium: B is below G (overturning moment).
    • Neutral equilibrium: B is at the same level as G.

Metacenter and Metacentric Height

  • Metacenter (M): Point where the line of action of the buoyant force intersects the vertical axis when tilted.
  • Metacentric height (GM): Distance between the center of gravity (G) and the metacenter (M).
  • Stability related to GM:
    • Positive GM: Stable equilibrium.
    • Negative GM: Unstable equilibrium.
    • Zero GM: Neutral equilibrium.

Equilibrium of Floating and Submerged Bodies

  • Equilibrium conditions (submerged bodies):
    • Vertical force balance: Buoyant force equals the body's weight.
    • Horizontal force balance: No net horizontal forces.
    • Moment balance: B and G are vertically aligned.
  • Equilibrium conditions (floating bodies):
    • Vertical force balance: Body weight equals buoyant force.
    • Horizontal force balance: No net horizontal forces.
    • Moment balance and stability: GM is crucial.
      • Stable equilibrium: Positive GM.
      • Unstable equilibrium: Negative GM.
      • Neutral equilibrium: Zero GM.
  • Practical applications: Ship design, submarine operation, marine engineering, and aerospace engineering.

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