Hydrostatics: Pressure, Buoyancy, and Stability

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Questions and Answers

What is hydrostatic pressure force primarily characterized by?

  • It is only relevant in dynamic fluid situations.
  • It acts parallel to the surface in contact with the fluid.
  • It only affects curved surfaces.
  • It acts perpendicular to any surface in contact with the fluid. (correct)

Which principle governs the concept of buoyancy?

  • Newton's third law
  • Archimedes' principle (correct)
  • Pascal's principle
  • Bernoulli's principle

What happens to an object that is less dense than the fluid it is immersed in?

  • It will dissolve in the fluid.
  • It will remain neutrally buoyant.
  • It will float. (correct)
  • It will sink quickly to the bottom.

Where does the buoyant force act on a submerged object?

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

What characteristic does an object need to maintain neutrality in buoyancy?

<p>It must have the same density as the fluid. (B)</p> Signup and view all the answers

What is the center of buoyancy defined as?

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

If the buoyant force is less than the weight of an object, what will happen?

<p>The object will sink. (C)</p> Signup and view all the answers

Which application is NOT related to the principles of buoyancy?

<p>Building bridges (D)</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 (B)</p> Signup and view all the answers

What is stable equilibrium in the context of floating bodies?

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

What happens when the center of buoyancy is below the center of gravity?

<p>The body will continue to tilt further away from its original position (A)</p> Signup and view all the answers

How is the metacentric height (GM) defined?

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

What indicates that a floating body is in unstable equilibrium?

<p>The metacentric height is negative (A)</p> Signup and view all the answers

What is required for a fully submerged body to achieve equilibrium?

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

What does neutral equilibrium signify for a floating body?

<p>The body remains in its new position after being tilted (C)</p> Signup and view all the answers

What role does the metacenter (M) play in the stability of floating bodies?

<p>It indicates the point of intersection of the buoyant force's line of action with the vertical axis (B)</p> Signup and view all the answers

What condition allows a floating body to remain at rest in the horizontal direction?

<p>There should be no horizontal forces acting on the body (C)</p> Signup and view all the answers

Which factor does NOT affect the position of the center of buoyancy?

<p>The weight of the object (B)</p> Signup and view all the answers

What occurs when there is an alignment of center of gravity and center of buoyancy?

<p>The object is in neutral equilibrium (D)</p> Signup and view all the answers

What does it imply if the metacentric height (GM) is zero?

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

In which application is understanding the center of buoyancy particularly critical?

<p>Designing floating platforms (D)</p> Signup and view all the answers

What happens when the vertical force balance is not maintained in a submerged body?

<p>The body will experience a net downward force and sink (C)</p> Signup and view all the answers

Flashcards

Hydrostatic Pressure Force

The force exerted by a stationary fluid acting perpendicular to any surface it contacts.

Buoyancy

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

Archimedes' Principle

The buoyant force on a submerged object equals the weight of the fluid displaced by the object.

Object less dense than fluid

Buoyant force is greater than object's weight, causing it to float.

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Object denser than fluid

Buoyant force is less than object's weight, causing it to sink.

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Object same density as fluid

Buoyant force equals object's weight; object remains neutrally buoyant.

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Center of Buoyancy

The centroid of the fluid volume displaced by the object; where the buoyant force acts.

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Fully Submerged Object Center of Buoyancy

The centroid of the submerged volume

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Center of Gravity

The point where the weight of an object acts vertically downward.

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Stable Equilibrium

A floating object will return to its original position after being tilted.

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Unstable Equilibrium

A floating object will continue to tilt after being tilted.

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Neutral Equilibrium

A floating object stays in its new position after being tilted.

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Metacenter

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

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Metacentric Height

The distance between the center of gravity and the metacenter.

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Positive Metacentric Height

Indicates stable equilibrium.

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Negative Metacentric Height

Indicates unstable equilibrium.

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Vertical Force Balance (submerged)

Buoyant force equals the weight of the body.

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Horizontal Force Balance

No horizontal forces are acting on the body.

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Moment Balance (submerged)

The centers of buoyancy and gravity must be vertically aligned.

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Vertical Force Balance (floating)

Gravity equals buoyant forces.

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Moment Balance (floating)

Stability depends on the center of gravity (G) and center of buoyancy (B).

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Metacenter above CG

Indicates stable equilibrium.

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Study Notes

Hydrostatic Pressure Force on Surfaces

  • Hydrostatic pressure force acts perpendicular to surfaces in contact with a fluid.
  • Its calculation and application are crucial in various engineering contexts.

Buoyancy and Floatation

  • Buoyancy: Upward force exerted by a fluid on an immersed object.
  • Archimedes' principle: Buoyant force equals the weight of the displaced fluid.
  • Conditions for Buoyancy
    • Object floats if less dense than the fluid.
    • Object sinks if denser than the fluid.
    • Object remains neutrally buoyant if densities are equal.

Center of Buoyancy

  • Center of buoyancy: Point where the buoyant force acts on a submerged or floating body.
  • It's the centroid of the displaced fluid volume.
  • For simple shapes, calculation is straightforward. Complex shapes require integration.
  • Position relative to the center of gravity is crucial for stability.
  • For floating objects, stability depends on relationship between the center of buoyancy and center of gravity.

Stability of Floating Bodies

  • Stable equilibrium: Center of buoyancy above center of gravity. Body returns to initial position after tilt.
  • Unstable equilibrium: Center of buoyancy below center of gravity. Body tilts further after disturbance.
  • Neutral equilibrium: Center of buoyancy and center of gravity are vertically aligned. Body stays in tilted position.

Metacenter and Metacentric Height

  • Metacenter: Point where the buoyant force intersects the vertical axis after tilt.
  • Metacentric height (GM): Distance between center of gravity and metacenter.
  • Positive GM: Stable equilibrium.
  • Negative GM: Unstable equilibrium.
  • Zero GM: Neutral equilibrium

Practical Applications (Buoyancy, Floatation, and Stability)

  • Ship design: Stability considerations related to centre of buoyancy and gravity.
  • Submarines: Adjusting ballast to control buoyancy.
  • Engineering structures: Designing stable floating platforms.
  • Medical devices: Designing devices using buoyancy principles.

Equilibrium of Floating and Submerged Bodies

  • Equilibrium condition for submerged bodies:

    • Vertical force balance: Buoyant force equals weight.
    • Horizontal force balance: No net horizontal forces.
    • Moment balance: Vertical alignment of center of buoyancy and gravity.
  • Equilibrium condition for floating bodies:

    • Vertical force balance: Weight of the body equals buoyant force.
    • Horizontal force balance: No net horizontal forces.
    • Moment balance and stability:
      • Stable equilibrium: Metacenter above center of gravity (GM>0).
      • Unstable equilibrium: Metacenter below center of gravity (GM<0).
      • Neutral equilibrium: Metacenter coincides with center of gravity (GM=0).
  • Practical Implications:

    • Ship and boat design.
    • Submarine operation.
    • Marine engineering.
    • Aerospace engineering (e.g., hot air balloons).

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