Fluid Mechanics: Buoyancy and Hydrostatic Pressure

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Questions and Answers

What determines whether an object will float, sink, or remain neutrally buoyant in a fluid?

  • The shape of the object
  • The temperature of the fluid
  • The density of the object relative to the fluid (correct)
  • The surface tension of the fluid

In hydrostatic pressure, how does the pressure at a point in a fluid generally change with depth?

  • Pressure decreases as depth increases
  • Pressure remains constant regardless of depth
  • Pressure increases then decreases with depth
  • Pressure increases as depth increases (correct)

What is the center of buoyancy related to a submerged object?

  • The highest point of the object above water
  • The lowest point of the object in the fluid
  • The centroid of the submerged volume displaced by the object (correct)
  • The center of mass of the object itself

According to Archimedes' principle, what does the buoyant force acting on an object equal?

<p>The weight of the fluid displaced by the object (A)</p> Signup and view all the answers

When an object is in a fluid and does not sink or float, it is said to be:

<p>Neutrally buoyant (A)</p> Signup and view all the answers

What happens to the buoyant force if the density of the object is greater than the fluid?

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

In the context of fluid mechanics, hydrostatic pressure is characterized by which of the following?

<p>Forces that act perpendicular to a surface (C)</p> Signup and view all the answers

Which statement accurately describes the relationship between buoyancy and fluid density?

<p>Buoyancy depends on the density difference between the object and the fluid (B)</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

Which condition must be satisfied for a fully submerged body to remain in equilibrium?

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

What indicates a positively stable equilibrium in a floating body?

<p>Metacentric height (GM) is positive (D)</p> Signup and view all the answers

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

<p>It indicates where the buoyant force acts when the body is tilted (B)</p> Signup and view all the answers

Which condition characterizes an unstable equilibrium for a floating body?

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

What must be true for a body to maintain neutral equilibrium?

<p>Center of buoyancy and center of gravity must coincide vertically (D)</p> Signup and view all the answers

In the context of floating bodies, what is the significance of achieving moment balance?

<p>It prevents the body from rotating or tipping over (A)</p> Signup and view all the answers

How do ballast tanks in submarines influence buoyancy?

<p>They allow adjustment of the center of buoyancy (B)</p> Signup and view all the answers

What happens when the center of buoyancy is vertically below the center of gravity when a body is tilted?

<p>The overturning moment will cause further tilting (A)</p> Signup and view all the answers

Which of the following is a practical application of understanding the center of buoyancy?

<p>Creating flotation aids and hydrometers (D)</p> Signup and view all the answers

What does a negative metacentric height (GM < 0) signify?

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

Which factor primarily affects the center of buoyancy for complex shapes?

<p>The dimensions of the submerging volume (B)</p> Signup and view all the answers

Which of the following reflects the equilibrium condition for floating bodies?

<p>Buoyant force must equal the weight of the displaced fluid (C)</p> Signup and view all the answers

What does the vertical alignment of the center of buoyancy and center of gravity determine?

<p>The stability and equilibrium of the floating body (C)</p> Signup and view all the answers

Flashcards

Hydrostatic pressure force

The force exerted by a stationary fluid on a surface.

Buoyancy

Upward force on an object in a fluid.

Archimedes' principle

Buoyant force equals weight of displaced fluid.

Object floats

Buoyant force > weight of object.

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Object sinks

Buoyant force < weight of object.

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Neutral buoyancy

Buoyant force = weight of object.

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Centre of buoyancy

Point where buoyant force acts.

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Submerged volume

Part of object below the fluid surface

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Center of Gravity

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

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Stable Equilibrium (Floating)

The floating object returns to its original position after disturbance, due to center of buoyancy being above the center of gravity

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Unstable Equilibrium (Floating)

The floating object tilts further away from its original position after disturbance, due to center of buoyancy being below the center of gravity

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Neutral Equilibrium (Floating)

The floating object remains in its new position after disturbance, due to center of buoyancy being at same level as center of gravity

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Metacenter

The point where the line of action of buoyant force meets the body's vertical axis, when tilted

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Metacentric Height (GM)

The vertical distance between the center of gravity (G) and metacenter (M).

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Positive GM

Indicates stable equilibrium for a floating object.

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Negative GM

Indicates unstable equilibrium for a floating object.

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Zero GM

Indicates neutral equilibrium for a floating or submerged object.

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Vertical Force Balance (Submerged)

Buoyant force equals the weight of the submerged object

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Horizontal Force Balance

No net horizontal forces acting on the submerged object

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Moment Balance (Submerged)

Center of buoyancy and center of gravity aligned vertically for equilibrium.

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Vertical Force Balance (Floating)

Weight of the floating object equals the buoyant force.

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Submerged equilibrium

Balancing forces and moments for an object completely underwater

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Study Notes

Hydrostatic Pressure Force

  • Hydrostatic pressure force is the force exerted by a stationary fluid.
  • This force acts perpendicular to any surface in contact with the fluid.

Buoyancy and Floatation

  • Buoyancy is the upward force a fluid exerts on an immersed object.
  • Archimedes' Principle: An immersed body experiences an upward buoyant force equal to the weight of the fluid displaced.

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.

Centre of Buoyancy

  • The center of buoyancy (B) is the centroid of the volume of fluid displaced by the object.
  • It's where the buoyant force acts.
  • For complex shapes, calculations might involve integration.

Stability of Floating Bodies

  • Stable equilibrium (GM > 0): Center of buoyancy (B) vertically above center of gravity (G) when tilted. The body returns to its original position.
  • Unstable equilibrium (GM < 0): Center of buoyancy (B) vertically below center of gravity (G) when tilted. The body tips further away from its original position.
  • Neutral equilibrium (GM = 0): Center of buoyancy (B) and center of gravity (G) are at the same vertical level; the body remains in its new position after tilting.

Metacenter and Metacentric Height

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

Practical Applications

  • Ship Design: Ensuring stability; preventing capsizing.
  • Submarines: Controlling buoyancy through ballast tanks.
  • Engineering Structures: Designing stable floating platforms and buoys.
  • Medical Devices: Hydrometers and flotation aids.

Equilibrium of Floating and Submerged Bodies

  • For a submerged body to be in equilibrium:
    • Vertical Force Balance: Buoyant force equals weight.
    • Horizontal Force Balance: No horizontal forces.
    • Moment Balance: Center of buoyancy and center of gravity are vertically aligned.

Equilibrium for Floating Bodies

  • Vertical Force Balance: Weight of the body equals buoyant force.
  • Horizontal Force Balance: No net horizontal forces.
  • Moment Balance: GM is crucial (see above)

Practical Implications

  • Ship design: Managing stability.
  • Submarine operation: Controlling buoyancy.
  • Marine engineering: Designing stable structures.
  • Aerospace engineering: Designing lighter-than-air vehicles.

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