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Questions and Answers
What determines whether an object will float, sink, or remain neutrally buoyant in a fluid?
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?
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?
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?
According to Archimedes' principle, what does the buoyant force acting on an object equal?
When an object is in a fluid and does not sink or float, it is said to be:
When an object is in a fluid and does not sink or float, it is said to be:
What happens to the buoyant force if the density of the object is greater than the fluid?
What happens to the buoyant force if the density of the object is greater than the fluid?
In the context of fluid mechanics, hydrostatic pressure is characterized by which of the following?
In the context of fluid mechanics, hydrostatic pressure is characterized by which of the following?
Which statement accurately describes the relationship between buoyancy and fluid density?
Which statement accurately describes the relationship between buoyancy and fluid density?
What determines the stability of a floating body?
What determines the stability of a floating body?
Which condition must be satisfied for a fully submerged body to remain in equilibrium?
Which condition must be satisfied for a fully submerged body to remain in equilibrium?
What indicates a positively stable equilibrium in a floating body?
What indicates a positively stable equilibrium in a floating body?
What is the role of the metacenter (M) in the stability of floating bodies?
What is the role of the metacenter (M) in the stability of floating bodies?
Which condition characterizes an unstable equilibrium for a floating body?
Which condition characterizes an unstable equilibrium for a floating body?
What must be true for a body to maintain neutral equilibrium?
What must be true for a body to maintain neutral equilibrium?
In the context of floating bodies, what is the significance of achieving moment balance?
In the context of floating bodies, what is the significance of achieving moment balance?
How do ballast tanks in submarines influence buoyancy?
How do ballast tanks in submarines influence buoyancy?
What happens when the center of buoyancy is vertically below the center of gravity when a body is tilted?
What happens when the center of buoyancy is vertically below the center of gravity when a body is tilted?
Which of the following is a practical application of understanding the center of buoyancy?
Which of the following is a practical application of understanding the center of buoyancy?
What does a negative metacentric height (GM < 0) signify?
What does a negative metacentric height (GM < 0) signify?
Which factor primarily affects the center of buoyancy for complex shapes?
Which factor primarily affects the center of buoyancy for complex shapes?
Which of the following reflects the equilibrium condition for floating bodies?
Which of the following reflects the equilibrium condition for floating bodies?
What does the vertical alignment of the center of buoyancy and center of gravity determine?
What does the vertical alignment of the center of buoyancy and center of gravity determine?
Flashcards
Hydrostatic pressure force
Hydrostatic pressure force
The force exerted by a stationary fluid on a surface.
Buoyancy
Buoyancy
Upward force on an object in a fluid.
Archimedes' principle
Archimedes' principle
Buoyant force equals weight of displaced fluid.
Object floats
Object floats
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Object sinks
Object sinks
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Neutral buoyancy
Neutral buoyancy
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Centre of buoyancy
Centre of buoyancy
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Submerged volume
Submerged volume
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Center of Gravity
Center of Gravity
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Stable Equilibrium (Floating)
Stable Equilibrium (Floating)
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Unstable Equilibrium (Floating)
Unstable Equilibrium (Floating)
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Neutral Equilibrium (Floating)
Neutral Equilibrium (Floating)
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Metacenter
Metacenter
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Metacentric Height (GM)
Metacentric Height (GM)
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Positive GM
Positive GM
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Negative GM
Negative GM
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Zero GM
Zero GM
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Vertical Force Balance (Submerged)
Vertical Force Balance (Submerged)
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Horizontal Force Balance
Horizontal Force Balance
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Moment Balance (Submerged)
Moment Balance (Submerged)
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Vertical Force Balance (Floating)
Vertical Force Balance (Floating)
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Submerged equilibrium
Submerged equilibrium
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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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