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?

At the center of buoyancy Signup and view all the answers

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

It floats freely at any depth. Signup and view all the answers

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

The centroid of the displaced fluid volume. Signup and view all the answers

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

It will sink. Signup and view all the answers

Which engineering applications primarily utilize the principles of buoyancy?

Ships and submarines Signup and view all the answers

What determines the stability of a floating body?

The relationship between its center of buoyancy and center of gravity Signup and view all the answers

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

The body is in stable equilibrium Signup and view all the answers

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

The buoyant force must equal the weight of the body Signup and view all the answers

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

It will tip further away from its original position Signup and view all the answers

The metacenter is defined as what?

The point where the line of action of the buoyant force intersects the vertical axis when tilted Signup and view all the answers

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

The metacenter coincides with the center of gravity Signup and view all the answers

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

Hydrometers Signup and view all the answers

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

Center of buoyancy positioned relative to the center of gravity Signup and view all the answers

What is a characteristic of unstable equilibrium for floating bodies?

The metacenter is below the center of gravity 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?

Neutral Equilibrium Signup and view all the answers

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

Center of buoyancy must be fixed at the waterline Signup and view all the answers

How can submarines control their center of buoyancy?

By using ballast tanks Signup and view all the answers

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

The weight of the body must equal the buoyant force 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?

Unstable Equilibrium Signup and view all the answers

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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Description

Test your knowledge on hydrostatic pressure and buoyancy concepts. This quiz emphasizes Archimedes' principle and the conditions that determine whether an object will float or sink in a fluid. Understanding these principles is essential for various applications in engineering and physics.