Fluid Mechanics: Archimedes' Principle Quiz
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Questions and Answers

Which scenario describes a body that is floating on the surface of a fluid according to Archimedes' Principle?

  • The density of the body is greater than the fluid.
  • The body is fully submerged in the fluid.
  • The density of the body is equal to the fluid.
  • The density of the body is less than the fluid. (correct)

What is the formula for surface tension as described in the content?

  • σ = pV/T
  • σ = A/S (correct)
  • σ = m/V
  • σ = F/l (correct)

What does surface tension allow insects to do on water?

  • Submerge completely without sinking.
  • Skip across the water's surface.
  • Float and slide on the water surface. (correct)
  • Dive underwater and resurface easily.

How is surface tension defined in terms of energy or work?

<p>The work needed to increase the surface area of a liquid. (C)</p> Signup and view all the answers

Which statement correctly describes a body in equilibrium in a fluid according to Archimedes' Principle?

<p>The body's density equals the fluid's density. (C)</p> Signup and view all the answers

Which measurement unit is used for surface tension?

<p>Dynes per centimeter. (C)</p> Signup and view all the answers

What is the relationship between force and length in the context of surface tension?

<p>Surface tension is directly proportional to force divided by length. (C)</p> Signup and view all the answers

What role does Archimedes' Principle play in determining breast asymmetry?

<p>It helps assess tissue density change after liquid immersion. (D)</p> Signup and view all the answers

What happens to a balloon when a needle disrupts its surface?

<p>Air is driven out due to a pressure gradient. (D)</p> Signup and view all the answers

According to Laplace's law, what is the relationship between extra pressure and curvature radius for spherical objects?

<p>Extra pressure decreases with increasing radius. (B), Extra pressure increases with decreasing radius. (C)</p> Signup and view all the answers

What conditions lead to a positive additional pressure in a convex meniscus?

<p>Convex curvature of the surface. (C)</p> Signup and view all the answers

What type of fluid displays a convex meniscus when interacting with solid materials?

<p>Non-wetting fluid (B)</p> Signup and view all the answers

What is the cosine angle relationship for a wetting fluid?

<p>Cos θ is less than 90 degrees (C)</p> Signup and view all the answers

In a long round cylinder, how do the curvature radii R1 and R2 relate to its structure?

<p>R1 equals R and R2 equals infinity. (D)</p> Signup and view all the answers

When the tangent angle between water and mercury equals 90 degrees, what does this indicate?

<p>Equal surface tension of the fluid and solid (B)</p> Signup and view all the answers

How does increasing the curvature radius affect tension in the balloon walls according to Laplace's law?

<p>Tension decreases with increasing curvature radius. (B), Tension increases to maintain the same delta P value. (D)</p> Signup and view all the answers

What impact does an increase in temperature have on the surface tension coefficient (σ)?

<p>It decreases (A)</p> Signup and view all the answers

Which formula correctly represents the additional pressure for a thin liquid membrane?

<p>ΔP = σ(K) (B)</p> Signup and view all the answers

What is the significance of the curvature radius in relation to extra pressure?

<p>Smaller curvature radius results in greater extra pressure. (A), Larger curvature radius results in reduced extra pressure. (D)</p> Signup and view all the answers

What does the equation F = σl represent regarding surface tension?

<p>Force is proportional to the length of the surface contour (A)</p> Signup and view all the answers

Which of the following statements is true for a fluid with a negative cosine angle value?

<p>It has a convex meniscus (D)</p> Signup and view all the answers

What concept explains why tension in balloon walls must increase when curvature radius increases?

<p>Laplace’s law of pressure difference. (B), Pascal's law regarding hydrostatic pressure. (C)</p> Signup and view all the answers

What does the drop detachment method measure in biological fluids?

<p>Surface tension coefficient (A)</p> Signup and view all the answers

What occurs when two fluids have equal surface tension at critical temperature?

<p>Surface tension becomes zero (A)</p> Signup and view all the answers

What term is used to describe energy per unit of area for solids as well as liquids?

<p>Surface energy (D)</p> Signup and view all the answers

What happens to surface free energy at fluid static equilibrium?

<p>It minimizes at minimum area (A)</p> Signup and view all the answers

Why do water droplets assume a spherical shape?

<p>To minimize surface free energy (C)</p> Signup and view all the answers

What does a concave meniscus indicate about the fluid properties?

<p>Fluid-solid interaction is stronger than fluid-fluid interaction (C)</p> Signup and view all the answers

What creates the tension on the surface of water?

<p>Resultant forces from water-air interaction (C)</p> Signup and view all the answers

What is NOT a characteristic of surface tension?

<p>It applies only to non-compressible fluids (A)</p> Signup and view all the answers

Which factor contributes to the downward force on water surface molecules?

<p>The interaction of air molecules above (C)</p> Signup and view all the answers

What is an example of a waiting fluid?

<p>One where fluid-solid interactions are stronger (B)</p> Signup and view all the answers

What happens to the walls of arteries with large radius according to Laplace's law?

<p>They can be thicker and have fibril belts. (D)</p> Signup and view all the answers

How does hypertension affect the structural integrity of blood vessels?

<p>It increases the tension leading to potential damage. (B)</p> Signup and view all the answers

What causes hydrostatic pressure to increase when diving deeper into water?

<p>Increased water height above the head (C)</p> Signup and view all the answers

During dilatative cardiomyopathy, how does the curvature of the heart change?

<p>It becomes more cylindrical. (A)</p> Signup and view all the answers

What risk does thinning of the heart walls pose during normal pressure conditions?

<p>It increases the risk of malfunction in blood pumping. (C)</p> Signup and view all the answers

How is fluid hydrostatic pressure determined?

<p>By the exertion of gravity forces on fluid mass (C)</p> Signup and view all the answers

What effect does an aortic aneurysm have on the aortic walls?

<p>They flat and thin while tension increases. (D)</p> Signup and view all the answers

According to Pascal's principle, what happens when pressure is applied to a fluid in a smaller diameter tube?

<p>Pressure is equally distributed in both tubes (C)</p> Signup and view all the answers

Why are gas bubbles in blood vessels particularly dangerous?

<p>They are resistant to the pressure of the blood and block circulation. (C)</p> Signup and view all the answers

What happens to the displacement distance of fluid in a smaller diameter tube compared to a larger diameter tube when pressure is applied?

<p>It is more in the smaller diameter tube (A)</p> Signup and view all the answers

What is required for a vapor bubble to expand according to the principles described?

<p>The temperature must be high enough for vapor pressure to exceed ambient pressure. (D)</p> Signup and view all the answers

What occurs in a U-tube filled with two different fluids with different densities?

<p>The pressure will be equal if densities are equal (B)</p> Signup and view all the answers

What phenomenon occurs when water is superheated?

<p>It remains stable despite high vapor pressure. (A)</p> Signup and view all the answers

Which of the following devices is an application of the U-tube principle?

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

What is typically used in manometers to measure pressure due to its properties?

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

What is a major advantage of using Pascal's principle in hydraulic systems?

<p>It allows for lifting heavy objects with less effort (D)</p> Signup and view all the answers

Flashcards

Fluid Hydrostatic Pressure

The pressure exerted by a stationary fluid due to the force of gravity acting on its mass.

Pascal's Principle

The pressure in a fluid is the same at all points at the same depth.

Hydraulic Press

A device that uses Pascal's principle to amplify force. It consists of two cylinders connected by fluid, with different diameters.

U-Tube Principle

The height difference between two columns of fluid in a U-shaped tube is proportional to the difference in their densities.

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Manometer

A device used to measure the pressure of liquids and gases. It typically consists of a U-shaped tube filled with a dense liquid like mercury.

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Pressure-Depth Relationship

The pressure exerted by a fluid at a given depth is directly proportional to the depth and the density of the fluid.

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Pressure Transmission in Fluids

A fluid in a closed container will transmit pressure equally in all directions.

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Pressure Equality at the Same Level

Pressure is equal at the same horizontal level in a connected fluid regardless of shape.

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Contact angle (θ)

The angle between a tangent to the liquid surface at the point of contact with the solid and the solid surface.

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Meniscus

The curved upper surface of a liquid in a narrow container.

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Wetting fluid

A liquid that tends to spread out on a solid surface, forming a concave meniscus. The fluid molecules have stronger attraction to the solid surface than to each other.

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Non-wetting fluid

A liquid that tends to minimize contact with a solid surface, forming a convex meniscus. The fluid molecules have stronger attraction to each other than to the solid surface.

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Surface tension

The force acting along the boundary line of a liquid surface, causing the surface to behave as if it were an elastic membrane.

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Surface tension coefficient (σ)

A measure of the force required to stretch or break the surface of a liquid.

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Surface Tension for Insects

Insects can float and slide on water even though they are denser because of this property of water.

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Archimedes' Principle

This principle states that buoyancy force acting on an object submerged in a fluid equals the weight of the fluid displaced by the object.

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Body Density and Buoyancy

The difference in density between a body and a fluid determines whether the body will float, sink, or remain in equilibrium.

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Buoyancy Force

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

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Specific Gravity

The ratio of an object's density to the density of a reference substance, usually water.

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Archimedes' Principle in Medicine: CNS

Cerebrospinal fluid (CSF) density changes are measured through this principle, helping diagnose spinal cord conditions.

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Archimedes' Principle in Medicine: Breast Density

Breast density changes related to pathology are identified using the buoyancy principle after breast immersion in liquid.

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Surface Free Energy

The energy required to increase the surface area of a liquid by a unit amount.

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Contact Angle

The angle formed between the surface of a liquid and a solid surface it's in contact with. It depends on the relative forces between the liquid molecules and the solid surface.

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Laplace's Law for Spherical Objects

The pressure difference between the inside and outside of a spherical object is directly proportional to the surface tension of the object and inversely proportional to the radius of curvature.

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Laplace's Law for Cylindrical Objects

The pressure difference between the inside and outside of a cylindrical object is directly proportional to the surface tension of the object and inversely proportional to the radius of curvature.

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Curvature Radius

The curvature radius is inversely proportional to the curvature of a surface.

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Pressure Difference in Liquid Drops and Gas Bubbles

The pressure difference between the inside and outside of a liquid drop or gas bubble is determined by the surface mean curvature of the membrane.

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Curvature Radius and Extra Pressure

When the curvature radius is greater at a given tension, the extra pressure will be less.

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Additional Pressure and Surface Mean Curvature

At any point on the surface of a thin liquid membrane, the additional pressure is dependent on the surface mean curvature at that point.

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Pressure Difference and Meniscus Shape

Pressure difference caused by surface curvature is positive for a convex meniscus and negative for a concave meniscus.

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Tension and Curvature Radius in a Balloon

The tension of a balloon is inversely proportional to the curvature radius, which means that larger areas of a balloon will have greater tension.

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Laplace's Law

A law stating that the tension in a curved surface, like a blood vessel wall, is proportional to the pressure inside and the radius of curvature. Thicker walls are needed for larger radii to maintain the same pressure.

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Dilatative Cardiomyopathy

A condition where a heart's chambers become wider and thinner, reducing their ability to pump blood efficiently. This is due to increased tension required to maintain pressure in a larger chamber, as per Laplace's Law.

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Aneurysm

A localized bulge in an artery caused by a weakened arterial wall. The wall becomes thinner and the pressure inside increases, creating a risk of rupture. Laplace's Law explains why this occurs.

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Gas Embolism

A condition where gas bubbles become trapped within blood vessels. These bubbles can obstruct blood flow despite the pressure exerted by blood. The surface tension of the gas bubbles helps them resist collapse, as per Laplace's Law.

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Pressure Inside A Sphere

The pressure exerted by a curved surface, like a bubble. The pressure is higher due to the surface tension pulling the liquid inwards. This is an example of Laplace's Law in action.

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Superheating

A phenomenon where a liquid remains in a liquid state even though its vapor pressure exceeds the surrounding atmospheric pressure. This is because the surface tension of the liquid prevents bubbles from forming and expanding.

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Study Notes

Fluids Biomechanics

  • Fluids statics studies fluids at rest or in equilibrium
  • Fluids dynamics studies fluids in motion

Hydrostatics

  • Fluid pressure is the force per unit area exerted by a fluid, caused by its weight
  • Pressure (P) is the force per unit area (F/A) acting perpendicular to a surface.
  • Liquid pressure is the force per unit surface area from a fluid layer or fluid itself. (P = F/A)

Pascal's Law

  • In a confined fluid (gas or liquid), a pressure change in one part is transmitted equally throughout the fluid and to the container walls.
  • Pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid.
  • The pressure ratio (initial difference) remains the same in all points of a horizontal plane, despite container shape, because height (h) is the same.

Hydrostatic Pressure

  • Hydrostatic pressure is the pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity.
  • Hydrostatic pressure increases proportionally to depth measured from the surface.
  • When diving deeper in water, hydrostatic pressure increases due to the increase in water height above your head.
  • (P = pgh), where p is the fluid density, g is acceleration due to gravity, and h is the height of the fluid column.

Fluid Hydrostatic Pressure at Different Points

  • Fluid hydrostatic pressure is the pressure of a non-moving (static) fluid.
  • It is determined by the exertion of gravity forces on the fluid (fluid mass).
  • The pressure created by a static fluid column (with height h) is proportional to the column height, and is calculated by the formula (P = pgh).

Hydraulic Press

  • Two interconnected cylinders (arms) with different diameters, filled with fluid.
  • When a compressor/piston pushes on a smaller diameter tube, the pressure is distributed equally (Pascal's principle), leading to a force gain in the larger diameter tube.
  • Gain in force is realized because the larger area generates a larger force, despite the same pressure. The same pressure applied to a larger area generates greater force.
  • This principle is used in various applications, especially in lifting heavy objects.

U-Pipe Principle

  • If a U-tube is filled with two different fluids with different densities (p1 and p2), the following equation applies: h1/h2 = p2/p1.
  • If the densities are equal(p1 = p2), the heights of the fluid columns (h1 and h2) will be equal.

Archimedes' Law

  • A body immersed in a fluid experiences an upward force (buoyant force) equal to the weight of the fluid displaced by the body.
  • (F_A = ρf g V_body), where F_A is the buoyant force, ρf is the fluid density, g is the acceleration due to gravity, and V_body is the volume of the body immersed.
  • Objects that are less dense than the surrounding fluid will float; those that are denser will sink; those with equal density are in equilibrium.

Surface Tension

  • Surface tension is the tendency of fluid surfaces to minimize surface area.
  • Surface tension allows insects to float on water.
  • Surface tension is measured in dynes/cm
  • Surface tension (σ) is equal to force per unit length (F/l)
  • Surface tension is also equivalent to energy per unit area (A/S)
  • The value of surface tension is dependent on the properties of the fluid, and neighboring area.
  • In case of deficiency of external forces, minimum surface energy matches with minimum area, which means fluid surface is smooth.

Wetting and Non-Wetting Fluids

  • Wetting fluids have a concave meniscus in a capillary tube, and their contact angle (θ) with the solid material is less than 90 degrees.
  • Non-wetting fluids have a convex meniscus in a capillary tube, and their contact angle (θ) with the solid material is greater than 90 degrees.

Capillary Effect

  • Capillarity is the ability of a liquid to flow in narrow spaces without external force or gravity, like in fine tubes (capillary tubes, porous materials etc).
  • It is related to fluid surface increase or decrease in thin open capillary compared to surrounding fluid level. (h = 2σ cosθ/p g r)
  • Capillarity is important in many biological and medical processes, including blood clotting time determination, and medical drain.
  • Liquid height in a capillary tube depends on the balance of upward forces (determined by surface tension and radius) and downward force (due to weight of the liquid).

Laplace's Law

  • Laplace's Law describes the relationship between pressure, tension, and curvature in curved surfaces.
  • Relates excess pressure inside a curved surface to the surface tension and radius of curvature.
  • For spherical surfaces: ΔP = 2T/R; for cylindrical surfaces: ΔP = T/R.
  • The larger the curvature radius, the lower the pressure difference.

Tension in Arterial Walls

  • The tension in arterial walls (and other vessels) is proportional to the internal pressure and radius.
  • T = PR, where T is the tension, P is the internal pressure, and R is the radius.
  • Larger arteries need stronger walls to withstand the higher internal pressure.
  • Arteries are reinforced by fibrous bands to prevent aneurysms.

Pressure Inside the Sphere

  • Superheating, which is when a liquid is heated above its boiling point without turning to vapor, is possible for large bubbles.
  • Smaller bubbles will be stable due to the higher tension, because at larger areas tension decreases.

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Test your understanding of fluid mechanics concepts focused on Archimedes' Principle and surface tension. This quiz covers key scenarios, formulas, and applications of these principles in real-world contexts. Dive into the physics that govern how objects interact with fluids.

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