Fluid Mechanics Chapter 13
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Questions and Answers

What does Pascal's Law state about pressure in a closed system?

  • Pressure is transmitted equally to all parts of the container. (correct)
  • Pressure is dependent on the size of the container.
  • Pressure varies at different points in the fluid.
  • Pressure decreases with increasing fluid depth.

How does fluid pressure change with depth according to hydrostatic principles?

  • It decreases as depth increases.
  • It only changes if the container shape varies.
  • It increases with depth. (correct)
  • It remains constant regardless of depth.

What is buoyant force proportional to according to Archimedes's Principle?

  • The weight of the object.
  • The volume of the fluid in the container.
  • The weight of the fluid displaced by the object. (correct)
  • The density of the object.

In a fluid at rest, how does the pressure compare at different elevations?

<p>Pressure is lower at the surface than in deeper levels. (B)</p> Signup and view all the answers

Which unit is used to measure pressure in the context of barometric pressure?

<p>Millimeters of mercury (mm Hg) (C)</p> Signup and view all the answers

What happens to an object's buoyancy when it is submerged in a fluid?

<p>It can float if the buoyant force exceeds its weight. (A)</p> Signup and view all the answers

How is gauge pressure defined in relation to absolute pressure?

<p>Gauge pressure excludes the atmospheric pressure. (A)</p> Signup and view all the answers

What factor primarily varies to affect the pressure transmitted throughout a fluid in a closed system?

<p>The depth of the fluid. (B)</p> Signup and view all the answers

What is the primary cause of hydrostatic pressure in a fluid?

<p>The density of the fluid (A)</p> Signup and view all the answers

Pascal's Principle states that when pressure is applied to a confined fluid, it increases uniformly in all directions. What is a practical application of this principle?

<p>Hydraulic lifts (D)</p> Signup and view all the answers

How does the pressure in a fluid change with increasing depth?

<p>It increases (C)</p> Signup and view all the answers

In incompressible fluids, what factor does NOT affect the pressure at a certain depth?

<p>Volume of the fluid (C)</p> Signup and view all the answers

What is the relationship between pressure and depth in a fluid at equilibrium?

<p>Pressure increases linearly with depth (C)</p> Signup and view all the answers

What is the hydrostatic pressure at a depth of 300 m in seawater, given that the surface pressure is 101 kPa and the density of seawater is 1030 kg/m³?

<p>30.9 atm (B), 3.13 × 10⁶ Pa (D)</p> Signup and view all the answers

According to Pascal's principle, what happens to the pressure at all points in an incompressible fluid when the pressure at one point is increased?

<p>Pressure at every point in the fluid increases by the same amount. (A)</p> Signup and view all the answers

What can be concluded about the pressures at two different depths in a fluid at rest?

<p>Pressure increases linearly with depth. (B), Pressure at shallower depth is less than at deeper depth. (D)</p> Signup and view all the answers

If pressure at the surface of a liquid is increased by 50 kPa, what will be the change in pressure at a point 10 m deep?

<p>50 kPa at all points including depth (A)</p> Signup and view all the answers

How does the density of a liquid affect the hydrostatic pressure at a given depth?

<p>Lower density decreases hydrostatic pressure. (A), Higher density increases hydrostatic pressure. (C)</p> Signup and view all the answers

Which equation correctly describes the relationship between pressure and depth in a fluid?

<p>p = p₀ + ρgd (D)</p> Signup and view all the answers

At what condition is the pressure equal at all points along a horizontal line in a connected fluid?

<p>In hydrostatic equilibrium (B)</p> Signup and view all the answers

Which of the following is true about the pressure at points 1 and 2 beneath a floating iceberg?

<p>Pressure at point 1 is equal to pressure at point 2. (A)</p> Signup and view all the answers

What is the effect of increasing depth on the pressure exerted by a fluid?

<p>Pressure increases with depth. (A)</p> Signup and view all the answers

What is the relationship expressed by Bernoulli's equation?

<p>It relates pressure, fluid speed, and height. (C)</p> Signup and view all the answers

In a fluid system, what does a decrease in fluid speed at one point imply according to Bernoulli's principle?

<p>An increase in height or pressure. (B)</p> Signup and view all the answers

How does the pressure change with depth in a fluid according to hydrostatic principles?

<p>Pressure increases with depth. (B)</p> Signup and view all the answers

How is Pascal's principle related to pressure in incompressible fluids?

<p>Pressure is constant throughout an incompressible fluid. (A)</p> Signup and view all the answers

What happens to fluid pressure when it flows through a pipe that narrows?

<p>Pressure decreases as velocity increases. (D)</p> Signup and view all the answers

What is the pressure gauge reading on the upper pipe if the lower pipe's gauge reads 75 kPa and the flow velocity changes?

<p>It is lower due to decreased pressure as velocity changes. (B)</p> Signup and view all the answers

Using Bernoulli's equation, if the speed of fluid decreases, what can be inferred about the pressure?

<p>Pressure must increase. (D)</p> Signup and view all the answers

What effect does height have on fluid pressure in a static fluid?

<p>Lower heights correspond to higher pressure. (D)</p> Signup and view all the answers

How does the velocity of water relate to the cross-sectional area in a pipe according to the equation of continuity?

<p>Velocity decreases as cross-sectional area increases. (A)</p> Signup and view all the answers

What can be inferred about the pressure at points in a connected fluid on a horizontal line?

<p>Pressure remains constant at all points on the line. (C)</p> Signup and view all the answers

If the pressure at point 1 is greater than that at point 2, what conclusion can be drawn about point 3?

<p>p2 = p3 and both are less than p1 (A)</p> Signup and view all the answers

What is the primary factor affecting hydrostatic pressure in a fluid?

<p>The density of the fluid and the depth (C)</p> Signup and view all the answers

In a closed tube filled with liquid, how does the pressure at the top compare to the pressure at the liquid's surface?

<p>The pressure at the top is lower than at the surface. (C)</p> Signup and view all the answers

How does the pressure at a given depth in a fluid change with an increase in the fluid density?

<p>Pressure increases proportionately to density. (A)</p> Signup and view all the answers

Which equation is correct for calculating the pressure at a certain depth in a fluid?

<p>p = p0 + ρgd (B)</p> Signup and view all the answers

What is the relationship between gauge pressure and absolute pressure?

<p>Absolute pressure includes atmospheric pressure. (A)</p> Signup and view all the answers

Which of the following best describes Pascal's principle?

<p>Pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid. (D)</p> Signup and view all the answers

When observing a liquid column, how does increasing the height of the column affect the pressure at its base?

<p>The pressure at the base increases linearly with height. (B)</p> Signup and view all the answers

What happens to the pressure in a liquid if it is incompressible when a piston is pushed down?

<p>Pressure increases throughout the liquid (C)</p> Signup and view all the answers

Flashcards

1 atm

Standard atmospheric pressure, equal to 101.3 kPa.

Pressure in a fluid (same elevation)

Pressure is the same throughout a fluid layer at the same depth, regardless of container shape or size.

Pascal's Law

In a closed system, pressure changes transmitted to a fluid are identical throughout the system. Changes in pressure are dependent on the fluid's depth.

Absolute Pressure

Total pressure, including atmospheric pressure, as opposed to gauge pressure (pressure relative to atmospheric pressure).

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Buoyant Force

Upward force exerted on an object submerged in a fluid. Equals the weight of the fluid displaced by the object.

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Archimedes' Principle

An object submerged in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.

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Buoyancy (upward force)

The upward force exerted on an object immersed in a fluid, caused by the difference in pressure at different depths within the fluid.

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Pressure Units

Different units used to measure pressure, including atm, mm Hg, in, psi.

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Hydrostatic Pressure

The pressure exerted by a fluid at rest due to the force of gravity.

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Hydrostatic Equilibrium

A state where a fluid is at rest and the pressure is the same at all points on a horizontal line.

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Pascal's Principle

If pressure changes at one point in an incompressible fluid, the pressure changes by the same amount at every other point in the fluid.

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Pressure at a Depth

The pressure at a depth in a fluid is equal to the pressure at the surface plus the pressure due to the weight of the fluid above it.

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Pressure in Connected Liquid

In hydrostatic equilibrium, a connected liquid rises to the same height in all open regions of the container, and the pressure is equal on a horizontal line.

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Pressure Variation

Changing pressure at the surface of a fluid results in a corresponding change in pressure at all depths.

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Submerged Object Pressure

Pressure increases with depth in a fluid.

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Submarine Pressure

The pressure on an object submerged in a fluid, like a submarine, is determined by the pressure at the surface, density of the fluid, and depth.

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Points 1 and 2 Pressure (QuickCheck 13.1)

If points 1 and 2 are at the same horizontal level, the pressures are equal, assuming the same fluid type. If 1 is at a higher depth, the pressure at 1 is higher.

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What is a fluid?

A substance that flows, like liquids and gases. Liquids are nearly incompressible, while gases are easily compressed.

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Density

The ratio of mass to volume of a substance. Measured in kg/m³. It tells you how much mass is packed into a given space.

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What's the difference between a liquid and a gas?

Liquids are nearly incompressible, meaning their volume doesn't change much under pressure. Gases are compressible, meaning their volume can easily change based on pressure.

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What is the SI unit of density?

The SI unit of density is kilograms per cubic meter (kg/m³). It's how many kilograms of a substance are crammed into 1 cubic meter.

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How do you calculate density?

Density is calculated by dividing the mass of an object by its volume. Density = Mass / Volume. This tells you how much mass is packed into a given space.

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Horizontal Line Pressure Equality

Pressure in a connected fluid is the same at all points on a horizontal line.

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Pressure at Different Points

In a connected fluid, the pressure varies with depth and remains the same on any horizontal line.

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Pressure at Open Surface

If a surface of a fluid is open to the atmosphere, the pressure there equals the atmospheric pressure.

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Gauge Pressure

Pressure measured relative to atmospheric pressure.

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Hydrostatic Pressure Equation

p = p0 + ρgd, where p is pressure, p0 is reference pressure, ρ is fluid density, g is acceleration due to gravity, and d is depth.

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Reference Pressure (p0)

The pressure at a chosen reference point of a system.

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Connected Fluid

Fluids that are joined or in contact such that pressure changes occur in one part of the system and propagate to other parts.

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Atmospheric Pressure

Pressure exerted by the Earth's atmosphere.

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Fluid Density

Mass per unit volume of a fluid.

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Bernoulli's Equation

Relates pressure, fluid speed, and height at two points along a streamline, assuming ideal fluid flow.

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Ideal Fluid

A theoretical fluid with no viscosity (no internal friction), incompressible, and irrotational (no swirling motion).

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Equation of Continuity

States that the mass flow rate of an incompressible fluid stays constant through a pipe.

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Pressure in a fluid (different elevations)

Pressure in a fluid decreases as height increases, assuming constant fluid speed.

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What does Bernoulli's equation tell us?

It explains how pressure, velocity, and height are related in ideal fluid flow.

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What is pressure gauge reading?

Measures the difference between absolute pressure and atmospheric pressure.

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How does pressure change in a pipe going uphill?

Pressure decreases as the elevation increases, assuming constant fluid speed.

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What happens to fluid velocity when the pipe narrows?

Fluid velocity increases as the pipe narrows, assuming constant flow rate.

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Why is pressure lower in a narrower part of a pipe?

The higher velocity in the narrower pipe requires a lower pressure to maintain energy conservation.

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What is 1 atm?

Standard atmospheric pressure, equal to 101.3 kPa.

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Study Notes

Chapter 13: Fluid Mechanics

  • Fluid mechanics is the study of fluids (liquids and gases) in motion and at rest.
  • Key concepts include density, pressure, buoyancy, surface tension, fluid flow, Bernoulli's equation, viscosity, and turbulence.

Section 13.1: Density

  • A fluid is a substance that flows. Liquids and gases are fluids.
  • Gases are compressible; the volume of a gas can easily be changed.
  • Liquids are nearly incompressible; the molecules are closely packed, yet they can move around.
  • Density is the ratio of mass to volume. (density = mass/volume)
  • SI units of mass density are kg/m³.

Section 13.2: Pressure

  • Pressure is the ratio of force to area on which the force is exerted. (pressure = force/area)
  • Liquids exert forces on the walls of their containers.
  • The pressure in a fluid is everywhere in the fluid, not just at the bottom or the walls of the container.
  • Pressure at a depth in a fluid depends on the vertical depth, not on horizontal direction
  • Hydrostatic pressure is pressure from the weight of a fluid acting on an object.
  • The pressure at depth is p = ρ₀ + ρgd, where ρ₀ is atmospheric pressure, ρ is the density, g is the acceleration due to gravity, and d is the depth below the surface.
  • Pascal's Principle states: If the pressure at one point in an incompressible fluid is changed, the pressure at every other point in the fluid changes by the same amount.

Section 13.3: Buoyancy

  • Buoyant force is the weight of the fluid displaced by the object.
  • Archimedes' principle: A fluid exerts an upward buoyant force on an object immersed in or floating on the fluid. The magnitude of the buoyant force equals the weight of the fluid displaced by the object.
  • Archimedes' principle in equation form is: FB = ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.
  • An object sinks if its weight is greater than the buoyant force, floats if the buoyant force is larger, and has neutral buoyancy if they are equal.

Section 13.4: Surface Tension and Capillarity

  • Molecules in a liquid are attracted to neighboring molecules.
  • At the surface, the unbalanced attractions cause the surface to resist being stretched, this is surface tension.
  • Interactions between the fluid and the container walls are significant, this is capillarity.

Section 13.5: Fluids in Motion

  • Two types of flow:
    • Laminar flow: regular and smooth
    • Turbulent flow: irregular and difficult to model.
  • Incompressible fluids: the volume of the fluid does not change with pressure.
  • Steady flow: the fluid velocity at each point in the fluid is constant.
  • Volume flow rate: Q (volume per second). Q = vA, where v is velocity and A is the cross-sectional area. The volume flow rate is constant in the same incompressible fluid tube.

Equation of Continuity

  • ( A_1V_1 = A_2V_2 )
  • This equation shows how the velocity of a fluid in a tube changes with the cross-sectional area of the tube. The speed of the fluid becomes faster in narrower portions of the tube.

Bernoulli's Equation

  • ( P_1 + \frac{1}{2} \rho v_1^2 + \rho g y_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g y_2 )
    • This equation relates pressure, velocity, and height of a fluid at different points in a tube. - P is pressure, ρ is density, v is velocity, and y is height.

Applications of Bernoulli's effects

  • Lift on airplane wings

  • Flow of fluids in tubes

  • Atmospheric pressure and weather.

  • Density values for various substances are provided in tables.

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Description

Explore the fundamental concepts of fluid mechanics in Chapter 13. This quiz covers key topics such as density, pressure, and the behavior of liquids and gases. Test your understanding of important equations and principles like Bernoulli's equation, viscosity, and turbulence.

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