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Fluids: Properties, Pressure, Buoyancy, and Fluid Dynamics (Lecture 22, Sections 13.1-13.4)

Study Guide - Smart Notes

Tailored notes based on your materials, expanded with key definitions, examples, and context.

Fluids and Density

Definition of Fluids

Fluids are substances that can flow and take the shape of their container. Both liquids and gases are considered fluids. The distinction between them is based on compressibility: gases are highly compressible, while liquids are nearly incompressible.

  • Fluid: A substance that flows; includes liquids and gases.

  • Compressibility: Gases can be compressed easily; liquids resist compression.

Density

Density is a fundamental property of fluids, defined as mass per unit volume.

  • Formula: , where is mass and is volume.

  • SI Units: kg/m3

  • Example: Gasoline has a density of 680 kg/m3, meaning 1 m3 of gasoline has a mass of 680 kg.

Table: Densities of Common Fluids at 1 atm

Fluid

Density (kg/m3)

Air

1.20

Water

1000

Seawater

1030

Gasoline

680

Mercury

13,600

Glycerin

1,300

Oil

900

Gold

19,300

Lead

11,300

Ice

917

Wood

600

Concrete

2,400

Iron

7,800

Alcohol

790

Additional info: Some entries inferred from standard tables.

Example: Mass of Air in a Room

  • Room dimensions: 4.0 m × 6.0 m × 2.5 m = 60 m3

  • Density of air: 1.20 kg/m3

  • Mass:

Pressure in Fluids

Definition of Pressure

Pressure is the force exerted per unit area. In fluids, pressure acts equally in all directions and is responsible for many phenomena, such as buoyancy and fluid flow.

  • Formula: , where is force and is area.

  • SI Unit: Pascal (Pa), where

Pressure in Liquids (Hydrostatic Pressure)

Pressure in a liquid increases with depth due to the weight of the liquid above.

  • Formula: , where is surface pressure, is density, is acceleration due to gravity, and is depth.

  • Hydrostatic Equilibrium: In a connected liquid at rest, pressure is the same at all points on a horizontal line.

Pascal's Principle

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.

Pressure Units

Unit

Abbreviation

Conversion to Pa

Common Uses

Pascals

Pa

1 Pa = 1 N/m2

SI unit, calculations

Atmosphere

atm

1 atm = 101,300 Pa

General, weather

Millimeters of mercury

mm Hg

1 mm Hg = 133 Pa

Barometers, medical

Pounds per square inch

psi

1 psi = 6,890 Pa

Engineering, industry

Example: Pressure at Depth (Submarine)

  • Depth: 300 m

  • Surface pressure: Pa

  • Density of seawater: kg/m3

  • Pressure: Pa

  • Convert to atm: atm

Buoyancy

Buoyant Force

Buoyancy is the upward force exerted by a fluid on an object immersed in it. This force arises because pressure increases with depth, resulting in a net upward force.

  • Archimedes' Principle: The buoyant force equals the weight of the fluid displaced by the object.

  • Formula:

  • Neutral Buoyancy: Occurs when the object's average density equals the fluid's density; the object neither sinks nor floats.

Example: Is the Crown Gold?

  • Weight in air: 8.30 N

  • Tension in water: 7.81 N

  • Buoyant force: N

  • Density calculation: kg/m3

  • Gold's density: 19,300 kg/m3; crown is not pure gold.

Float or Sink?

  • If , the object floats.

  • If , the object sinks.

  • If , the object is neutrally buoyant.

Example: Measuring Density of an Unknown Liquid

  • Wooden block floats with different submerged lengths in two fluids.

  • Equate buoyant forces:

  • Calculate using measured lengths.

Fluids in Motion

Laminar vs. Turbulent Flow

Fluid flow can be classified as laminar (smooth, orderly) or turbulent (chaotic, irregular). The transition depends on the Reynolds number, which compares inertial and viscous forces.

  • Laminar Flow: Fluid moves in parallel layers; velocity at each point is constant.

  • Turbulent Flow: Fluid motion is irregular and mixed.

  • Reynolds Number: High values favor inertial forces (laminar), low values favor viscous forces (turbulent).

Equation of Continuity

For an incompressible fluid, the volume flow rate is constant throughout a tube or pipe.

  • Formula:

  • Volume Flow Rate: (SI units: m3/s)

  • Consequence: Fluid speeds up in narrower sections and slows down in wider sections.

Example: Speed of Water Through a Hose

  • Given: Hose diameter = 16 mm, fills 10 L in 20 s

  • Flow rate:

  • Area:

  • Speed:

  • To quadruple speed, halve the nozzle diameter.

Summary Table: Key Equations

Concept

Equation

Density

Pressure

Hydrostatic Pressure

Buoyant Force

Continuity Equation

Volume Flow Rate

Additional info:

  • Some tables and values inferred from standard physics references.

  • Examples expanded for clarity and completeness.

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