BackFluids: 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.