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Fluids

In this unit we study the physics of fluids. So we start with the obvious question, what precisely is a “fluid?” In colloquial English people mistakenly think that “fluid” and “liquid” are the same thing, but that isn’t quite right.

A fluid is any substance that

  • continually deforms (flows) under an applied force.

So this includes not only liquids, but also gases and plasmas.

Example of a plasma
Plasma ball
Example of a liquid (lake water)
seeming-momentum-violation-canoe-jumping-in-lake
Example of a gas – an airplane flying through air (illuminated by a laser.)
newtons 3rd law airplane reaction
.

Why study fluid dynamics?

Flows are beautiful and complex. A swollen creek tumbles over rocks and through crevasses, swirling and foaming. A child plays with sticky taffy, stretching and reshaping the candy as she pulls and twists it in various ways. Both the water and the taffy are fluids, and their motions are governed by the laws of nature.

Our goal is to introduce readers to the analysis of flows using the laws of physics and the language of mathematics. On mastering this material, readers can harness flow to practical ends or create beauty through fluid design.

In this text we delve into the mathematical analysis of flows; however, before beginning, it is reasonable to ask if it is necessary to make this significant mathematical effort.

After all, we can appreciate a flowing stream without understanding why it behaves as it does. We also can operate machines that rely on fluid behavior—drive a car, for example—without understanding the fluid dynamics of the engine. We can even repair and maintain engines, piping networks, and other complex systems without having studied the mathematics of flow.

What is the purpose, then, of learning to mathematically describe fluid behavior? The answer is quite practical: Knowing the patterns that fluids form and why they are for med, and knowing the stresses that fluids generate and why they are generated, is essential to designing and optimizing modern systems and devices.

from An Introduction to Fluid Mechanics, Faith A. Morrison, Cambridge Univ Press

Fluid dynamics 1

This infographic is from Océ, A Canon company.

One example of using fluid dynamics is in inkjet printers.

Fluid dynamics 2

This infographic is from Océ, A Canon company.

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Topic outline from Giancoli Physics, Chapter 10: Fluids

Giancoli PPT Chap 10 Fluids Pascal’s Principle Buoyancy

Topic outline from College Physics, OpenStax

Rice University, by Paul Peter Urone, California State University, Sacramento, and Roger Hinrichs, State University of New York, College at Oswego, Creative Commons Attribution License v4.0

11.1 What Is a Fluid?

  • State the common phases of matter.
  • Explain the physical characteristics of solids, liquids, and gases.
  • Describe the arrangement of atoms in solids, liquids, and gases.

11.2 Density

  • Define density.
  • Calculate the mass of a reservoir from its density.
  • Compare and contrast the densities of various substances.

11.3 Pressure

  • Define pressure.
  • Explain the relationship between pressure and force.
  • Calculate force given pressure and area.

11.4 Variation of Pressure with Depth in a Fluid

  • Define pressure in terms of weight.
  • Explain the variation of pressure with depth in a fluid.
  • Calculate density given pressure and altitude.

11.5 Pascal’s Principle

  • Define pressure.
  • State Pascal’s principle.
  • Understand applications of Pascal’s principle.
  • Derive relationships between forces in a hydraulic system.

11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement

  • Define gauge pressure and absolute pressure.
  • Understand the working of aneroid and open-tube barometers.

11.7 Archimedes’ Principle

  • Define buoyant force.
  • State Archimedes’ principle.
  • Understand why objects float or sink.
  • Understand the relationship between density and Archimedes’ principle.

11.8 Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action

  • Understand cohesive and adhesive forces.
  • Define surface tension.
  • Understand capillary action.

11.9Pressures in the Body

  • Explain the concept of pressure the in human body.
  • Explain systolic and diastolic blood pressures.
  • Describe pressures in the eye, lungs, spinal column, bladder, and skeletal system.

11.10. Glossary

11.11. Section Summary

11.12. Conceptual Questions

11.13. Problems & Exercises

12.1 Flow Rate and Its Relation to Velocity

  • Calculate flow rate.
  • Define units of volume.
  • Describe incompressible fluids.
  • Explain the consequences of the equation of continuity.

12.2 Bernoulli’s Equation

  • Explain the terms in Bernoulli’s equation.
  • Explain how Bernoulli’s equation is related to conservation of energy.
  • Explain how to derive Bernoulli’s principle from Bernoulli’s equation.
  • Calculate with Bernoulli’s principle.
  • List some applications of Bernoulli’s principle.

12.3 The Most General Applications of Bernoulli’s Equation

  • Calculate using Torricelli’s theorem.
  • Calculate power in fluid flow.

12.4 Viscosity and Laminar Flow; Poiseuille’s Law

  • Define laminar flow and turbulent flow.
  • Explain what viscosity is.
  • Calculate flow and resistance with Poiseuille’s law.
  • Explain how pressure drops due to resistance.

12.5 The Onset of Turbulence

  • Calculate Reynolds number.
  • Use the Reynolds number for a system to determine whether it is laminar or turbulent.

12.6 Motion of an Object in a Viscous Fluid

  • Calculate the Reynolds number for an object moving through a fluid.
  • Explain whether the Reynolds number indicates laminar or turbulent flow.
  • Describe the conditions under which an object has a terminal speed.

12.7Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

  • Define diffusion, osmosis, dialysis, and active transport.
  • Calculate diffusion rates.

12.8. Glossary

12.9. Section Summary

12.10. Conceptual Questions

12.11. Problems & Exercises

Learning standards

2016 Massachusetts Science and Technology/Engineering Standards
HS-PS1-3. Cite evidence to relate physical properties of substances at the bulk scale to spatial arrangements, movement, and strength of electrostatic forces among ions, small molecules, or regions of large molecules in the substances. Make arguments to account for how compositional and structural differences in molecules result in different types of intermolecular or intramolecular interactions.

HS-ETS4-4(MA). Calculate and describe the ability of a hydraulic system to multiply distance, multiply force, and effect directional change. Clarification Statement: • Emphasis is on the ratio of piston sizes (cross-sectional area) as represented in Pascal’s law

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

PS1.A Structure of matter (includes PS1.C, nuclear processes)

That matter is composed of atoms and molecules can be used to explain the properties of substances, diversity of materials, how mixtures will interact, states of matter, phase changes, and conservation of matter. States of matter can be modeled in terms of spatial arrangement, movement, and strength of interactions between particles. Characteristic physical properties unique to each substance can be used to identify the substance.

PS1.A: STRUCTURE AND PROPERTIES OF MATTER

The arrangement and motion of atoms vary in characteristic ways, depending on the substance and its current state (e.g., solid, liquid). Chemical composition, temperature, and pressure affect such arrangements and motions of atoms, as well as the ways in which they interact. Under a given set of conditions, the state and some properties (e.g., density, elasticity, viscosity) are the same for different bulk quantities of a substance, whereas other properties (e.g., volume, mass) provide measures of the size of the sample at hand.

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