Sinopsis
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 formed, and knowing the stresses that fluids generate and why they are generated, is essential to designing and optimizing modern systems and devices. The ancients designed wells and irrigation systems without calculations, but we can avoid the waste and tedium of the trial-and-error process by using mathematical models. Some inventions, such as helicopters and lab-on-a-chip reactors, are sufficiently complex that they never would have been designed without mathematical models. Once a system is modeled accurately, it is then straightforward to calculate operating variables such as flow rates and pressures or to evaluate proposed design or operating changes. A mathematical understanding of fluids is important in fields such as airplane and space flight, biomedicine, plastics processing, volcanology, enhanced oil recovery, pharmaceuticals, environmental remediation, green energy, and astrophysics. Although a trial-and-error approach can get us started in fluids-related problems, significant progress requires formal mathematical analysis.
Content
- Why Study Fluid Mechanics?
- How Fluids Behave
- Modeling Fluids
- Molecular Fluid Stresses
- Stress-Velocity Relationships
- Microscopic Balance Equations
- Internal Flows
- External Flows
- Macroscopic Balance Equations
- How Fluids Behave (Redux)
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