9. Hydroelectric dams: Most dramatic examples of fluid mechanics in action are hydroelectric dams. They are huge in size and equally impressive in power they can generate using completely renewable resource; water. The steel and concrete structure of hydroelectric dam holds back millions of tons of water from the river or other body. The water nearest the top has enormous potential energy. Hydroelectric power is generated by allowing controlled streams of this water to flow downward, collecting kinetic energy that is then transferred to powering turbines, which in turn creates electric power.
Partial differential equations arise naturally in mathematical physics and have numerous applications in real life. The present book mainly focuses on fluid mechanics, elasticity, and their interactions. As a typical model of such phenomena, one may consider the fluid-structure interactions between the wind and a suspension bridge. Not much is known about the mechanisms generating instabilities (in a broad sense) and many problems are still open, while an interdisciplinary approach is necessary for a betterunderstanding of all the involved phenomena.
Shear: can be defined as the strain that is created when the layers of the fluid are shifted in comparison to others, because of the application of some pressure over the structure of the fluid. One concept that needs to be looked into detail is shear rate; this is the proportion at which the different layers of the fluid will move past the neighbouring layers; it is dependent on the geometry of the flow and also on its speed.
Some fluids present a stress that is linearly relational to the strain at each point of it. The stress and the strain are directly proportional. These are called Newtonian Fluids. There are several examples of Newtonian fluids that are used in everyday life, such as water, hydrocarbons (oil and gas), alcohol, glycerine and many others.
Several factors control the behaviour of the dilatant fluids, namely, the profile, particle size, spreading and the proportion of particle density that are suspended in the fluid. The so-called suspension observes this behaviour when it changes from a stable state to one of flocculation, under the application of some type of stress . This happens because in cases where the material is subjected to high levels of stress, they quickly become very stiff.
There have been studies on the applications of shear thickening fluids; it has been noticed that this type of material can be used for many commercial applications such as body armours, sporting protective clothing and other products.
Recently, there have been a huge amount of studies that aim to look into the applications of shear-thickening fluids to solve problems that have been observed in protective gear. This paper is going to introduce this new technology and explain how it helps and contributes for this industry.
This procedure just helps to prove that shear-thickening fluids indeed improve the penetration forces and also improve the resistance of the equipment. I would suggest the application of this process for protective armours for the police or other entities responsible for the protection of the country, because it reduces the necessity of creating heavier armours, which were in the past considered to be more effective in responding to impacts.
It is clear that Rheology it is a very broad science and that many concepts make part of it. There are basically two types of fluids, which are, Newtonian and non-Newtonian fluids. There are several examples of Newtonian fluids in our daily lives, such as water, hydrocarbons and others .
There is now a world of possibilities because of this new technology that has been studied. However, although the dilatant fluids have been the main focus globally, it would be a good step to look now into the benefits of the other types of non-Newtonian fluids, because they might also be very useful for other industries and areas that are highly dependent on the viscosity of the materials. It is time now to take these fluids out of the laboratories and implement their properties into daily life issues, so that they can be used to solve the problems of the populations. Surely, with the advance of researches and technologies, the world is looking forward to a new era, where the focus is not only on those fluids whose behaviour is already known and understood (Newtonian fluids), but also into what for so long had been a mystery.
This course presents an introduction to the (broad) discipline of fluidmechanics and describes the relationship between fluid mechanics and geologicalprocesses. A lecture outline is given below.The principles of conservation of mass, momentum and energy that arethe basis of fluid mechanics are relatively straightforward, and can beeasily derived. Finding solutions to these equations is in general notstraightforward, and only in very special cases can exact solutions beobtained. Most often (justifiable) approximations must be made to the equationsand boundary conditions in order to obtain solutions. In this class wewill derive or present the very simple governing equations of fluid mechanics(they only appear simple -- these equations describe the rich complexityof flows we see in everyday life: flows in rivers, the atmosphere, wavesin the ocean, flows in the bathtub and kitchen sink, flying airplanes,etc.); we will then look at the different simplifications that can be madefor various classes of problems that allow us to understand the main featuresof common problems in geological and environmental fluid mechanics.For more information about fluid mechanics people and courses at UC Berkeleyvisit Berkeley FluidsClass meeting times:Formal lectures are held Monday and Wednesday from 1:30-3:00 pm.There can be an optional discussion section (time to be arranged) to reviewbasic math, and discuss progress with term projects.Prerequisites:We will be solving ordinary AND partial differential equations in thisclass. We will also be doing lots of vector calculus (sometimes involvingsecond, third and even fourth rank tensors). The first problem set willcover some of the basic mathematical topics that will be commonly used(and are also commonly useful). Integral relations and equations are alsovery useful, but are unfortunately not usually covered in undergraduateclasses.Text and notes:The most suitable book for this class is probably Fluid Physicsin Geology by D.J. Furbish (Oxford University Press,1997). You can compare its table of contents with the topics we coverin class in order to determine what pages you should read.In the outline below I provide references to books other that Furbish.I also include at the end of the outline a list of recommended references.Instructor:Michael Manga (3-8532), McCone 177manga@seismoThere is no GSI for this class.Course evaluation:Homework 25 %Midterm 15 %Final exam 15 %Term paper/project 35 %Term paper/project presentation 10 %Term projects:The term project clearly accounts for a substantial part of the evaluation.The topic of the project is chosen by each student. For undergraduate students,a critical literature review is sufficient. Graduate students, however,must also describe a research project aimed at understanding some processor addressing an unsolved problem. All students are encouraged to attemptto actually solve a problem, wither numerically, or experimentally; equipment,facilities and/or computers may be available.If appropriate studentsmay also work in groups in order to work on more involved projects.Students who register in the class can receive a more detailedlist of suggested projects as a pdf file by email -- contact firstname.lastname@example.org once you register
OutlineIntroduction and governing equations (August 27, 29)What are fluids? The continuum hypothesis (Batchelor, pp 1-6; Faber 2-4;Heuberger et al., Science, vol. 292, 905-908, 2001;Arfken, pp 10-37; handout -- all these will be made available)Vectors, tensors, stress Conservation equations for mass, momentum, energy (Leal, chapter 2)Boundary conditionsHomeworknumber 1 due Wednesday September 5; you can download Wood's editorial hereHomeworknumber 2 due Monday September 10Homeworknumber 3 due Monday September 17Supplemental notes onthe conservation equations and some useful vector identitiesScaling and unidirectional flows (September 5, 10)Scaling and dimensional analysis (Middleton and Wilcock, chapter 3; Fowler, chapter 1)Homeworknumber 4 due Wednesday September 19Unidirectional flows (Leal, chapter 3)Homeworknumber 5 due Monday September 24Special limits, features of flows (September 17, 19, 24 and 26)Different limits, e.g., Stokes flows, incompressible flow, irrotational flows, etc. (Hinch, Chapter 3 in Disorder and Mixing;Tritton, chapters 8, 10)Check out NASA's airfoil pageVorticity (Tritton, sections 6.4-6.6)Boundary layersLubrication theoryHomeworknumber 6 due Monday October 1Homeworknumber 7 due Monday October 8Waves (October 1, 3)Waves (Lighthill, chapter 3; Cushman-Roisin, appendix A)Lab, time TBD (perhaps October 29 or 31?) -- Kelvin-Helmholtz instabilities Homeworknumber 8 due Monday October 17Turbulence (October 8)Turbulence (Middleton and Wilcock, chapter 11; Tritton, section 20.4)MIDTERM ON WEDNESDAY OCTOBER 10Gravity currents (October 15, 17)Gravity currents (book by Simpson)Rheology of geological materials and fluidsHomeworknumber 9 due Wednesday November 7Convection (October 22, 24)Convection, including double-diffusive convection (paper by Kadanoff, Physics Today, 2001; Tritton, chapters 14, 22, 23)Homeworknumber 10 due Wednesday November 14Porous materials (November 5, 7)Flow in porous materials (Turcotte and Schubert, chapter 9)Optional questionsMicrohydrodynamics (bubbles and crystals in liquids) (November 14, 19, 26)A few other topics (November 26, 28)Effects of rotation (Cushman-Roisin, chapter 1)Life in moving fluids (Vogel, Life in Moving Fluids)Second midterm Dec 5, in classTerm project presentations (time and date TBD)This is obviously a lot of material, and as a result the course will bemore descriptive than most fluid mechanics classes with an emphasis onscaling analysis.Recommended referencesMy favorite general fluid mechanics books:Batchelor, G.K., An introduction to fluid dynamics, Cambridge UniversityPress, 1967.Faber, T.E., Fluid dynamics for physicists, Cambridge UniversityPress, 1995.Van Dyke, M., An album of fluid motion, Parabolic, 1982.Tritton, D.J., Physical fluid dynamics, Oxford University Press,1988.Landau, L.D. and E.M. Lifshitz, Fluid mechanics, Pergamon Press,1987.Some other books that are very useful references:Middleton, G.V. and P.R. Wilcock, Mechanics in the earth and environmentalsciences, Cambridge University Press, 1994.Furbish, D., Geological fluid mechanics, Oxford University Press.Pedlosky, J., Geophysical fluid dynamics, Springer-Verlag, 1987.Phillips, O.M., Flow and reactions in permeable rocks, CambridgeUniversity Press, 1991.Cushman-Roisin, B., Introduction to geophysical fluid dynamics,Prentice Hall, 1994.Lighthill, J., Waves in fluid, Cambridge University Press, 1978.Turcotte, D.L. and G. Schubert, Geodynamics, John Wiley and Sons,1982.Leal, L.G., Laminar flow and convection transport processes, Butterworth-Heineman,1992.Simpson, J.E., Gravity currents, Cambridge University Press, 1997.Turner, J.S., Buoyancy effects in fluids, Cambridge University Press,1973.Guyon, E., et al., Physical hydrodynamics,Oxford Univ Press, 2001.Whitaker, S., Introduction of Fluid Mechanics,Prentice-Hall, 1968 (nice, simple explanations without sacrificingrigour). 2b1af7f3a8