Environmental Fluid Mechanics - Chapter 11 ppsx

... 0att>0,x D1 11. 3.7c The Laplace transform of Eqs. (11. 3.6), (11. 3.7b), and (11. 3.7c), respectively, yields ∂ 2 C ∂x 2  V D ∂ C ∂x  p C D 0whereC D Cx, p 11. 3.8 C D C 0 p at x D 0 11. 3.9a C ... D y ∂ 2 C ∂y 2 11. 4.13 For steady-state conditions, we apply the following approximations (refer to Eqs. 11. 3.14 and 11. 3.27): D y D a T V (11. 4.14a) C D C 0 1 Á n Á D y υ (1...

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... students with appro- priate fluid mechanics backgrounds. Although the book addresses principles of fluid mechanics relevant to the entire environment, the emphasis is mostly on water-related issues. The ... Rights Reserved. Contents Preface Part 1 Principles of Environmental Fluid Mechanics 1. Preliminary Concepts 1.1 Introduction 1.2 Properties of Fluids 1.3 Mathematical Preliminarie...

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... to D  V Dt C2   ð  V C D   Dt ð  r C   ð   ð  rD  g  1   rp Cvr 2  V 2.9 .11 For problems in environmental fluid mechanics, the frame of reference is the earth’s surface, so that   represents ... to Eq. 2.8 .11) , then Eq. (2.9.20) becomes  V Ð  rgH Dε2.9.22 If ε ¾ D 0, then this is the Bernoulli equation, also derived in Sec. 2.8. Note that for steady flow, the...

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... solutions of these equations, as shown below. 3.2 ONE-DIRECTIONAL FLOWS One-directional flows are characterized by parallel streamlines. For conve- nience, consider that the flow is along the x coordinate ... fluid mechanics refers to different methods of solving these differential equations. For the present section, we consider only the numer- ical solution of creeping flows. In such flows the r...

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... two- dimensional flows, which are the most common situation for analysis using potential flow theory. There also is some discussion of axisymmetric flows, and numerical solutions of two- and three-dimensional ... three-dimensional flows. 4.2 TWO-DIMENSIONAL FLOWS AND THE COMPLEX POTENTIAL 4.2.1 General Considerations In cases of potential, incompressible, two-dimensional flows, velocity compo- nen...

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... discussion of its application to several specific issues of environmental fluid mechanics. Special attention also is given to the development and prop- agation of waves in open channels and rivers. Internal ... moving observers can be traced on the x–t plane, as shown in Fig. 8 .11. The first family of characteristics shown in Fig. 8 .11, referring to the observer moving with velocity V C...

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... oceans. Another interesting effect of rotation can be seen on wind-driven cur- rents, where the velocity field is formed into the so-called Ekman spiral. Consider a flow far from any boundaries, with ... NJ. Pedlosky, Joseph, 1987. Geophysical Fluid Dynamics, 2 ND Ed. Springer-Verlag, New York. Rossby, C. G., 1932. A generalization of the theory of the mixing length with appli- cation to atmo...

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... in the x-direction are shown in Fig. 10.6, but similar fluxes may be defined for the y-andz-directions. Using a truncated Figure 10.6 Fluid element, showing fluxes of species 1 in the x-direction. Copyright ... Rights Reserved. 10 Environmental Transport Processes 10.1 INTRODUCTION The field of environmental fluid mechanics spans a broad range of topics. Though based primarily on fluid mec...

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... and Ghosh, U., 1995. Surface aeration. J. of Environmental Engineering 121(1) :113 118 . Chapra, S. C., 1997. Surface Water Quality Modeling. McGraw-Hill, Boston. Danckwerts, P. V., 1951. Significance ... This is the same as the steady-state solu- tion for C BOD , if dispersion is neglected and time t is replaced with travel time (x/U). In other words, for a steady-state problem in which dis...

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... D. R. F., 1961. Stratified flow. In Handbook of Fluid Mechanics, ed. V. L. Streeter, ch. 26, McGraw-Hill, New York. Lighthill, James, 1978. Waves in Fluids. Cambridge University Press, Cambridge. Philips, ... mean (time- averaged) quantities, and U is the time-averaged velocity in the upper layer. The left-hand side of this equation is the time rate of change of TKE, the first term on the rig...

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