Environmental Fluid Mechanics - Chapter 12 ppt

... also that D  V Dt Ð  V D D Dt  V 2 2  12. 3.5 we substitute Eqs. (12. 3.2) and (12. 3.3) into Eq. (12. 3.1), rewriting the surface integral in Eq. (12. 3.1) as a volume integral, and combine ... important environmental transport pathway, as noted above. The usual approach for calculating volatilization or mass transfer rates is the two-layer model discussed in Sec. 12. 4. Equation (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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... center of gravity, G. The total torque is expressed by Torque D  S 12 C 1 2 ∂S 12 ∂x 1 dx 1  dx 2 dx 1 2 C  S 12  1 2 ∂S 12 ∂x 1 dx 1  dx 2 dx 1 2   S 21 C 1 2 ∂S 21 ∂x 2 dx 2  dx 1 dx 2 2   S 21  1 2 ∂S 21 ∂x 2 dx 2  dx 1 dx 2 2 2.6.2 Copyright ... points. Applying this expression, we obtain a second-order tensor that describes the rate of change of the coordinate inter...

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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 ... that of the kinematic wave. 8.8 NUMERICAL ASPECTS Previous sections of this chapter refer to several typical cases of environmental water waves. The basic concepts are based on th...

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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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... much larger than is usually required, according to continuum mechanics of single-phase materials. In single-phase materials, continuum mechanics requires reference to an elementary volume significantly ... one-and two-dimensional domains, as well as parabolic partial differential equations. However, without denying the value of other books on numerical methods, we find that this textbook in...

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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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