Environmental Fluid Mechanics - Chapter 13 pot

... developed from Eqs. (13. 3.37)– (13. 3.39), along with Eqs. (13. 3.49) and (13. 4.5), ∂u j ∂x j D 0 13. 4.6 ∂u ∂t D 1  0 ∂p 0 ∂x C r 2 u 13. 4.7 ∂ v ∂t D 1  0 ∂p 0 ∂y C r 2 v 13. 4.8 ∂w ∂t D 1  0 ∂p 0 ∂z   0  0 g ... ∂z  ∂ 2 w ∂y 2  13. 4.12 Making a substitution as in Eq. (13. 2.17) for the velocity gradients, this becomes  ∂ ∂t  r 2  r 2 w Dgr 2 h ˛T 0 C ˇS 0  13....

Ngày tải lên: 11/08/2014, 13:21

... issues of environmental fluid mechanics. Special attention also is given to the development and prop- agation of waves in open channels and rivers. Internal waves are presented in Sec. 13. 2. Copyright ... h]gcosωt  kx 8.5.13b Using Eq. (8.3.12), w is found from Eq. (8.5 .13) for z D 0, and the resulting expression is integrated over time to obtain the relationship between the poten-...

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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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... for the stresses of soil mechanics. It can easily be verified that the equations (13. 8) are equivalent to (13. 6) and (13. 7) if K = E 3(1 − 2ν) , (13. 9) G = E 2(1 + ν) . (13. 10) For the description ... both must be positive, K > 0 and G > 0. 13. 3 A non-linear material In the previous chapter it has been argued that soils are non-linear and non-elastic. Furthermore, soils are of...

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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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... are equal to zero. In such a flow the velocity vector originates from a potential function, namely E V Dr or u i D ∂ ∂x i 2.3 .13 Potential flows are discussed in greater detail in Chap. 4. The circulation ... points. Applying this expression, we obtain a second-order tensor that describes the rate of change of the coordinate intervals per unit length. This second-order tensor can be separa...

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... potential (irrota- tional) vortex with circulation ,givenby  D 2 1 r 2 1 3.2.32 The solution of the Navier–Stokes equations given by Eq. (3.2.31) is an inter- esting case in which the potential ... 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...

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... 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- nents are derived from the potential ... 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 th...

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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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