Environmental Fluid Mechanics - Chapter 8 pot

... of Eqs. (8. 7.19) and (8. 7.20) are given, respectively, by dx dt D V C c dx dt D V  c 8. 7.21 If the terms on the right-hand sides of Eqs. (8. 7.19) and (8. 7.20) are small, then Eq. (8. 7.19) indicates ... x  ∂Q ∂t C ∂QV ∂x  8. 7 .8 Combining Eqs. (8. 7.7) and (8. 7 .8) yields   ∂Q ∂t C ∂ ∂x QV  DA ∂h ∂x   0 P 8. 7.9 where h is the elevation of the water surface, given b...

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... NJ. Pedlosky, Joseph, 1 987 . 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 atmospheric ... models that consider constant values of ˇ are called beta-plane models. The first term on the right-hand side of Eq. (9.5 .8) is the vertical compo- nent of the curl of the wind stress vect...

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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, 19 78. Waves in Fluids. Cambridge University Press, Cambridge. Philips, ... Oxford. Sherman, F. S., Imberger, J. and Corcos, G. M., 19 78. Turbulence and Mixing in stably stratified waters. Ann. Rev. Fluid Mech. 10:267– 288 . Stommel, H., Arons, A. B. and Bla...

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... by υU i υt D   ∂U i ∂x k C i  jk U j   dx k dt 1.3. 38 The left-hand side of Eq. (1.3. 38) represents a contravariant vector. The term dx k /dt also is a contravariant vector. Therefore, the expression between paren- theses of Eq. (1.3. 38) is ... Rights Reserved. Contents Preface Part 1 Principles of Environmental Fluid Mechanics 1. Preliminary Concepts 1.1 Introduction 1.2 Prop...

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... of Eq. (2 .8. 5) is neglected. Introducing Eqs. (2 .8. 3)–(2 .8. 5) into Eq. (2 .8. 2), we obtain dQ dt  dW s dt   S p E V ÐEndS D ∂ ∂t  U e dU C  S  V 2 2 C gz C u   E V ÐEndS 2 .8. 6 Using ... (2 .8. 7) yields dQ dt  dW s dt D  V 2 1 2 C gz c  1 C h 1   1 V 1 A 1 C  V 2 2 2 C gz c  2 C h 2   2 V 2 A 2 2 .8. 8 where z c is the elevation of the center of gravity of...

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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 ... tank, as shown in Fig. 3.10. The oil density is  D 80 0 kg/m 3 and its viscosity is  D 8 ð 10 2 Pa s. The difference in elevation between the oil-free surface in the tank and the outlet...

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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 ... same magni- tude as q. (a) Find the complex potential, potential, and stream functions. (b) Plot the flow-net. (c) Find the pressure distribution along a radial coordinate. Problem 4 .8 Cons...

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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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... intro- duced in Chap. 2. Rewriting the surface integrals as a volume integral, again using the divergence theorem, the total work rate is  dW dt D  8    g Ð  V CrÐ Q S Ð  V  d8 D  8    g ... Interface Gas K g (cm/hr) K L (cm/h) K H SO 2 1,600 34,420 0.0 38 N 2 O 1,900 20 1.6 CO 2,400 20 50 CH 4 3, 180 20 42 CCl 4 1,030 10.7 1. 08 CCl 3 F 1, 085 11.3 5 Source: Adapted from...

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