Environmental Fluid Mechanics - Chapter 1 pdf

... of Eq. (1. 3.58) are given by X 11 h 2 1 X 12 h 1 h 2 X 13 h 1 h 3 X 21 h 2 h 1 X 22 h 2 2 X 23 h 2 h 3 X 31 h 3 h 1 X 32 h 3 h 2 X 33 h 2 3 1. 3.59 Copyright 20 01 by Marcel Dekker, Inc. All Rights ... Reserved. Contents Preface Part 1 Principles of Environmental Fluid Mechanics 1. Preliminary Concepts 1. 1 Introduction 1. 2 Properties of Fluids 1. 3 Mathem...

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... 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 ... the linear or normal strain rate. It is represented by u 1 C u 1  u 1 x 1 D ∂u 1 /∂x 1 x 1 x 1 D ∂u 1 ∂x 1 2.3.4 C...

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... obtain  iC1,j C  i 1, j C  i,jC1 C  i,j 1  4 i,j D k 2 w w iC1,j C w i 1, j C w i,jC1 C w i,j 1  4w i,j D 0 3.5.8 Copyright 20 01 by Marcel Dekker, Inc. All Rights Reserved. where C 1 and C 2 are ... approximations:  ∂ ∂x  i,j ³  iC1/2,j   i 1/ 2,j x 3.5.4  ∂ ∂y  i,j ³  i,jC1/2   i,j 1/ 2 y 3.5.5  ∂ 2  ∂x 2  i,j ³ 1 x   ∂ ∂x  iC1/2,j   ∂ ∂x  i 1/...

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... D gd 2  32v D 9. 81 ð 0 .1 10 3  2 ð 0.3 32 ð 10 6 D 9.2 ð 10 4 m/s D 79.5m/day (b) Re D qd v D 1 ) q D Re v d D 1 ð 10 6 0 .1 ð 10 3 D 10 2 m/s q D KJ ) J D q K D 10 2 9.2 ð 10 4 D 10 .9 Unsolved ...  nC1 i,j 1 C  n i,jC1  C 1 ω n i,j 4.5 .18 a or  nC1 i,j D  n i,j C ω 4   nC1 i 1, j C  n iC1,j C  nC1 i,j 1 C n i,jC1  4...

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... gives q 2 g  y 2  y 1 y 1 y 2  D 1 2 y 2 2  y 2 1 8.7.30 Assuming that y 1 and y 2 are not equal, this is rewritten as q 2 gy 3 1 D Fr 2 1 D 1 2  y 2 y 1  y 2 y 1 C 1  8.7. 31 where Fr 1 is the ... waves is given by a cosω 1 t  k 1 x C a cosω 2 t  k 2 x D  2a cos  1 2 ω 2  ω 1 t  1 2 k 2  k 1 x  ð cos  1 2 ω 2 C ω 1 t ...

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... this value, we obtain the following table:  10 ° 20 ° 30 ° 40 ° 50 ° 60 ° 70 ° 80 ° 90 ° f ð 10 4 0.252 0.497 0.727 0.935 1. 114 1. 259 1. 366 1. 432 1. 454 Unsolved Problems Problem 9.3 The usual ... written as p h D p a C gf 1 tan   tan  i x C 2 h C x tan  i g 9.2 .10  Equating Eqs. (9.2.9) and (9.2 .10 ) then results in tan  i Dtan   1  2   1 9.2 .11  T...

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... result is (for t ½ t 1 ) C D q 0 expxU/2E x  4E x E y  1/ 2   U 2 t/4E x CKt 0 1  1 exp   1  ˇ 2 2  1  d 1  10 .7. 21 where  1 D  U 2 4E x C K  t  t 1  10 .7.22 ˇ 2 D [E y x 2 C ... D ∂C Ł 1 ∂t C  rÐC Ł 1  k 1  rÐC Ł 1  D R 1  H) ∂C Ł 1 ∂t C C Ł 1   rÐ  V C  V Ð  rC Ł 1 D  rÐk 1  rC Ł 1  C R 1  10 .4.9 This...

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... Kh av 11 .2 .12  where h av is an average value of the aquifer thickness. By introducing Eq. (11 .2 .12 ) into Eq. (11 .2.9), we obtain rÐTrh D  ∂h ∂t 11 .2 .13  Equations (11 .2 .10 ) and (11 .2 .13 ) are ...  T m i 1/ 2 h mC1 i  h mC1 i 1/ 2 ] (11 .6.5b) By introducing Eq. (11 .6.5) into Eq. (11 .6 .1) , a set of linear equations is obtained as h mC1 i 1 t S m i x 2 T m i...

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... Ghosh, U., 19 95. Surface aeration. J. of Environmental Engineering 12 1 (1) :11 3 11 8. Chapra, S. C., 19 97. Surface Water Quality Modeling. McGraw-Hill, Boston. Danckwerts, P. V., 19 51. Significance ... K 0 H C  1 K g C K 0 H K L  1 D  C g K 0 H  C  1 K L C 1 K 0 H K g  1 12 .4.8 or, J D Ä g C g  K 0 H C D Ä L  C g K 0 H  C  12 .4.9 where 1 Ä g D 1 K g...

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... the left-hand side of Eq. (13 .3 .15 ) may be written as  ∂ ∂t C U ∂ ∂x  D ikU c 13 .3 .16  Then, combining Eqs. (13 .3 .14 ) and (13 .3 .15 ) gives Ow 1 j zD0 C D ikU 1  cOÁ D C 1 13 .3 .17 a Copyright ... 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...

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