KUNDU Fluid Mechanics 2 Episode 3 ppt

... Mapping 14 8 15 0 1 52 15 4 15 6 15 7 15 7 15 9 16 0 16 3 16 6 17 0 17 1 17 3 17 5 17 6 18 1 18 4 18 5 18 7 18 8 .I 89 19 0 1 92 1 92 chi!pter 7 Gravity Waves 1 . Introduction 19 4 2 . ... 2 . Analogy between Heat and Vorticity Diffusion 3 . Pressure Change Due to Dynamic Effects 20 9 21 3 21 6 21 8 22 1 22 5 22 7 23 0...

Ngày tải lên: 13/08/2014, 16:21

... whcrc the two are related as (2. 26) (2. 27) As a check, Eq. (2. 27) givcs R11 = 0 and R 12 = -~ 123 ~3 = -w, which is in agree- ment with Eq. (2. 26). (In Chapter 3 we shall call ... (Figure 2. 7). Using Eq. (2. 12) , the components of he stress tensor in the rotated frame are 431 I& -43 .;I = CllC21t 12 + C2ICllt21 = TZU + TlU - TU, ti...

Ngày tải lên: 13/08/2014, 16:21

... il, i2, and i3 changc with time. To this observer the time derivative of P is d ( $)F = Z(plil+ P2i2 + - . dPi . dP2 . dP3 dir di2 di3 - 11 - + 12- + 1 .3 - + ... that a@ aY u -, (3. 34) a$ ax ' v E then Eq. (3. 33) is automatically satisfied. Therefore, a streamfunction JI can be defined whenever Eq. (3. 33) is valid. (A...

Ngày tải lên: 13/08/2014, 16:21

... 'Itucsdcll, C. A. (19 52) . Stokes' principle of viscosity. JoumZ oJRationol Mechanics ud Analysi.s 1: physical Journul131: 4 42 4 47 . Univemity Press. 22 8 -23 1. Supplernim?al Reading ... (5 .22 ) can be written as -V&nqi&ijkWk,jq = -V(&jSqk - &~haqj)wk.jq = -vWk,nk + vOn,jj = v%,jj. (5 .25 ) If we use Eqs. (5 .23 H5 .25 ),...

Ngày tải lên: 13/08/2014, 16:21

... ha2, 25 r 2n 2n m m 25 r 2? r =- 1n(x~-y*-u~+i2xy) 11na~. (6.48) Wc know that the logarithm of any complex quantity C = I< I exp (iQ) can be written as In 5 = In 15 ... 22 1 Logcr of ( hsiant Depth 22 3 Laycr of Vnriahle Depth H (.r) 22 4 Yotilir!fnr Stwpeniirg it1 CI .Voriili'pmii .v Mi~iiinti 22 5 H!rlruulir Jiunp 2...

Ngày tải lên: 13/08/2014, 16:21

... dc/h = 0 in Eq. (7 .66 ), and assuming the deep-water approximation tanh(2aHlA) 2 I valid for H > 0 .28 A, we obtain (7 .67 ) For an &-water interface at 20 "Cy the surface ... the flow. To see this, consider the mechanical energy of a fluid particle at the surrace. E = u2 /2 + gH = Q2/2H2 + gH. Eliminatjng Q by Eq. (7.88) we obtain,...

Ngày tải lên: 13/08/2014, 16:21

... 26 8 Intcrd Fmiidt: Number 26 8 RiclmnLqm Aimher. 26 9 Mwh Niuihs 27 0 I’ra~idtl R’i~nhrx. 27 0 ficrc&es 27 0 Litemlure Cited 27 0 Siipplementul Reading 27 0 ... usccl p” = 6’ N4p ,2/ 2w2g2, found from Eq. (7. 166) after taking its real part. Use of thc dispersion rclation w2 = k2N2/(k2 + m’) shows that Ek = Ep. (7. 169) w...

Ngày tải lên: 13/08/2014, 16:21

... derivatives from Eq. (10 .22 ): rlll (10 .26 ) (10 .27 ) (10 . 28 ) (10 .29 ) (1 0.30) dS 3 Uqf" dS - - - u- -[f - fq] = a2+ a+ - = Uf', ay i 12+ Uf" a$ 6 ' ... = p(a2+/ay2)oY where the subscript zero stands for y = 0. Ushg a2$/ay2 = Uf"/S given in Fq. (20 .29 ). we obtain to = pVf "(0)/6, and finally 0.3...

Ngày tải lên: 13/08/2014, 16:21

... convcrgcnt series for a Bessel function Jo(x), given by x2 x4 X6 J()(X) = 1 - - + - - - + ~ 2& apos; 22 42 22 426 2 with the first term of its asymptotic expansion (10.64) (1 ... scheme of numerical integration. 2. A flat platc 4 m wide and 1 m long (in the direction of flow) is immerscd in kcroscnc at 20 'C (u = 2. 29 x 10-6m2/s, p = 800 kg/m...

Ngày tải lên: 13/08/2014, 16:21

... nonzero ones are pupcd as element matrices and vectors, At (1 1 .22 1) (I 1 .22 2) ( 11 .22 3) (1 1 .22 5) ( 1 1 .22 6) Thc prohlern can be nondirnensionalized using the djameter of the ... 1 .20 4) for all the vclocity nodes A and pressure nodes R. Equations (1 1 .20 2)-( I 1 .20 4) can be organized into a matrix .form, (1 1 .20 5) whcrc and (1 1...

Ngày tải lên: 13/08/2014, 16:21

... sinhq*z, (0‘ - K’)2W = A(qi + K’)’ COSqoZ + B(q2 - K2 )2~ ~~hq~ + C(q*? - K2j2 cosh 4*z. The boundary conditions ( 12. 27) then require 4* cosh - 2 4 cash - 2 4 q sinh - ... substitution K Equations (1 .2. 16) and ( 12. 17) bccome ( 12. 16) ( 12. 17) (1 2. 18) ( 12. I 9) where gord4 RaG-, KV The basic slate satisfies d2T dZ2 0 = K ( 12....

Ngày tải lên: 13/08/2014, 16:21

... 2. 38) Eq. (1 2. 38). and ( 12. 40), the cigcnvalue problem for determining the marginal stale (a = 0) is ( D2 - k2)’i,. = (1 + ax)&, ( D2 - k2)2he = -Fd k%,: (1 2. 87) ... Eq. ( 12. 72) : the iirst and third of Eq. ( 12. 72) are added; the rest are simply transformed. The result is iki + i,, = 0. These equations are exactly the sanc as Eq. (...

Ngày tải lên: 13/08/2014, 16:21

... eddies irrotational fluid irrotational fluid turbulent fluid turbulent fluid 4 Figure 13. 14 htrainmcnt of a nonturbulent fluid and its assimilation into turhuleni fluid by viscous ... reached after n - 1 steps. Using rule (13. 84) successively, we get R; = R;-~ + L~ = R' ,, -2 + 2L2 - = R: + (n - l)Lz = nL2. The rms distance...

Ngày tải lên: 13/08/2014, 16:21

... dz2 2 +A- =O. (14. 101 j (14. 1 02) In Eq. (14. 101) the term d2A/dz2 is negligible because its ratio wilh the second term is 1 d2 A/dz2 Am2 H2m2 "" Equation (14. 101) ... = - gp. az (14. 12) (14. 13) (14. 14) Eliminating p between Eqs. (14. 12) and (14. 14), and also between Eqs. (14. 13) and (1 4 .14) , we obtain, respectivel...

Ngày tải lên: 13/08/2014, 16:21

... 13.715 I 13.9549 14.1 984 14.4456 14.6965 14.9513 15.2099 15.4724 15.7388 16. 0092 16. 2837 16. 5622 16. WY 17.1317 17.4228 17.71 81 18.01 78 18.3218 18.6303 18.9433 19.2608 19.5828 ... involving thc hc Lwo powers of (M: - 1) do not appear in Bq. (16. 36). U.siug the pressure ratio (16. 31), Eq. (16. 36) can be written 85 3 &-Si y2- 1...

Ngày tải lên: 13/08/2014, 16:21