KUNDU Fluid Mechanics 2 Episode 7 pdf

... 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

... 'Itucsdcll, C. A. (19 52) . Stokes' principle of viscosity. JoumZ oJRationol Mechanics ud Analysi.s 1: physical Journul131: 4 424 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 ), vor...

Ngày tải lên: 13/08/2014, 16:21

... a2u f, av =gH- a (-+E), au at2 3t ax ax Now take a/at of Eq. (14 .73 ) and use &. (14. 72 ) , to oblain (14. 72 ) (14 .73 ) + gHa (e + g)] = gH- a2 (e + E). (14 .74 ) at3 ... dAd4 d24 -+A ml- - +r2 +iA-=O. d2A dz2 [ (:TI dz dz dz2 Equating rhe real and imaginary parts, we obtain fi dz2 + A[& - ( 32] = 0, dAd4 d24 dz dz dz2 2...

Ngày tải lên: 13/08/2014, 16:21

... 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 23 2 23 4 23 8 24 0 24 2 24 5 24 a 25 0 25 4 25 5 ... 22 5 22 7 23 0 23 2 23 4 23 8 24 0 24 2 24 5 24 a 25 0 25 4 25 5 25 6 25 7 26 1 26 2 26 4 26 6 26 8 27 0 27 0 27 0 27 1 27 3 27 3 theory i...

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,...

Ngày tải lên: 13/08/2014, 16:21

... vectors 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 ... then the volume integral of Eq. (4. 17) finally gives dM . I F = dr +Mo", (4 .22 ) where Eqs. (4.18X4 .21 ) have been used. Equation (4 .22 ) is the law of conservation...

Ngày tải lên: 13/08/2014, 16:21

... 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 22 7 193 ... techniques of computational fluid dynamics. Chapter 7 Gravity Waves 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . IO . I1 . 12 . in1rr)rlidctioti 194 77 1 Uin...

Ngày tải lên: 13/08/2014, 16:21

... Multiplying Eq. (7. 82) by c6 and using Eq. (7. 86) we obtain am am - + cg- = 0. at ax (7. 84) (7. 85) (7. 86) (7. 87) (a) Example @) Stationary (c) Propagating Fwre 7 .23 Hydraulic ... given by Eq. (7. 57) , namely where E = pga2 /2 is the average energy in the water column per unit horizontal area. Using Eq. (7. 77) , we conclude that I...

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

... Substituting Eq. (10 .75 ) into Eqs. (10 .74 ), (1O. 72 ) , and (10 .73 ), we obtain subject to uo(o) + CUI (0) + E2uz(o) + oe3) = 0, (10 .77 ) uo(i)+EU,(i)+E2u2(i)+~(E3) = 1. (10 .78 ) Equations ... 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 asympto...

Ngày tải lên: 13/08/2014, 16:21