hw8 - Homework Assignment #8 Read Chapter 12 in Wilcox up...

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Unformatted text preview: Homework Assignment #8 Read Chapter 12 in Wilcox up through section 12.7 not including section 12.4 Do problems 12.6, 12.8, 12.10, 12.12, 12.15, 12-A, 12-B and 12-C (from virtual handout) A5 The velocity for incompressible flow in a converging nozzle can be approximated by _ g._ g. u—U(1+2L)I 2UL, where U and L are constant velocity and length scales, respectively. Compute the vorticity vector and the strain-rate tensor. \flzs Suppose the velocity components for a two-dimensional, incompressible flowfield are given by u = H11) and v = 9(z) where f (y) and g(x) are arbitrary functions. (a) What must these two functions be in order to have irrotational flow? (b) Compute the strain-rate tensor if the flow is irrotational. fine The pote‘htiiikfidw solution for flow past a rotating cylinder of radius R is u, = U (1 — 12%?) c059 and no = —U (1+ 122/1?) sine + L 2771' where F is circulation and r is radial distance. Compute the strain-rate tensor. \/12.12 The velocity components for Hill '3 spherical vortex are as follows: rz Z 2 1' 2 may, We, W414?) 4(5)] where U and R are constant velocity and length scales, respectively, while r and z denote radial and axial distance. Compute the vorticity vector and the strain-rate tensor. fills Close to a solid boundary, the velocity for an incompressible, viscous flow is given by u=U%i where U and 6 are constant velocity and length scales, respectively. If an initially square fluid particle has one Side parallel to the 1: axis, what is the shape of the fluid particle after a time At, where At << 6 / U? ‘ l i g r..." . \Z—A 3 7774 -’X- Compcwcwg" Vela/1+7 m a AMI/33f“ boundar/ /-341<{‘m ! vva‘Ler w approx/mains, at: U = U6m(rzr V45) when: U3 3M4” and 6= 2mm. '7713 y—OOMPonem-Lé ofl vcu/ocw-F/y )5 mulch smaHer :4. OHam can axprcéémpn 7&0!" 4A5, he-‘J' a a i éhear“ "gar-cc, Per“ Urn-L Voiuma Ir) +116, M—c’arccfion an 3 amount elémC-rngl Pk} K'V’z‘a’wmum value} #or 45w filo“). i i i ; Incomprcsstbb 4/42“) case‘s (A) U = 34+xl; V: X—Y (an U=x£+27; v: Xzay-LZ (5) U: 34*277 V= \AZ—‘lz ‘ (e3 U: *ch; v: 30/7154“)?— I «A u= 4W7 ; v: x-vl \Z—L FZJr 21 films: m +8; «7 piano, 4%; y compact/>4: 01" Vé/ongy u, gzvm by \I= yz— 2x a- 27 De+errv1m¢ a possnblc 'W—CQMFeonca‘é 1am" 542-345, Incar’lprcséilbic. flA/ou. Is IJ' 2/50 Veins} #or u0543347, IflCOmprc-bélblc; fill/03,0 \A/hy Haw man $Iblc, d—wm 0’0"}: are +17ezro 7 pa PO ...
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This note was uploaded on 10/28/2009 for the course AERSP 311 at Pennsylvania State University, University Park.

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hw8 - Homework Assignment #8 Read Chapter 12 in Wilcox up...

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