{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}