HW02sols - J 2 Probleln.3 9.3 A vbc*r,rxtr.luiri i slxareri...

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J Probleln 2.3 [Difficulty:2] 9.3 A vbc*r,rx tr.luiri i* slxareri bet$c**rf trmr p.tr:alf*t ttisllix th* ffpfler di* r$reres and ttx hrwer *1* l* l!:r*rl" 'lh* r*krcity It*,t.d tret*ren tttt dfuk* ix glv** h,gil .o. itur*:i.'r&. {'t'he *rigi*t *f *rrurdi*ate* i$ k:*sed at tlr* tr$trr crf ttx [rm'f r *JLsk th* $pFer disk fu [<xat*ri 8t i * &.1 Wh*t ar* ttre rlinxttxitrtt* *f thia r,+hrcity fic H ? t)*xx th Lr v* bcity fie t rl :*at l-r $ :rpgrrryrr'i ate $ty*hat trrund*ry *rrnditi*r,*? 1*turt *r.* *rey3 Given: Viscous liquid sheared between parallel disks. Uppet disk rotates, lower fixed. Velocity field is: Find: a. Dimensions of velocity field. b. Satisff physical boundary conditions. $olution: To find dimensions, compare to The given field is Flow must satisfy the no*slip condition: l. At lower distq F *0 since stationary. - ratU z : Ao so Y = 8r #= 0, so satisfied. h ,? ^ f(OZ y =€e h tr =f(x,y,z\ form. f =f(r,r) 2. At uppr dislq f = ErrCI since it rotates as a solid body. z: h, * f = Arry = [email protected], so satisfied. n
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Problem 2.14 [Difficulty:2] ;1.i,q lic|tir;nir",g lritl, tltt' rrlmtlt li*ld *l llr*.rhlrr: l.J. lliptl: tl,;it tl1c p;rr;rt::*tri* tquntir.ttlr lrtr p*rfrc,ls t:tr'ttirur: :tt t t..l\ .;1: h: .b r',t"'"1i irtPJ r- '':-i' t. {.)l',t*tr: tl:* *rtu;rti*rt: lrrr lli;- ;uitl:lir:r lrt the pirrti'*l* l*,i.r-atrri:i;rt tl:s 1xrirt i.t. ri ,,t1. li:rt thr' rr:,.,litr:l i , ii. {.rritpnr* fhi'';lati:ht:l rritl: ths -tl*;**llr:* tl:r, tuql: tl:,-: $rr:lr lririr:t. Given: Find: Solution: Governing equations: Assumption: 2D flow Hence for pdhlines So, separating variables Integrating The pathlines are Eliminating t For streamlines So, seprating variables Integrating The solution is dx up=E=e-* tn(x) = A't + Cl A.t+C, Cl A.r
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