Question

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(a) Using dimensional analysis, express the characteristic length, velocity and time scales for near-wall flow in terms of the density, viscosity and wall shear-stress. Show that the length scale can also be expressed as where v is the kinematic viscosity and uy is the friction velocity (10 marks) Ut

Answer 1

[i] = mºltº (8) - m'1-340 CVJ = mºL'74 [llegam' z's [7] =mºlt' [tje m'2"-2 D [4] = [$jº [u]" Cajo mºz'tº= mº2-34 mb-by- medor -C-24 at htcro -3a-b-c=1 b-2020 -36426-6=) b =.-20 a-2C+c=0 A:C c:-/ b 1 ca.-12 -112 [L] = [5] Lujacej! 3/2 √ST 2) [V] : [$]*[u] "Ct] E eta mara mbibyth me qer-2c athte=0 2306%-ci - b-20 a=-(b+c) 6+2C2+12 3Cb+c) - (6+)) - [b+c) = 1/2 .. a= -112 b = 6 = 1/2 -12 112 [lj' [E] τ :[v] - [s] v= o 3) [I] = [579[4]" Cayo 'T'= mathte -3a-h-c -b-20 T -3a-b-c=0 -6-26-1 athte=0 bicara :-3a-(-a)=0 Jaro .-6+21=-1 :b+c=0 bel C--)

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