Final Exam Fall 13

63 e 822 e 654 e 114 e 130 e specific weight g n m3 1

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Unformatted text preview: x ∂ψ ∂φ v=− = ∂x ∂y 1 ∂ψ ∂φ Vr = = r ∂θ ∂r ∂ψ 1 ∂φ Vθ = − = ∂r r ∂θ ( ∂w ∂v + ( ∂u ∂w + ( ∂v ∂u + ˆ ζ = 2ω = ∇ × V = * − -ˆ + * − -ˆ + * − -k i j ) ∂y ∂z , ) ∂z ∂x , ) ∂x ∂y , ρVl µ V Fr = gl p Eu = ρV 2 Re = € € € € € € € € € ρV 2 Ca = Ev V Ma = c ωl St = € V 2 ρV l We = € σ le = 0.06 Re for laminar D le = 4.4 (Re)1 / 6 for turbulent D 4 lτ w € Δp = D * # 2r &2 # ΔpD2 &* # 2 r & 2 € u( r) = % (,1 − % ( / = Vc ,1 − % ( / $ D' . 16 µl '+ $ D ' . $ + € 4 πD Δp Q= 128 µl 64 f= € Re u yu* = for viscous sublayer in pipe u* ν 1/ n u$ r' V 2n 2 = &1 − ) where = Vc % R ( Vc ( n + 1)(2 n + 1) $l 'V 2 p1 V12 p V2 + + z1 = 2 + 2 + z2 + & f + ∑ K L ) %D ( 2g γ 2g γ 2g € *$ ε / D '1.11 6.9 1 = −1.8 log ,& / )+ Re . f +% 3.7 ( *$ ε / D ' 2.51 1 = −2.0 log ,& )+ / f +% 3.7 ( Re f . € € € ∞ δ* = 0 € $ u' ∫ &1 − U )dy % ( ∞ Θ= u$ u' ∫ U &1 − U )dy % ( 0 δ 5 = where δ = y when u = 0.99U x Re x for Blasius flow:...
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This test prep was uploaded on 03/11/2014 for the course ME 3340 at Georgia Tech.

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