Assignment 8 - Special Problem 2

Assignment 8 - Special Problem 2 - SpecialProblem2

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y x p 0 p L V yx yy τ yx y Shell Special Problem 2 Same as Special Problem 1, but solve the problem on pages 311 12 of your text. Then answer the questions of Problem 8.25. LMB with no acceleration: 0 Force from stress component at : ( ) = Force from stress component at ( ) = Force from pressure at x : ( ) = x yx yx yx yx xx F y y xz yx z x z pxy p ττ = + ΔΔ Δ Δ Δ −Δ Δ Δ Δ Force from pressure at x ( ) = Sum the forces, divide by shell volume and take limit: 0 or since first term is a function of y and yx xy xp y z p y z p Δ Δ −= ∂∂ 1 second a function of x: yx d dp c dy dx == Shell volume: xyz ΔΔΔ x p x x p
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Special Problem 2 (cont) () 0 1 0 0 1 2 Integrating the pressure equation: or Integrating the stress equation: Using Newton's law of visc L p L p L yx dp c dx pp p c LL p yc L τ = Δ == Δ =− + ∫∫ 2 2 2 3 3 2 osity: Integrating: 1 2 BC 1: 0 at 0 0 BC 2: at 2 The velocity is then x yx x x x dv p dy L pc vy y c L c Vp vV y a c a aL τμ μμ μ Δ + Δ ⎛⎞ + + ⎜⎟ ⎝⎠ = Δ = + 2 2 2 : 1 2
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Assignment 8 - Special Problem 2 - SpecialProblem2

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