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Fluid Mechanics: 2D Laminar Flow

  1. Oct 21, 2016 #1
    1. The problem statement, all variables and given/known data
    A reasonable approximation for the two-dimensional incompressible laminar boundary layer on the flat surface in Fig. P4.17 is

    u ≈ U(2*(y/δ) - 6*(y34) + y44)

    δ = Cx1/2 where C is a constant

    y ≤ δ
    2. Relevant equations


    3. The attempt at a solution
    Incompressible so density is constant, 2D flow so no z component, continuity equation reduces to
    ∂u/∂x + ∂v/∂y = 0


    For the x component, I got [ (-2y/δ2) + (6*y34) - (4*y45) ]

    But there is supposed to be a dδ/dx term attached to each term. Where does this term come from? Is it some kind of chain rule thing? Thanks!
     
  2. jcsd
  3. Oct 23, 2016 #2

    haruspex

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    I assume you mean 6(y33).
    Yes. ∂/∂x of f(y, z) where z is a function of x is given by ∂f/∂z dz/dx.
     
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