Problem 5.43[Difficulty: 2]Given: X component of a 2-dimensional transient flow. Find: Y component of flow and total acceleration. Solution: Governing Equations: 0zwyvxu(Continuity Equation for an Incompressible Fluid) tVzVwyVvxVuDtVDap(Material Derivative) Assumptions: Incompressible fluid No motion along the wall (x= 0) limited to two dimensions (w= 0). The given or available data is: TtAxu2sin0wSimplify the continuity equation to find v: TtAxuyv2sinIntegrate: CTtAyv2sinUse the boundary condition of no flow at the origin to solve for the constant of integration Give the velocity in vector form: jyixTtAVˆˆ2sinUse the material derivative to find the acceleration. Start with the convective terms. yVvxVuaconv
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