b) Using the characteristic magnitudes of u and v, find the approximate size of the following...

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b) Using the characteristic magnitudes of u and v, find the approximate size of the following terms. u V J2u 2 J2u V v 02v 2 Laminar boundary layer U p(u 5x +v Laminar velocity boundary layers over a flat plate Jux /au + Transition region CP) x , v v +v pluox + == == Turbulent boundary. layer Boundary layer thickness, 8 au x y (av 0 v) + ax ay + l du dv + = 0 x y Uo + (p - Po)gx + (p - po)gy Turbulent layer -Overlap layer Buffer layer Viscous sublayer a) Assuming that the boundary layer is very thin and the characteristic magnitude of the horizontal velocity (u) is U, use the continuity equation to find the characteristic magnitude of the vertical velocity (v). c) Using your findings in part (b), find an approximate and simplified form of the governing equations (i.e. the boundary layer equations, 1st proposed by Ludwig Prandtl in 1904): J2u 02u == +1 + 2 10 2 plu +v tv + + (p-pogx + + (- + = 0 d) Define the suitable boundary conditions for the approximate governing equations. e) Find the pressure field in the boundary layer. b) Using the characteristic magnitudes of u and v, find the approximate size of the following terms. u V J2u 2 J2u V v 02v 2 Laminar boundary layer U p(u 5x +v Laminar velocity boundary layers over a flat plate Jux /au + Transition region CP) x , v v +v pluox + == == Turbulent boundary. layer Boundary layer thickness, 8 au x y (av 0 v) + ax ay + l du dv + = 0 x y Uo + (p - Po)gx + (p - po)gy Turbulent layer -Overlap layer Buffer layer Viscous sublayer a) Assuming that the boundary layer is very thin and the characteristic magnitude of the horizontal velocity (u) is U, use the continuity equation to find the characteristic magnitude of the vertical velocity (v). c) Using your findings in part (b), find an approximate and simplified form of the governing equations (i.e. the boundary layer equations, 1st proposed by Ludwig Prandtl in 1904): J2u 02u == +1 + 2 10 2 plu +v tv + + (p-pogx + + (- + = 0 d) Define the suitable boundary conditions for the approximate governing equations. e) Find the pressure field in the boundary layer.