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Chapter 3 Integral Boundary Layer Equations for Three-Dimensional Flows 3.1 Definitions The three-dimensional integral boundary layer equations derived using a Cartesian coordi nate system are: 68C Cr aE K(cl/a -C) (31) 0()+1()+m1+m =2D 02(a92n)+02(0:)+p2a due +Pele= az =T2 (33) 02(an) )+(a:9x)+p +Pe les a Equation 3.1 is the two-dimensional turbulent shear stress lag equation, 3.2 is the kinetic energy equation, and 3.3 and 3.4 are the z and z momentum equations. The origin of equation 3.1 is given in reference[21] and the derivation of equations 3.2-3.4 may be found in[38]. Ke is an empirical constant set to 5.6. is the lag direction which is taken to be the chordwise direction, and the z-z coordinate system is an arbitrary, local, 2-D surface coordinate system in a plane tangent to the 3-D BL surface. The main assumptions in these equations are that pressure is constant in the normal direction through the thickness of the boundary layer, and that only diffusion normal to the wall is significant
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