Appendix D Equations of Motion in Cylindrical Coordinates The equations of motion of an incompressible newtonian fluid with constant u, k, and C, are given here in cylindrical coordinates (r , 0 , 2), which are related to cartesian coordinates (x, y, z ) as in Fig. 4.2: (D.1 ) The velocity components are v, Vy, and v.. Here are the equations: Continuity: --(ru) + -(1) + (V_) = 0 (D.2 ) Convective time derivative: V. V = +-Vo Laplacian operator: (D. 3) -+ TT (D.4 ) The r-momentum equation: The 6-momentum equation: se pot v = v) == v ă este gat got ofvir, >= 2 (.5) heyat ( v • Povo + twins - + o fv*, - (0.9) + (VV), -UV 1 op + ? + 8 + viv — + The z-momentum equation: pr do + go + vyʻu. (D. 7) The energy equation: + m2(+ + + + + €] (0.8) where eu vou (D. 9) Viscous stress components: Toy = 2ue r Tre = LE NO Angular components: velocity Too = 2uen To Tx = 2ue: T E = ple, = PLEA (D.1 0 ) (D.1 1)