0,= 0 Parabolic velocity distribution (1) U2, max Trz=0 Linear momentum- flux distribution Trz, max P.-PR 2L Fig. 2.3-2 The momentum-flux distribution and velocity distribu- tion for the downward flow in a circular tube a) Compute divergence V.v and the rr, rz, zr and zz components of the gradient of velocity field. b) Using results from (a), calculate viscous stresses Tor, Trz, Izr and Tzz everywhere in the domain. c) Evaluate normal viscous stresses Try and Tzz at the slit wall:r=R Note: Handy formulas for calculation of stress in cylindrical coordinates are available in Appendix B.2. Cylindrical coordinates (, 0, z): + Cu - kv) (B.1-87 0 + TO = + - )() (B.1-9) 22 = --[201m + %)] + Gu x36V-v> ( -- [ 2 ] + Gu x3 =v) ---; (*) du, az + - () (B.1-10) re = 1 ou + ro0 (B.1-11) due Tec 28 - (B.1-12) T = n -A : + az ar (B.1-13) in which (5.v) = 1. (-0, + av. du az (B.1-14)