2. Flow through vertical cylinder (analysis): We have worked through flow in a vertical cylinder, and a derivation of the velocity field is also available in the textbook, Chapter 2.3. The velocity in cylindrical coordinates is: (P.-PL)R 4L V = 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 Trr, trz, tzr and Tzz everywhere in the domain. c) Evaluate normal viscous stresses Trr and tzz at the slit wall: r= R d) Plot shear stress trz and velocity vz as a function of using any software you would like (Python plotting was taught in PGE 310/PGE311), that is, replot the figure above. You can use any values you like. Where are the locations stress trz and velocity vz maximized and minimized (in their absolute value)? Note: Handy formulas for calculation of stress in cylindrical coordinates are available in Appendix B.2. 5-0 Dr. max Fr=0 (P-PR 21 Parabolic velocity distribution p, (r) Linear momentum- flux distribution Tr(r). [1 (1-(-/-)) Fig. 2.3-2 The momentum-flux distribution and velocity distribu- tion for the downward flow in a circular tube.

2. Flow through vertical cylinder (analysis): We have worked through flow in a vertical cylinder, and a derivation of the velocity field is also available in the textbook, Chapter 2.3. The velocity in cylindrical coordinates is: V2=4L(P0PL)R2[1(Rr)2] a) Compute divergence ,v+and the r,rz,z and zz components of the gradient of velocity field. b) Using results from (a), calculate viscous stresses trr, rrz, tzr and tzz everywhere in the domain. c) Evaluate normal viscous stresses trr and tzz at the slit wall: r=R d) Plot shear stress trz and velocity vz as a function of using any software you would like (Python plotting was taught in PGE 310/PGE311), that is, replot the figure above. You can use any values you like. Where are the locations stress rz and velocity vz maximized and minimized (in their absolute value)? Note: Handy formulas for calculation of stress in cylindrical coordinates are available in Appendix B.2. 2. Flow through vertical cylinder (analysis): We have worked through flow in a vertical cylinder, and a derivation of the velocity field is also available in the textbook, Chapter 2.3. The velocity in cylindrical coordinates is: V2=4L(P0PL)R2[1(Rr)2] a) Compute divergence ,v+and the r,rz,z and zz components of the gradient of velocity field. b) Using results from (a), calculate viscous stresses trr, rrz, tzr and tzz everywhere in the domain. c) Evaluate normal viscous stresses trr and tzz at the slit wall: r=R d) Plot shear stress trz and velocity vz as a function of using any software you would like (Python plotting was taught in PGE 310/PGE311), that is, replot the figure above. You can use any values you like. Where are the locations stress rz and velocity vz maximized and minimized (in their absolute value)? Note: Handy formulas for calculation of stress in cylindrical coordinates are available in Appendix B.2