CM4650 Polymer Rheology
1. (10 points) 2.37 (what are the orders of various quantities?)
2. (10 points) 3.8 (write boundary conditions
mathematically for several flows)
3. (10 points) 4.4 (Discuss shear and elongational flows as
standard flows)
4. (10 points) 4.8 (Calculate magnitude of gammadot tensor for three
elongational flows)
5. (10 points) 4.13 (calculate gamma dot for a given v)
6. (30
points) 4.14 (follow points in shear, elongation) Note this is a 30 point question. Hint:
review discussion on page 111 for shear and on page 118 for elongation.
Extra
exercises for those who would like more math practice
1. (0 points) Beginning with equation 3.170 on page 86 of the text,
derive the pressure distribution (equation 3.177), the velocity
distribution (equation 3.178), and the flow rate per unit width
(equation 3.181) for Poiseuille flow in a slit.
2. (0 points) Beginning with equation 7.85 of the text and using
equation 7.91, calcluate the flow rate for the flow discussed, which is
given in equation 7.92.
3. (0 points) For Poiseuille flow in a tube of a Newtonian fluid
(section 3.5.3), calculate the total force on the walls of the
tube. Hint: you need to write the total force as a stress
times an area and then integrate. Does your answer make sense?