1. (20 points) (modified 4.3) Using Matlab, plot arrow plots of steady shear and steady uniaxial extensional flow.  Detailed instructions are at this link.
2.  (10 points)  4.7 (calculate three invariants for steady elongational flow)
3.  (10 points) A key reason that shear flow was chosen as a standard flow is that in the shear coordinate system (1=flow direction, 2=gradient direction, 3=neutral direction), t₃₁=t₃₂=t₂₃=t₁₃=0.  How were we able to prove that these coefficients of stress are zero for this sysem?  Just explain in a few sentences.
4. (10 points) For a Newtonian, incompressible fluid subjected to steady shear flow, what is the predicted stress tensor?  (Hint:  start with the velocity field; substitute it into the constitutive equation and calculate the stress tensor).
5. (10 points) For a Newtonian, incompressible fluid subjected to steady uniaxial elongational flow, what is the predicted stress tensor?
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?