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Homework 3 2008

CM4650 Polymer Rheology

    Due Friday February 22, 2008 in my mailbox or my office.

    NOTE:  The errata page for your text is on the web at this link.

    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?



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