520 ADV FLUID MECH I  
                      Fall Term 2003

                  
Hwk 3 (Due Oct. 28)

1. Perform an experimental study showing the viscoelastic properties of a mixture of white glue and liquid starch ("silly putty").  You may wish to compare these to experiments with "more standard" liquids and solids.

2. Show that T_ij v_i,j >0 for a Newtonian Fluid with  µ>0 and l + 2/3µ >0. (Hint use the coordinate system where the stress tensor is diagonal, i.e., along the principle axes.)

3.Find the unsteady differential equations in time for the following three quantities as a response to the unsteady shear flow u = H(t)gy of a Generalized Maxwell Fluid. (H= Heaviside step function). Solve the equations for the linear case as g®0 to show the exponential approach to the Newtonian solution.
     t_xy            =
     t_xx -t_yy  =
     t_yy -t_zz  =

4. Find the steady response of a 2D (¶/¶z=0) simple elongational flow such that ¶u/¶x = g (constant) for a upper-convected Maxwell fluid (a-1=l₂=0). Ignore inertia. What is required of the other velocity components?  What is the force/width (in z-direction) as a function of time required to pull this material in this way? What is the result when l₁=0?