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Homework 3

CM3110

  1. Geankoplis 2.10-1 (Calculate viscosity from Hagen-Poiseuille equation). SOLUTION
  2. Beginning with the Navier-Stokes equations and the equation of continuity, calculate the velocity profile for steady state flow of an incompressible, Newtonian fluid down an inclined plane (the problem we did in class as a shell-balance problem). Use the same coordinate system as we did in class. You may assume the flow is well developed, and you may neglect edge effects. The inclined plane makes an angle b with gravity. SOLUTION
  3. Geankoplis 3.8-8, Flow between two rotating coaxial cylinders. (Note: the differential equation of momentum he refers to is the Navier-Stokes equation). SOLUTION
  4. In class we gave the solution for Poiseuille flow (pressure-driven flow) in a tube of a power-law fluid as, .
    1. Non-dimensionalize this equation, i.e., cast it in the form .
    2. Using a computer (for example, Excel, Matlab, Mathematica), plot the non-dimensional velocity function versus the non-dimensional radius for n=1, 0.8, 0.6, 0.4, and 0.2.
    3. What is the effect of the power-law index, n, on the shape of the non-dimensional velocity?
    4. What is the solution for vz(r) when n=0? SOLUTION
  5. Geankoplis 2.5-1 (Calculate Reynolds number for flow of milk in a pipe). SOLUTION
  6. HONORS Problem: The equations of motion (components of the vector differential momentum balance equation) in terms of stresses (txy, txx, txz, etc.) are useful in dimensional analysis of the behavior of non-Newtonian fluids. Show for the power-law, non-Newtonian fluid that the dimensionless groups obtained by writing the equations of motion in dimensionless form are
and .
SOLUTION
     

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