Geankoplis 2.10-1 (Calculate viscosity from Hagen-Poiseuille equation).
SOLUTION
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
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
In class we gave the solution for Poiseuille flow (pressure-driven flow)
in a tube of a power-law fluid as, .
Non-dimensionalize this equation, i.e., cast it in the form .
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.
What is the effect of the power-law index, n, on the shape of the
non-dimensional velocity?
Geankoplis 2.5-1 (Calculate Reynolds number for flow of milk in a pipe).
SOLUTION
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