Homework 3

CM3110

Geankoplis 2.10-1 (Calculate viscosity from Hagen-Poiseuille equation). SOLUTION
Using the microscopic momentum balance, calculate the velocity profile and shear stress profile for steady Poiseuille flow in a tube. The problem is the same as that which we solved in class using shell balances. The solution is the same as that which we obtained using shell balances.
Using the microscopic momentum balance, calculate the velocity profile and shear stress profile for steady state flow of an incompressible, power-law fluid down an inclined plane (similar to the problem we did in class but this time with the power-law equation instead of Newton's law of viscosity). 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 I showed the plots of the solution for Poiseuille flow (pressure-driven flow) in a tube of a power-law fluid. The complete solution is:.

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?
What is the solution for v_z(r) when n=0? SOLUTION

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 (t_xy, t_xx, t_xz, 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