Viscous Fluid (UMAP)

Author: Philip M. Tuchinsky

This module uses Poiseuille's Law to compute total flow of fluid through a pipe, sets up a moderately complicated integral sum, and calculates it in three ways. The result is also used to find the viscosity of certain fluids. Students replace a simple integral, reduce simple Riemann-Stieltjes integrals to Riemann integrals and calculate the latter, discuss how well Poiseuille's Law models a specified viscous fluid flow situation, describe a lab procedure for finding the coefficicent of viscosity of a fluid, and identify local vs. global information.

Table of Contents:

1. LAMINAR FLOW

2. POISEUILLE'S LAW

3. WHEN DOES THIS LAW HOLD?

4. THE VELOCITY OF FLOW AND THE AMOUNT OF FLOW

5. THE TOTAL FLOW THROUGH A PIPE OF RADIUS R

6. THE RIEMANN INTEGRAL

7. THE RIEMANN-STIETJES INTEGRAL

8. DISCRETE SUMMATION

9. INTEGRATION: LOCAL DATA YIELDS GLOBAL RESULTS

10. CALCULATION OF VISCOSITY

11. EXERCISES

12. REFERENCE

13. SOLUTIONS OR HINTS TO EXERCISES