Homework 6 Due: November 17, 2003
From Chapra and Canale:
Chap 22
22.10
Chap 24
24.6, 24.11, 24.13
5. Fournier, Basic Transport Phenomena in Biomedical Engineering,
Section 3.9, pages 71-73:
Integrate the equation
U =
4Q
1 τ 2 dτ
=
γ (τ rz )τ rz
∫
rz
3 0
π D 3 2τ w
w
for τ w = 0.1 to 50 dynes/cm2 , using the constants
τ y = 0.0289 dynes/cm2 and s = 0.229 units as given in your text. You
are to use Gaussian Quadrature, as given in the Matlab script
gausslegendre.m for integration.
Compare this numerical result to the analytical solution of the integral
4
1 τy τy
1 τw 4
U =
[
− τ y τw −
+ ]
84 τ 3
3
2s 2 4 7
w
Compute the relative error in the numerical estimate of the integral for
τ w = 0.1 to 50 dynes/cm2 . Determine if the relative error is uniformly
distributed over the range τ w = 0.1 to 50 dynes/cm2 .