53:081 Computers in Civil Engineering

Final

May 13, 2003

Problem 1

For fluid flow in pipes, friction is described by a dimensionless number, Fanning friction factor f.  The Fanning friction factor is dependent on a number of parameters related to the size of the pipe and the fluid, which can all be represented by another dimensionless quantity, the Reynolds number Re.  A formula that predicts f given Re is the von Karman equation, Typical values for the Reynolds number for turbulent flow are 10000 to 500000, and for the Fanning friction factor are 0.001 to 0.01.

(a)          Plot f as a function of Re for Re from 10000 to 500000;

(b)         Assume you only know f for two values of Re=100000 and Re=300000.  Estimate the value of f for Re=200000.  Provide the true relative error (in %) of your estimate.  Provide a graphical illustration of your estimation approach on the same plot that you developed in (a) above.

What to submit:

(All in one folder called Final)

1.   Source code (called ‘final.m’) and other codes as appropriate;

2.   Plot (in ‘final.jpg’);

3.   Other results in a text file (‘final.txt’).

How to submit:

Send to ‘cee081_final’

grade –d cee081_final Final