# the molecular diffusion coefficient

A student injects 5 mL of 20% Rhodamine solution in water (with specific gravity 1.15 g/mL) instantaneously and uniformly over the tube cross-section (π΄π΄ = 0.8 cm3) at the point π₯π₯ = 0 and the time π‘π‘ = 0. The tube is filled with stagnant water. Assume the molecular diffusion coefficient if π·π· = 0.13Β·10-4 cm2/s.

β’ What is the concentration at π₯π₯ = 0 at the time π‘π‘ = 0?

β’ What is the standard deviation of the concentration distribution π‘π‘ = 1 second after injection?

β’ Plot the maximum concentration in the tube, πΆπΆππππππ(π‘π‘), as a function of time over the interval π‘π‘ = [0, 24 h].

β’ How long does it take until the concentration over the region π₯π₯ = [-1, +1] meters can be treated as uniform? (A uniform distribution is one where the minimum concentration within a region is no less than 95% of the maximum concentration within that same region.)

BIOE2397 Homework #6

SUBMISSION FORMAT:

You will need to include the plots generated by MATLAB code into your homework document, and convert this document into a PDF. Submit your PDF and MATLAB code files in a single ZIP archive file to:

o Ms. Madeleine Lu (mlu5@uh.edu)

o Prof. Sergey Shevkoplyas (sshevkoplyas@uh.edu)

The filename must start with your last name, first name ββ for example, for a student named John Doe, the filename is “Doe, John β Homework 6.zip”