Blood cells can be damaged by turbulent flow. Estimate the maximum size of a device that
could be introduced during surgery on the aortic valve without creating turbulent flow around the
device. Reynolds number is a dimensionless number important in fluid mechanics to
characterize fluid flow as turbulent, laminar, or transitional. One form of the Reynolds number
(Re) equation is
=
where is density of the fluid, v is velocity of the fluid, L is a characteristic length of an object
moving through the fluid, and is viscosity of the fluid. The blood flow velocity through the aortic
valve1 is typically 6 m/s, the density of arterial blood2 is 1050 kg/m3, and the viscosity of arterial
blood3 is 4 x 10 -3 Pas. For laminar flow to be maintained, Re should be less than 1000.
Write a MATLAB script that calculates the maximum size of a device that could be introduced
during surgery on the aortic valve without creating turbulent flow around the device. Display size
of the device with preceding text to describe the numbers to the user (including units).
HINT: Solve this problem on paper first. Then translate to MATLAB. Identify input parameters,
and create variables in a MATLAB script to store the input values. Create the equation to
calculate the size of the device. Use the MATLAB disp command to display the size of the
device to the Command Window. See example MATLAB scripts posted to eCourseware.
In order to receive full credit you must:
1. Begin your program file (.m file) with a comments section including the following:
a. The assignment number (Homework 1), the name of the program, and a brief
description of the purpose of the program.
b. The date created and the creators name in the second line.
c. The definitions of the variable names for every input and output variable. Include
definitions of variables used in the calculations and units of measurement for all
input and all output variables.
2. Include comments throughout your program that explain your calculations.
3. Use the disp command to display the output to the Command Window. Also use the
disp command to display text to describe the output, including appropriate units for
displayed values.
4. Publish your MATLAB script (.m file) to html. Go to the Publish tab and click Publish
icon.
5. Upload your html file (filename.html) to eCourseware (elearn.memphis.edu) under
the Dropbox. Your html file will be stored in a folder named html under your current
working directory in MATLAB. Only html files will be accepted as submissions. All .m
files will be ignored.
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