Question 1 and 3 do not need to be completed. Please do only question 2
Instructions: The HW5 start.m Matlab file makes 2 figures. As usual, paste these two completed
figures into a single Word document that you submit with the written answers of the other parts. Name
your file HW5 LastName.docx (e.g., mine would be HW5 Harig.docx) and a single Matlab script similarly
named (mine would be HW5 Harig.m) to the D2L Dropbox. You will need to modify the HW5 start.m
to add the equations from lecture to do the calculations. It provides some structure for print statements,
2. In class we talked about the Stokes settling velocity for particles (spheres) as they fall in a fluid.
Here we wish consider single spheres, and develop settling velocity graphs and codes to understand, for
example, the effect of particle size on the settling speed.
Figure 1: This corrects a typo from lecture. See the red ?f .
Use the equations we derived in class for a specified isolated sphere settling in a fluid. For now take it
to be quartz in water. There is a file hw5start.m which does most of the setup for you. I also supply a
scrap of code dragcoeff.m in which the relationship between drag coefficient, Cd, and Reynolds number,
Re, is tabulated (from Ferguson and Church, 2004).
a) Plot the time evolution of the vertical speed, w(t). Report three cases, with D = 10 micrometers,
1 mm and 10 cm. You will need to add expressions to calculate w max, re, and dwdt. I put
‘REPLACE’ in capital letters to help you find where.
0 1 2 3 4
Time in seconds #10-6
Velocity in cm/sec
#10-3 Particle Diameter = 10 micrometers
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
Figure 2: This is what your graph should look like for D = 10 micrometers.
b) For panel 2 of your first figure, which is for D = 1mm, also plot the horizontal line which represents
w¯ in red. If we tried to also plot this for D = 10cm it would not match what we calculated. Why
might it not match? The second figure below will help with this as well.
c) Now we will do this process again but make a plot of terminal velocity vs. particle diameter.
We will do this for two materials: quartz sinking in water, and quartz sinking in air. I created
another copy of the calculation loop in the HW5start.m Take D to go from 10-5 m to 1 m, with 5
logarithmically spaced increments in each decade of particle size. See the matlab file where we use
the command logspace to do this.
d) Why do the lines agree with the red D2
line that I drew for part of the diameters and then disagree
at large diameters?