# Reynolds Number and Plankton

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```					III. Plankton and Reynolds Number
Most plankton are exceptionally small. Sure there are many well known examples where
this is not true (i.e., many gelatinous zooplankton, such as large jellyfish, some algae,
etc.), but the fact remains, most of the plankton are very tiny organisms. In class we
learned about the various size classifications of the plankton (pico, nano, micro, etc..) and
that a huge amount of the primary production and primary consumption is being done in
the 1-10 micron size range. At this size range, life is a very different place. Even a
simple thing like moving your body from one location to another can take a huge effort!
A lot of this can be explained, or at least investigated, with a general body of study called
fluid dynamics. What we will attempt to do in this lab is get a sense of how both small
and large things move in and through a fluid. To do this we have a convenient parameter
that allows us to look at anything, large or small, and in any kind of fluid (water or air,
for example). This metric is called the Reynolds number and is a cornerstone of fluid
dynamics and used extensively in engineering and the biological sciences. The Reynolds
number is named after Osborne Reynolds (1842-1912) who conducted an experimental
study to see how and when laminar and turbulent flows occur through a pipe.

The equation can be written in a few different forms, we will use simple form that
combines a few different variables into one easily managed formula:

Re = LS/Vk
where Re = Reynolds number (dimensionless number)
L = length of the moving object (m)
S = velocity of the moving object (m s-1)
Vk = kinematic viscosity (m-2 s-1)

The only oddball here is the kinematic viscosity(Vk). This is a measure of how “sticky”
the water is, or how viscose (resistant to shear or flow). Within this measure is the
dynamic viscosity of the water and also its density. Instead of needing both of those, we
can used this combined Vk, which makes life a little easier. Some common values of Vk:

Fluid          Temp (oC)              Vk (measured in cSt = 10-6 m2s-1)
Seawater       0                      1.787
Seawater       5                      1.519
Seawater       10 (50oF)              1.307
Seawater       20                     1.004
Seawater       30                     .801
Air            20                     15
Honey          37.8 (100oF)           73.6
Olive oil      37.8                   43.2

In general, the Re is used to determine if something is being ruled by inertial forces, or by
viscous forces. This is a fancy way to describe whether something can move easily in a
fluid, and “coast” (has lots of inertia), or if something is living in a thick, sticky world
where there is no coasting and everything is like molasses or tar. As you can imagine,
this has some major implication on how life works! Which force rules your world when
you swim?

There is no hard and fast rule here, but in general:
Re is less than around 1,000 then things are slow and sticky (viscous, doesn’t flow well)
Re is over around 4000, then things are moving, slipping, and flowing.

This is an order of magnitude thing, so don’t worry about the significant figures here.
http://simscience.org/fluid/red/reynolds.html

What to do:
You are going to calculate the Re for three very different organisms, a jellyfish, an algae,
and yourself (while swimming). You need two critical pieces of information to figure out
the Re number for each of these.
1. The organism’s size, (height for you, diameter for the jelly and algae)
2. The organism’s swimming speed.

You can get both of these without too much trouble by watching the organisms swim
around for a while with a ruler in hand or while looking under the microscope. Then use
the dissection scope to get an accurate measurement of its size. One of the best things
about Re is that you need not be super exact to get a reasonable calculation. Looking
through the side of the clear plastic containers, try your best to “guestimate” the speed of
the jelly while swimming unobstructed. Just try to measure this a few times and then
take an average. The online calculator can use the size measurement in centimeters and
the speed in centimeters/sec. For yourself, estimate your height in meters and estimate
how fast you can swim in meter/sec. For the unicellular algae, you will need to use the
compound scopes (see below for measurement tips).

Then plug in your values into the calculator and compare the Re for our jellyfish (Aurelia
aurita, the Moon jelly) to those of yourself and the algae. How do all these things
compare to the list of Re values below? Does the jelly live in a slippery, flowing world,
or a thick goopy one? What about you? What is life like for unicellular organisms?

Some common values:                    Re
Whale at 10 m s-1                      300,000,000
Tuna at 10 m s-1                       30,000,000
Duck at 20 m s-1                       300,000
Dragon fly at 7 m s-1                  30,000
Copepod on speed 0.2m s-1              300
Larvae 1 mm long at 1mm s-1            0.3
Bacterium at 0.01mm s-1                0.00001

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