Movement through fluids
Introduction
One of the strongest effects on the morphology (body shape) of animals is through the
interaction with the physical requirements of their environment. In particular, the need to move
efficiently has produced drastic effects on animal form. Efficient motion benefits the organism
in a variety of ways, for example, by decreasing energy costs and/or increasing speed (important
for both predators and prey). One of the areas where this is most obvious is in movement
through fluid environments. The term fluid applies to both liquids and gases since these objects
are able to flow, meaning that organisms moving through both air and water are subject to the
physics of fluids. When the fluid is moving relative to an object in the fluid, the object is acted
on by a drag force. The relative nature of the motion is important – it can be caused by motion
of a body through motionless fluid, movement of fluid past a stationary body, or a combination
of both the body and the fluid moving. The drag force is in the same direction as the relative
movement of the fluid.
Three factors determine the amount of drag force on a particular object in a given fluid:
1. The drag coefficient – this is a particular value for each object that has to be determined
by experiment, and can vary somewhat with the object’s velocity.
2. The cross-sectional area of the object – the measurement of the largest area that the
object presents perpendicular to the direction of the motion (figure 1).
Direction of
motion relative
to fluid
Direction
of drag
force
Figure 1: Motion of an object in a fluid. The dashed line indicates the plane that would
indicate the cross-sectional area for this object.
3. The velocity of the object – the faster the object is moving, the more drag it experiences.
Biophysics of Movement through Fluids
When moving through air, the drag force is generally minor, until high speeds are reached. This
is something that you have experienced when riding in a car with open windows. At slow speeds
the amount of air that is moving is minor, but as speed increases so does the amount of air
movement, and with it the amount of drag. Due to the greater density of water, drag forces are a
Movement Through Fluids - 1
major factor for an organism moving through an aquatic environment, even at low speeds. This
fact has lead to some of the strongest examples of convergent evolution – evolution that
produces very similar morphologies in unrelated species. Among aquatic animals, a particular
body shape has evolved in several different lineages of vertebrates due to the strong drag forces
present in water. An object moving through an aquatic environment causes the water to flow
around the object. As the water moves around the object, it flows in lines parallel to the object (a
process known as laminar flow). When the water reaches the back side of the object, if the flow
pathways of water interact too abruptly, they produce turbulence, a chaotic mixing of the water
flows that increases the drag on an object as it moves (figure 2a). If the water can continue with
laminar flow after it passes by then turbulence is decreased (figure 2b). A round object moving
through water experiences turbulence quite often, while a teardrop-shaped object experiences
less. The amount of turbulence that develops is also affected by the speed of motion, but at any
given speed the teardrop shape will experience less. For this reason, evolution has repeatedly
produced aquatic organisms that possess this sort of body shape, including fish, dolphins, and
aquatic reptiles.
A
B
Figure 2: Motion of differently shaped objects through water. Arrows indicate the
direction of motion. The blue lines represent the displacement path of the water.
While it is true that organisms moving through air generally encounter less drag and turbulence
there is at least one situation where these issues can have important effects on movement: flight.
When a bird is flying, the movement of air over its wings is the source of lift to keep the bird in
the air. If air flow is too slow or too turbulent, the animal will not be able to keep itself in the air.
To address this problem, the wings of flying animals can change shape, taking on a particular
shape called an airfoil (figure 3).
Figure 3: cross-section of an airfoil. Blue lines represent movement of air around the wing.
The arrow represents the direction of movement.
Figure 3 shows the movement of air over an airfoil; the path of air differs on top and bottom of
the airfoil. Partly due to the different paths of airflow, lift is produced. In actuality, this
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description applies more to a rigid, non-moving wing, like that found on an airplane – the
situation is much more complex in animals, and is still being studied in an attempt to develop an
understanding of the biophysics. While this explanation is an over-simplification, the basic ideas
that we encountered in aquatic organisms apply as well – a particular shape to the body (and the
wings) tends to evolve by convergent evolution to produce the minimum amount of drag during
flight. The effects of convergent evolution can be seen in the wings of birds, bats, and
pterosaurs, the only vertebrates to develop true flight.
During flight, the angle of the wing as it moves through the air has important implications for the
ability of the wing to provide lift. The angle of attack is the amount that the wing deviates from
a horizontal line. As this angle goes up, the risk of turbulence increases (figure 4).
A
B
Angle of
attack
Figure 4: angle of attack. As the angle of attack increases, turbulent airflow increases.
Blue lines represent movement of air around the wing. The arrow represents the direction
of movement.
Unfortunately, as a flying object comes in to land, the angle of attack must increase, and the
velocity of flight must decrease. These two factors together tend to increase turbulence, causing
an increase in drag, making it very difficult for flight to be maintained. To avoid crashing,
planes use a structure called a flap to maintain laminar flow and prevent turbulence. Bird wings
have a similar structure called an alula (figure 5) that serves the same function. The wings of
bats have a similar ability, showing another example of convergent evolution in action.
Movement Through Fluids - 3
Figure 5: the alula is visible on the leading edge of this wing, serving to maintain laminar
flow as the bird prepares to land.
Additional Readings
Fish, F.E. and Lauder, G.V. 2006. Passive and active flow control by swimming fishes and
mammals. Annual Review of Fluid Mechanisms. 38: 193-224.
Halliday, D., Resnick, R., and Walker, J. 1993. Fundamentals of physics, extended, 4th ed. John
Wiley & Sons, Inc. New York.
Kardong, K.V. 2006. Vertebrates: comparative anatomy, function, evolution, 4th ed. McGraw
Hill. New York.
Koehl, M.A.R. 1996. When does morphology matter? Annual Review of Ecology and
Systematics. 27: 501-542.
Pettersson, L.B. and Hedenstrom, A. 2000. Energetics, cost reduction and functional
consequences of fish morphology. Proceedings: Biological Sciences. 267: 759-764.
Walker, J.A., and Westneat, M.W. 2000. Mechanical performance of aquatic rowing and flying.
Proceedings: Biological Sciences. 267: 1875-1881.
Movement Through Fluids - 4
Experiment
In this activity you will be studying the effects of body shape on drag. Specifically, you will take
various body designs of similar masses and try to determine which factors are most important in
producing an efficient swimming body shape.
Needed materials
1.
2.
3.
4.
5.
6.
Tea candles (4)
Swim tank (this should be assembled by your instructor before you arrive in lab)
Fishing line with leaders attached
Various objects to attach to your candles to change their area
Stopwatch
Calipers
In this exercise, you will build various models using the tea light as a base and adding various
pieces of plastic or other material to the candle to vary its cross-sectional area. By testing the
ability of different body plans to “swim” through the water, you can test your understanding of
the dynamics of movement through a viscous substance like water. The design of the apparatus
is shown below in figure 1.
Pulley
Test object
Movement
mass
Stabilizing
mass
Figure 1: basic apparatus for experiment.
By attaching the test object to a string running down to a movement mass, the test object will
“swim” across the container until it strikes the opposite wall. This will allow you to time the
movement of the test object and make relative comparisons between different body shapes. You
should note that the movement mass is held above the bottom of the container by fishing line.
This is to prevent friction with the bottom of the container from affecting the movement of the
object. You will also attach a “stabilizing mass” to the opposite end of the test mass to prevent it
from moving too quickly. You will want to check with your instructor for the amounts that you
Movement Through Fluids - 5
start these masses with. You may want to experiment with them – an object that moves too
quickly may provide inaccurate data just like one that moves too slowly.
Procedure
1. You should work with a group of students to form a group of 3-5 students.
2. For each group, students should get a container, enough material to build four test
objects, one movement mass, and one stabilizing mass.
3. Use the screws provided by your instructor to attach the fishing line leaders to your first
test object (a single tealight candle). Pull the candle out of its aluminum holder. There is
an aluminum piece attached to the bottom of the wick. By putting the candle back into its
aluminum holder backwards (figure 2), you will have two metal pieces to attach to your
screws, and the candle should be held more tightly.
Figure 2 - Tealight candle. A) Candle in its holder. B) Candle out of its holder, showing
the aluminum piece on the bottom of the candle.
4. Assemble your movement and stabilizing mass as instructed.
5. Build your other test objects. The students in each group should decide on the shape of
their test objects before they begin building them. As part of this process, you should
develop hypotheses about how the different shapes will move through the water and why
that is the case. Once you have decided on the appropriate shapes, you should build each
one using a candle as your starting point. Begin by inserting a screw with a loop to into
each side of the candle – these will serve as the point to attach the line that pulls on the
test object (figure 3)
Figure 3 – Candle with eye screws attached
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6. Use glue to attach the projections to the candle (figure 3). When you attach material to
your movement object, you’ll want to make sure that the pieces are as even as possible.
You should attach your projections to the same side of the candle (although you can use
either side). The “front” of the candle will be the screw that is attached to the candle
holder, not the side with the wick of the candle, as this might cause additional drag,
which could distort your results.
Figure 4: A test object with projections attached to the “front” of the candle
7. Weigh the movement mass, stabilizing mass, and the test objects. Record these values on
the data sheet.
8. Use the calipers to measure the size of each candle and projections that are attached to it,
perpendicular to the direction the object will be moving. Use this to calculate the crosssectional area for each object. Sketch a diagram of each object with the appropriate
measurements on the data sheet.
9. Measure the length of the container. You should only measure the space between the
pulleys as the object can only move through this distance (figure 5). You may also need
to adjust this based on the actual distance the test object can move, as the fishing line
leaders may further limit the distance the object can move.
Figure 5 – container with length indicated
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10. Attach one end of the string to the movement mass and the other end to the stabilizing
mass. The movement and stabilizing masses should be suspended over the edge of the
lab bench so that when the test object is released the movement mass will drop downward
and pull the test object through the water. (figure 6)
Figure 6 – container with movement and stabilizing masses attached
11. Fill the container with water so that it will easily cover the test object (the amount of
water needed will vary with the size of the container).
12. Designate one group member to each of the following jobs:
a. Timer
b. Data recorder
c. Releaser
d. Observer
13. The releaser will take the test object to be tested, pull it to the end of container opposite
the pulley and hold it there. You will want to be sure that you pull on the string, as
opposed to pulling on the object itself, as this runs the risk that the string will
detach. You want to be sure that the object is at the same point for each trial.
14. The releaser will release the test object and say “start” so that the timer can start the
stopwatch.
15. The observer will need to watch the motion of the object, and describe that motion,
making note of factors such as:
a. Whether or not the test object moved constantly
b. If the test object moved in a straight line or if it “tumbled”
c. Any other factors that could have affected the motion of the object.
16. When the test object reaches the opposite side of the container, the releaser says “stop” so
the timer can stop the stopwatch.
17. The data recorder records all the data for the trial.
18. Repeat the procedure a total of ten times for that test object.
19. Replace the first test object with the second and repeat the procedure.
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20. Repeat the procedure for all four test objects.
There are several considerations to bear in mind when running this experiment:
1. Because you have two masses hanging from strings, they are going to tend to swing. You
want to do your best to minimize swinging as it will affect the ability of your test object
to move smoothly.
2. When you attach pieces of plastic to your movement object, you’ll want to make sure that
you cut them as evenly as possible.
3. This experiment is concerned only with relative differences between the different body
shapes. For that reasons the procedure avoids extensive mathematical analysis. The
results are not concerned with a mathematical measurement of the forces involved, only a
qualitative understanding of the differences.
4. We assume the forces of friction that are not caused by the shape of the test object are
identical in all tests. This includes friction to the pulley and the friction of air against the
movement mass as it drops. These assumptions are probably not strictly true, but for the
purposes of this experiment they should not have drastic effects on the outcome.
5. We also assume that the amount of drag on the test object is only affected by the crosssectional area of the test object. This assumption has the potential to drastically affect the
outcome of the experiments, so make sure that your test objects have as few rough spots
or bumps as possible.
Data Analysis
1. Calculate the average velocity of the object during each trial, and then calculate the
overall average for the 10 trials for a particular object.
2. Students should graph their results as instructed on the data sheets.
3. After all the data are collected, the students should work to compare their results to their
hypotheses. The observer’s notes should be used to understand and interpret any
anomalous data points. This should include discussions of the results of all groups. A
graph of the dataset for the entire class could be useful for finding trends.
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Name : _________________________________ Lab Section: _________________________
Draw each of your test objects, with all the appropriate measurements marked:
Object 1
Object 2
Object 3
Object 4
Length of container = _____ cm
Motion mass = _____ g
Stabilizing mass = ______ g
Test Object 1
Area = _____ cm2
Mass = ____ g
Test Object 2
Area = _____ cm2
Mass = ____ g
Test Object 3
Area = _____ cm2
Mass = ____ g
Velocity
(cm / s)
Time (s)
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Velocity
(cm / s)
Time (s)
Velocity
(m / s)
Time (s)
Velocity
(cm / s)
Time (s)
Trial
1
2
3
4
5
6
7
8
9
10
Avg
Test Object 4
Area = _____ cm2
Mass = ____ g
Graph the velocity of your objects vs their cross-sectional areas.
Graph the velocity of your objects vs. their mass.
Movement Through Fluids - 11
1. What was your hypothesis for the experiments you performed?
2. Do the data support your hypothesis? Why or why not?
3. Based on your test objects, what other factors in the experiment might be affecting the
outcomes of the experiment and why do you come to this conclusion?
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4. Which of the factors you identified in question 3 could be removed by changing your
experimental design. Describe how you would make the appropriate change(s) and why
you think this would improve your results.
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