The following table of values is provided for your convenience.
Viscosities and Densities at 20°C
Viscosity, u (Pa s) Density, p (kg m)
18.1 x 10-6
1.00 x 10
1.00 x 10
1.07 x 10
1.02 x 10
1) (15 pts)
You are studying the hydrodynamics of swimming in the large Bluefin tuna, which can reach 4.5 m in
length, weigh 600 kg, and swim at speeds of up to 21 m sł. To better understand how lift and drag are
generated by fish as they swim, you build a
small flow tank to test a range of models.
1 st dorsal fin
2nd dorsal fin
The pectoral fins primarily produce lift and
can be modeled as a hydrofoil.
a. Carefully draw a force diagram of a
hydrofoil that would maximize lift. Please
include all force vectors and an explanation
of how maximum lift is generated.
b. To build a model of the tuna to test in the flow tank, you need to scale down the length to 0.25 m. What
adjustments would you make to ensure an appropriate Re? What is the Re for a large tuna swimming at
c. What is the lift-to-drag ratio for the model tuna in part (b)? The following values are available from
measurements and the literature: projected area of 0.1 m², planform area of 0.2 m², Cp of 0.01, and CL of
1.2. How could the tuna improve its lift-to-drag ratio? Be specific.
2) (10 pts) Animals that swim or fly generate movements of the fluid medium. By traveling together,
some individuals can take advantage of these fluid movements to save energy. There are hydrodynamic
benefits to dolphin calves swimming near their mothers, as shown in the figure on
the right. The animals swim side by side, with the calf beside the rear half of the
a. Explain how this positioning helps the dolphin calf move forward,
using the fluid movements created by the mother and little of its own
b. Explain the fluid dynamic principle that helps keep the dolphin calf
close to its mother.
3) (15 pts) While walking on Scripps beach toward the tide pools, you observe a seagull soaring along the
cliffs, from the glider port all the way to the pier. As it reached the pier, it suddenly changed course
and started flapping its wings to fly vertically, up higher into the sky. After taking this biomechanics
course, how would you explain to your friend (a) the ability of the seagull to fly without flapping its
wings, and (b) how the seagull can fly vertically. Include for each flying situation a diagram of an
airfoil that shows all of the appropriate force vectors and be sure to describe each vector.
4) (15 pts) The parchment worm Chaetopterus lives in U-shaped tubes in the sediment with both tube
openings reaching into the free stream flow. It is a filter feeder and beats its three fans to create a
current through the tube that can reach 0.0003 Ls!. The tube openings are 0.015 m in diameter while
the rest of the tube is 0.05 m in diameter.
a. What is the velocity of water as it flows over the mouth?
cirrus or tentacle
b. What is the water pressure at the mouth?
dorsal cupule with food bolus
c. How does this tube construction help the animal filter
5) (10 pts) What, qualitatively, might be the explanation for the following curious phenomena?
a. The drag of the body of a locust is nearly doubled when the angle between the long axis of the
animal and the wind is increased from 0° to 15º. Yet, the same change in orientation in a fruit fly
produces a drag increase of only about 11%.
b. Wings, fins, flukes, and webbed feet are all relatively flat surfaces, but the locomotory
appendages of small organisms are far more often cylindrical than flattened.
6) (15 pts) Estimate (making appropriate assumptions) the maximum flying speed for the following
insects. Wing length refers to one wing.
a. A dragonfly with a wing length of 6 cm and a wingbeat frequency of 35 s'.
b. A wasp with a wing length of 1.5 cm and a frequency of 120 s'.
c. A butterfly with a wing length of 0.8 cm and a frequency of 180 s'.
d. A mosquito with a wing length of 0.4 cm and a frequency of 400 si!
7) (10 pts) Blood speeds up as it travels from the capillaries toward the heart. Pull from the heart is
negligible, and viscosity continuously exerts its retarding effect. How then can blood speed up without
violating the notion of energy conservation?
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