Question: a) E. coli swims at about 20 m/s by rotating a bundle of helical flagella. If the motors were to turn 10 times faster than

a) E. coli swims at about 20 µm/s by rotating a bundle of helical flagella. If the motors were to turn 10 times faster than normal, what would their swimming speed be? If their fluid environment were made 10 times more viscous, but the motors were to turn at the same rate, what would the swimming speed be? How does the power output of the motor change in these two hypothetical situations?

b) Two micron-sized spheres, one made of silver and the other gold, sediment (that is, fall under gravity) in a viscous fluid. The silver sphere has twice the radius of the gold one. Which sediments faster?

c) The left ventricle of the human heart expels about 50 cm ³ of blood per heartbeat. Assuming a pulse rate of 1 heartbeat per second and a diameter of the aorta of about 2 cm, what is the mean velocity of blood in the aorta? What is the Reynolds number?

d) What is the Reynolds number of a swimming bacterium? A tadpole? A blue whale?

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