Problems
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4.15 Some bacteria move by twirling their tail (flagellum) (up to 1000 revolutions
per second). This propels them forward, at speeds up to 10 μm/s. Assume the
bacterium is in the shape of a ball 1.0 micrometer in diameter, and use Stokes’
law and the viscosity of water to estimate the power (joules per second) that this
bacterium must expend to move at top speed. If there were a colony of one billion
such bacteria, how much heat (in calories) would be generated per second just for
their movement?
4.16 If the compliance of a lung is found to be 90 ml/mmHg, with a capacity of
1.2 l, how much pressure is needed to inflate the lung?
4.17 A non-viscous fluid of density 1.6 gm/cm 3 flows in a horizontal tube of
varying diameter. The pressure drops by 0.010 mmHg from one end to the other.
If the velocity starts at 7.0 cm/s, what is the velocity at the other end? By what
factor does the diameter change?
4.18 Consider the design of a bionic heart. List those factors which might affect
cardiac output, peak pressure, minimal turbulent flow, minimal erythrocyte rupture,
heat dissipation, material stress, material failure, and possible power sources.
111
4.15 Some bacteria move by twirling their tail (flagellum) (up to 1000 revolutions
per second). This propels them forward, at speeds up to 10 μm/s. Assume the
bacterium is in the shape of a ball 1.0 micrometer in diameter, and use Stokes’
law and the viscosity of water to estimate the power (joules per second) that this
bacterium must expend to move at top speed. If there were a colony of one billion
such bacteria, how much heat (in calories) would be generated per second just for
their movement?
4.16 If the compliance of a lung is found to be 90 ml/mmHg, with a capacity of
1.2 l, how much pressure is needed to inflate the lung?
4.17 A non-viscous fluid of density 1.6 gm/cm 3 flows in a horizontal tube of
varying diameter. The pressure drops by 0.010 mmHg from one end to the other.
If the velocity starts at 7.0 cm/s, what is the velocity at the other end? By what
factor does the diameter change?
4.18 Consider the design of a bionic heart. List those factors which might affect
cardiac output, peak pressure, minimal turbulent flow, minimal erythrocyte rupture,
heat dissipation, material stress, material failure, and possible power sources.