5.4. Further reading[[Student version, December 8, 2002]] 165
- Reynolds: The viscous critical force for a fluid isfcrit=η^2 /ρmwhereρmis the mass density
of the fluid andηits viscosity (Equation 5.5). The Reynolds number for a fluid flowing at
velocityvand negotiating obstacles of sizeaisR=vaρm/η(Equation 5.11). Laminar flow
switches to turbulent flow whenRexceeds about 1000. - Rotary drag: Foramacroscopic (many nanometers) cylinder of radiusaand lengthL,
spinning on its axis in a fluid at low Reynolds number, the drag torque isτ =4πωηa^2 L
(Equation 5.18 and Problem 5.9), whereηis the fluid viscosity. - Hagen–Poiseuille: The volume flux through a pipe of radiusRand lengthL,inlaminar
flow, isQ=πR
4
8 Lηp,wherepis the pressure drop (Equation 5.17). The velocity profile is
“parabolic,” that is, it’s a constant timesR^2 −r^2 ,whereris the distance from the center of
the pipe.
Further reading
Semipopular:
Fluid flows: (van Dyke, 1982)
The idea of physical Law: (Feynman, 1965)
Intermediate:
Much of this chapter was drawn from E. Purcell’s classic lecture (Purcell, 1977), and H. Berg’s
book (Berg, 1993) (particularly Chapter 6); see also (Berg, 2000).
Fluids: (Feynmanet al.,1963b,§§40–41); (Vogel, 1994), chapters 5 and 15
Technical:
Bacterial flagellar propulsion: (Berg & Anderson, 1973; Silverman & Simon, 1974)
Other bacterial strategies: (Berg & Purcell, 1977)
Low-Reynolds fluid mechanics: (Happel & Brenner, 1983)
Vascular flows: (Fung, 1997)
DNA replication: (Albertset al.,2002)