  The experiments by Darbyshire and Mullin (J. Fluid Mech. 289, 83 (1995)) on
the transition to turbulence in pipe flow show that there is no sharp border
between initial conditions that trigger turbulence and those that do not. We
here relate this behaviour to the possibility that the transition to turbulence
is connected with the formation of a chaotic saddle in the phase space of the
system. We quantify a sensitive dependence on initial conditions and find in a
statistical analysis that in the transition region the distribution of
turbulent lifetimes follows an exponential law. The characteristic mean
lifetime of the distribution increases rapidly with Reynolds number and becomes
inaccessibly large for Reynolds numbers exceeding about 2200. Suitable
experiments to further probe this concept are proposed.
