  Transition to turbulence in straight pipes occurs in spite of the linear
stability of the laminar Hagen--Poiseuille flow if the amplitude of flow
perturbations as well as the Reynolds number exceed a minimum threshold
(subcritical transition). As the pipe curvature increases centrifugal effects
become important, modifying the basic flow as well as the most unstable linear
modes. If the curvature (tube-to-coiling diameter $d/D$) is sufficiently large
a Hopf bifurcation (supercritical instability) is encountered before turbulence
can be excited (subcritical instability). We trace the instability thresholds
in the $Re-d/D$ parameter space in the range $0.01\leq\ d/D \leq0.1$ by means
of laser-Doppler velocimetry and determine the point where the subcritical and
supercritical instabilities meet. Two different experimental setups were used:
a closed system where the pipe forms an axisymmetric torus and an open system
employing a helical pipe. Implications for the measurement of friction factors
in curved pipes are discussed.
