  The drag reduction induced by superhydrophobic surfaces is investigated in
turbulent pipe flow. Wetted superhydrophobic surfaces are shown to trap gas
bubbles in their asperities. This stops the liquid from coming in direct
contact with the wall in that location, allowing the flow to slip over the air
bubbles. We consider a well defined texture with streamwise grooves at the
walls in which the gas is expected to be entrapped. This configuration is
modelled with alternating no-slip and shear-free boundary conditions at the
wall. With respect to classical turbulent pipe flow, a substantial drag
reduction is observed which strongly depends on the grooves' dimension and on
the solid fraction, i.e. the ratio between the solid wall surface and the total
surface of the pipe's circumference. The drag reduction is due to the mean slip
velocity at the wall which increases the flow rate at a fixed pressure drop.
The enforced boundary conditions also produce peculiar turbulent structures
which on the contrary decrease the flow rate. The two concurrent effects
provide an overall flow rate increase as demonstrated by means of the mean
axial momentum balance. This equation provides the balance between the mean
pressure gradient, the Reynolds stress, the mean flow rate and the mean slip
velocity contributions.
