  The rheology of surface granular flows is investigated by means of
measurements of velocity and number density profiles in a quasi-two-dimensional
rotating cylinder, half-filled with mono-disperse steel balls. The measurements
are made at the center of the cylinder, where the flow is fully-developed,
using streakline photography and image analysis . The stress profile is
computed from the number density profile using a force balance taking into
account wall friction. The profiles for the mean velocity superimpose when
distance is scaled by the particle diameter and the velocity by a
characteristic shear rate and the particle diameter. The mean velocity is found
to decay exponentially with depth in the bed with a decay length of
$\lambda=1.1d$. The r.m.s. velocity is nearly constant near the free surface
and below a transition point it decays linearly with depth. The shear rate,
obtained by numerical differentiation of the velocity profile, shows a maximum
which occurs at the same depth as the transition in the r.m.s. velocity
profile. The velocity distribution is Maxwellian above the transition point and
a Poisson velocity distribution is obtained deep in the layer. The variation of
the apparent viscosity ($\eta$) with r.m.s. velocity ($u$) shows a relatively
sharp transition at the shear rate maximum, and in the region below this point
the apparent viscosity varies as $\eta\sim u^{-1.5}$. The experimental data is
compared to predictions of three models for granular flow.
