Summary: Motivated by examples of erosive incision of channels in sand, we investigate the motion of individual grains in a granular bed driven by a laminar fluid to give us new insights into the relationship between hydrodynamic stress and surface granular flow. A closed cell of rectangular cross-section is partially filled with glass beads and a constant fluid flux \(Q\) flows through the cell. The refractive indices of the fluid and the glass beads are matched and the cell is illuminated with a laser sheet, allowing us to image individual beads. The bed erodes to a rest height \(h_{r}\) which depends on \(Q\). The Shields threshold criterion assumes that the non-dimensional ratio \(\theta \) of the viscous stress on the bed to the hydrostatic pressure difference across a grain is sufficient to predict the granular flux. Furthermore, the Shields criterion states that the granular flux is non-zero only for \(\theta > \theta _{c}\). We find that the Shields criterion describes the observed relationship \(h_{r}\propto Q^{1/2}\) when the bed height is offset by approximately half a grain diameter. Introducing this offset in the estimation of \(\theta \) yields a collapse of the measured Einstein number \(q^*\) to a power-law function of \(\theta - \theta _{c}\) with exponent \(1.75 \pm 0.25\). The dynamics of the bed height relaxation are described well by the power-law relationship between the granular flux and the bed stress.