Hyporheic flows stem primarily from near-bed pressure gradients induced by the interaction between stream flow and topography. They mix in-stream and pore waters through a pumping mechanism, which drives surface water (downwelling flux) in the streambed sediment in high-pressure zones and subsurface water (upwelling flux) into the stream in low-pressure zones. Downwelling fluxes carry river biological oxygen demand (BOD), dissolved oxygen (DO) and ammonium (N) into the sediment where biochemical reactions (respiration and nitrification) consume DO. Here, we present an analytical model for quantifying the benthic oxygen uptake rate (BUR) in gravel bed rivers with alternate-bar morphology and we show the relationship among stream morphodynamic parameters and solute (BOD, DO and N) concentrations on BUR. Our model analytically solves the hyporheic flow field and the solute transport equations with advection, longitudinal diffusion and reactions modeled as first order kinetics because of low solute concentrations in a Lagrangian framework.