Open-channel distribution networks are subject to algal developments that can induce major disturbances such as clogging of hydraulic devices (pipes, weirs, filters, flow meters). Flushes can be used as a strategy to manage these algae developments. A flush is carried out by increasing the hydraulic shear conditions using hydraulic control structures of the canal network. In response to the shear stress increase, a part of the fixed algae is detached, then re-suspended into the water column, and finally transported downstream. This leads to a peak of turbidity that has to be controlled. In this paper, we develop a distributed linear model of the turbidity dynamics that is used for real-time adaptive control of the flushes. Simulations show the effectiveness of the adaptive controller, which can, at the same time, estimate the gain of the system, linked to the amount of initial fixed biomass, and perform a flush without exceeding the turbidity limit.