This paper presents a coordinated model predictive control scheme for the Mid-Columbia hydropower system. The Mid-Columbia system consists of seven hydropower plants on the Columbia River in the United States. The state-space model used in the control scheme accounts for system hydraulics, modeling time-delayed hydraulic coupling and dynamic tailrace elevations. We approximate the power generation from a hydropower plant using a piecewise planar function of turbine discharge and hydraulic head, and we demonstrate how this approximation can be written as a set of linear constraints and integrated into a quadratic program. We introduce a flow minimizing objective function that maximizes system hydraulic potential by efficiently allocating water. Compared to historical operations, the proposed control scheme reduces ramping, increases total system hydraulic head, increases system energy content, and operates the system within all elevation and flow constraints.