Linear momentum actuator disc theory is extended to address the power available to a tidal turbine array spanning the cross-section of an open channel flow. A generalised formulation is presented, which relaxes constraints in previous models on the Froude number of the flow and the geometry of the turbine array, and also considers the effects of far-wake mixing on the overall power removed from the flow. In the limiting case of no free surface deformation, the rigid lid model is recovered. Blockage, the ratio of turbine frontal area to the cross-sectional area of the surrounding flow passage, has the greatest effect on available power, with the peak power coefficient increasing by 55% from 0·60 to 0·93 as the blockage ratio increases from 0·05 to 0·20. A further 3% increase in peak power coefficient is achieved as the Froude number increases from 0·05 to 0·20. The efficiency of energy extraction may be determined relative to the total power extracted from the flow, comprising the power available to the turbines, and the power dissipated in wake mixing. Higher blockage turbines operating at low thrust coefficients are shown to be more efficient than lower blockage turbines.