This thesis is focused on river and tidal stream power assessment, focussing particularly on uncertainties in power estimates resulting from inaccurate characterisation of bed roughness and turbine drag. It presents analytical and numerical models for the transfer of these uncertainties through to turbine power uncertainty in a strait, exploring how this affects metrics such as mean power and its standard deviation. Perturbation methods are used to determine the leading-order effects of friction and drag uncertainty in tidal stream power assessment. The methods for uncertainty transfer presented in this thesis could readily be applied to numerous other problems encountered in hydraulic engineering, such as flow routing, urban flood risk, and reservoir sedimentation. It will therefore be of interest to researchers, engineers, and students in these fields.