Existing models of tidal motion in narrow, uniform channels are improved by incorporating a spatial application of Lorentz' principle of equivalent work into the characteristic velocity and tidal friction factor estimates used to linearize the bottom shear stress. The characteristic velocity is evaluated using numerical integration. A steady flow analogy is involved to relate the tidal friction factor to channel roughness and fluid viscosity. These two parameters in turn yield expressions for the viscous wave number, damping modulus and damping frequency which describe the wave motion. The procedure is applied to existing analyses of closed end and sea level canals and models are tested against laboratory and field data with accurate and physically plausible results.