Hydraulics as empiricism

Although thoroughly founded in physics, many hydraulic relationships require empirical coefficients to account for unmeasured or estimated processes. One of the parameters that has a significant influence on hydraulic calculations is surface roughness, in the form of Manning’s n value, the Chézy C, or the Darcy-Weisbach friction factor. While the Darcy-Weisbach friction factor is generally considered to be more theoretically based, Manning’s n is more commonly used for most stream design and restoration analysis. Roughness is a function of many stream physical properties including bed sediment size, vegetation, channel sinuosity, channel irregularity, and suspended sediment load. As a result, many of the estimates have inherent degrees of empiricism in their estimate.

Sediment transport also requires empirical input. Sediment particles vary in size and properties, from tiny silt particles that adhere to large boulders, sometimes redirecting a stream and sometimes transported downstream. Sediment transport is influenced by velocity vectors near the water/sediment boundary, and these bed velocities may not be well predicted by an average cross-sectional velocity. Many of the analytical sediment predictive techniques include many empirical estimates of specific parameters.