Conversion between Quadratic and Power Law for Non‐Darcy Flow

Power laws are widely used in hydraulic engineering because they are simple compact expressions that generate straight lines on log-log paper. The relationship between hydraulic gradient and bulk velocity for one-dimensional non-Darcy flow is often modeled by a power law. Other investigators use a zero-intercept quadratic equation to model the same phenomenon. In this technical note, general expressions are derived to express the coefficients of one form in terms of the coefficients of the other form. Simpler expressions, specific to the study of non-Darcy flow, are also presented.