A method for a hydraulic model for subterranean drilling fluids includes acquiring first and second axially spaced temperature and pressure measurements in the wellbore. The pressure measurements may be processed to obtain an interval density of drilling fluid between the measurement locations. A tool string including a large number of axially spaced pressure sensors (e.g., four or more or even six or more) electronically coupled with a surface processor via wired drill pipe may be used to obtain a plurality of interval densities corresponding to various wellbore intervals. The interval density(ies) may be processed in combination with the temperature and pressure measurements to compute one or more unknown coefficients of the hydraulic model.