Experimental and analytical evaluation of friction factor along spatially varied flow

This paper investigates the Darcy–Weisbach friction factor (f) under spatially varied flow conditions with lateral inflow, a scenario common in irrigation networks, urban drainage systems, and natural rivers. An extensive experimental program of 162 tests was conducted using physical model with 6.2 m long, 2 m wide, and 1.5 m height with an asphalt bed (n = 0.016). The tests considered base discharges (Q) of 10, 30, and 50 m³/hr, nozzle discharge (q) of 5 and 12 m³/hr, and longitudinal slopes (SL) of 1.0%, 1.5%, and 2.5%. Measurements were obtained at nine stations (P1–P9) to capture hydraulic variability. The results reveal that f decreases with increasing Reynolds number (Re), reflecting the transition from laminar to turbulent regimes, and decreases with increasing Froude number (Fr) under supercritical conditions. Interestingly, contrary to uniform flow theory, f increased with slope in spatially varied flow, highlighting the role of turbulence and inflow mixing. Comparisons with the Keulegan and Blasius equations showed that Keulegan performs well when q/Q is small, whereas Blasius consistently underestimates resistance.