Estimating Manning’s coefficient n for sheet flow during rainstorms

Abstract

Many hydrological and soil erosion models employ Manning’s coefficient (n) to calculate the velocity of sheet flow (SF). However, Manning’s coefficient of SF cannot be estimated accurately due to the strong influences of rainfall, slope gradient, ground surface roughness, sediment size, etc. The effects of rainfall, especially rainstorms, on Manning’s n are usually ignored. In this study, flume tests were conducted with rainfall intensities ranging from 40 to 120 mm h−1, unit width inflow discharges ranging from 0.02 to 0.06 m2 min−1, bed surface roughness values ranging from 0.009 to 0.25 mm, and slope gradients ranging from 3° to 7°. Manning’s n and the correction (Δnr) induced by raindrops were calculated. The results indicated that Manning’s n without rainfall increased with increasing surface roughness and decreasing unit width inflow discharge. In rainstorms, Manning’s n increased with increasing rainfall intensity and surface roughness and decreasing unit width inflow discharge. Δnr increased with increasing rainfall intensity and surface roughness and decreased slightly with increasing unit width inflow discharge. Manning’s n significantly decreased with increasing Froude number (Fr) according to a power function, while Δnr significantly decreased logarithmically with increasing Fr. The Δnr values of this study were greater than 0 when Fr was less than approximately 2.15. For slope gradients of 3°, 5° and 7°, the rainfall increased n by 1.47–49.33 %, 0.44–21.81 % and 0.43–23.94 % for the cases of Fr < 2.15, respectively. This result indicates that the effects of rainfall on Manning’s n of SF cannot be ignored for laminar flows and low Reynolds numbers (<900). Additionally, two empirical equations for predicting Manning’s n and Δnr under rainfall conditions were devised. The correction Δnr due to raindrop impact was affected by the inflow or base flow regimes. This study experimentally provides basic insights into the effects of rainfall on Manning’s coefficient.