Abstract
The equation, h=kqp, is generally used in the kinematic runoff model to express the relation between depth, h, and discharge, q, of a two-dimensional overland flow. In this equation, exponent p is believed to be governed by a state of flow such as p=1/3 for laminar flow and p=3/5 for turbulent flow.
This paper points out that the two-dimensional overland flow is a hypothetical flow transformed by the modeling of a slope in which rainwater flows along rills, and that the value of p is then changed inevitably beyond recognition.
First, the sectional characteristics of a rill are investigated in detail in a field plot over a natural slope. Next, how the depth-discharge relation changes is examined by transforming a shallow flow of laminar or turbulent state along a rill over a slope surface into the imaginal sheet plane flow over the full-width of the rill or the whole-width of the slope surface under a given rate of rainfall.
As a result, it was disclosed that the value of p changes outwardly to 0.40-0.53 for a laminar flow and to 0.67-0.75 for a turbulent flow, and that we may assume p=0.5-0.7=0.6 from a practical engineering view point.
