Abstract
In order to clarify its physical meanings and obtain it as a simple and useful form, the rational formula is theoretically derived as an explicit analytical formula in this paper. The authors declare that the rational formula is derived from the basic formula of runoff in a hill under the assumption that the flow resistance of runoff takes the steady velocity such as saturated Darcy's law. Synthesized rational formula can be expressed by superposing the analytical linear formula of rational formula. Since given rainfall is expressed as a summation of unit step functions, which is the same form of the general rainfall data, derived analytical formulas can accept rainfall data with no modification. With this formula of synthesized rational formula, to investigate the effect of time-resolution of rainfall data for urban-runoff simulations, numerical simulations are conducted in the end of the paper. The results show that when the arrival time of flood is short, enough time-resolution is required to obtain fine calculation results.
