Optimal Furrow Design. I: Time of Advance Equation

A particularly simple equation is developed to explicitly calculate the time of advance in surface irrigation. The proposed equation can be used for routine furrow irrigation design. The equation is derived as an extension of the small-time, large-time explicit solutions. Systematic comparisons of dimensionless solutions indicated that the prediction of the equation is in agreement with the accurate zero-inertia numerical solutions. The accuracy of the simple U.S. Soil Conservation Service explicit time of advance empirical equation was also evaluated. Comparisons have shown that the U.S. Soil Conservation Service equation generally performed poorly. The suggested equation is also compared with observed furrow data and with the accurate zero-inertia model. The provided predictions are in agreement with the numerical model and observed data.