An experimental and analytical study to analyze hydraulic behavior of nozzle-type underdrains in porous media filters

•A set of experiments with a scaled sand filter were carried out.•Ergun equation underpredicts pressure drop in the whole sand filter.•Ergun equation does not take into account the effect of the underdrain.•We developed a new analytical model which considers a nozzle-type underdrain.•The new model is well suited to predict head losses in commercial sand filters. Sand filters are commonly used to protect drip irrigation systems especially when large amounts of organic contaminants are present. Moreover sand filters have the advantage of simplicity and large capacities in comparison with other types of filters. The main objectives of this paper are firstly to develop an analytical equation to calculate the total pressure drop in a sand filter taking into account the pressure drop in the underdrain and secondly to validate this equation comparing its results with the obtained experimentally. An experimental study with a scaled commercial porous media filter was conducted with different media bed depths and sand grain sizes. The results obtained with different media bed depths revealed that the Ergun equation underpredicted the pressure drop in the porous media filter.Subtracting the pressure drop caused by experiments with different sand heights shows that Ergun equation works well for predicting the pressure drop in a region of the sand bed sufficiently far from the underdrain, but fails in the region immediately next to this element. To overcome this problem, a new model based on a set of connected channels of the same diameter and progressive reduction of its number as the flow approaches the nozzles has been developed. The results of the model were compared with the ones obtained in the scaled sand filter as well as the ones obtained in commercial sand filters (Mesquita et al., 2012). The new analytical equation improves the results of the Ergun equation to predict the pressure drop produced by the entire sand bed by taking into account the effect of the underdrain (nozzle-type) and can be applied to accurately predict pressure drop in the commercial sand filters commonly used in drip irrigation.