water Article Evaluating the Effects of Sediment Transport on Pipe Flow Resistance Vito Ferro * and Alessio Nicosia   Citation: Ferro, V.; Nicosia, A. Evaluating the Effects of Sediment Transport on Pipe Flow Resistance. Water 2021, 13, 2091. https:// doi.org/10.3390/w13152091 Academic Editor: Achim A. Beylich Received: 15 July 2021 Accepted: 29 July 2021 Published: 30 July 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Department of Agricultural, Food and Forest Sciences, University of Palermo, Viale delle Scienze, Building 4, 90128 Palermo, Italy; alessio.nicosia@unipa.it * Correspondence: vito.ferro@unipa.it Abstract: In this paper, the applicability of a theoretical flow resistance law to sediment-laden flow in pipes is tested. At first, the incomplete self-similarity (ISS) theory is applied to deduce the velocity profile and the corresponding flow resistance law. Then the available database of measurements carried out by clear water and sediment-laden flows with sediments having a quasi-uniform sediment size and three different values of the mean particle diameter D m (0.88 mm, 0.41 mm and 0.30 mm) are used to calibrate the Γ parameter of the power-velocity profile. The fitting of the measured local velocity to the power distribution demonstrates that (i) for clear flow the exponent δ can be estimated by the equation of Castaing et al. and (ii) for the sediment-laden flows δ is related to the diameter D m . A relationship for estimating the parameter Г v obtained by the power-velocity profile and that Г f of the flow resistance law is theoretically deduced. The relationship between the parameter Г v , the head loss per unit length and the pipe flow Froude number is also obtained by the available sediment-laden pipe flow data. Finally, the procedure to estimate the Darcy-Weisbach friction factor is tested by the available measurements. Keywords: pipe flow; velocity profile; flow resistance; dimensional analysis; self-similarity; sedi- ment transport 1. Introduction The sand-water mixture flow is affected by the physical properties of the fluid and the kind, size and concentration of the transported particles [1]. From a practical point of view, the process of transporting solids and liquid phases through closed pipes is widely applied and economic considerations support the em- ployment of this method of transportation. Sediment transport through pipes is used in dredging process to remove sand, silt and other material from rivers, channels, watersheds, and harbors. Sewerage engineers use a self-cleaning velocity as that which allows to transport sediments in the flow without deposition processes on the sewer bed. Hydraulic transport is also widely applied to transport mine and quarry products. The character- ization of sand particles’ transport in different flow systems, such as sand-multiphase mixtures, is very important to predict the sand transport velocity and entrainment pro- cesses in oil and gas transportation pipelines. A production system affected by sand should be designed to operate above the critical sand deposition velocity to assure that solid particles are dispersed in fluid phases [2]. Notwithstanding the numerous applications of the sediment transport through pipes, information about this process is inadequate and limits a rational approach to the design issues [3,4]. Friction factor evaluation for pipe sediment-laden flows is a theme to be discussed as a limited number of studies were conducted before [3,5]. Resistance of clear flows moving in rough pipes and fixed boundary channels can be certainly estimated. On the contrary, the assessment of flow resistance for sediment-laden flow moving in pipes is not completely solved. Water 2021, 13, 2091. https://doi.org/10.3390/w13152091 https://www.mdpi.com/journal/water