The downward shift of the mean velocity profile in the logarithmic region, known as roughness function, ΔU + , is the major macroscopic effect of roughness in wall bounded flows. This speed decrease, which is strictly linked to the friction Reynolds number and the geometrical properties which define the roughness pattern such as roughness height, density, shape parameters, has been deeply investigated in the past decades. Among the geometrical parameters, the effective slope (ES) seems to be suitable to estimate the roughness function at fixed friction Reynolds number, Re . In the present work, the effects of several geometrical parameters on the roughness function, in both transitional and fully rough regimes, are investigated by means of large eddy simulation of channel flows characterized by different wall-roughness textures at different values of Re up to 1000. The roughness geometry is generated by the superimposition of sinusoidal functions with random amplitudes and it is exactly resolved in the simulations. A total number of 10 cases are solved. With the aim to find a universal correlation between the roughness geometry and the induced roughness function, we analyzed the effect of more than a single geometrical parameter, including the effective slope, which takes into account both the roughness height and its texture. Based on data obtained from our simulations and a number of data points from the literature, a correlation between the ES and the root mean square of the roughness oscillation, as well as between ES and the mean absolute deviation of the roughness, satisfactorily predicts the roughness function.

Efficient management of water distribution networks (WDNs) is currently a focal point, especially in countries where water scarcity conditions are more and more amplified by frequent drought periods. In these cases, in fact, pressure becomes the fundamental variable in managing the WDNs. Similarly, WDNs are often obsolete and affected by several points of water losses. Leakages are mainly affected by pressure; in fact, water utilities usually apply the technique of pressure management to reduce physical losses. It is clear how pressure plays a fundamental role in the management of WDNs and in water safety. Even though the technologies are quite mature, these systems are often expensive, especially if a capillarity monitoring system is required; thus, water managers apply the measurement of the flow rate and pressure at very few points. Today, the implementation of the Internet of things (IoT) can be considered a key strategy for monitoring water distribution systems. Once the sensors are installed, in fact, it is relatively easy to build a communication system able to collect and send data from the network. In the proposed study, a smart pressure monitoring system was developed using low-cost hardware and open-source software. The prototype system is composed of an Arduino microcontroller, a printed circuit board, and eight pressure transducers. The efficiency of the proposed tool was compared with a SCADA monitoring system. To investigate on the efficiency of the proposed measurement system, an experimental campaign was carried out at the Environmental Hydraulic Laboratory of the University of Enna (Italy), and hydrostatic as well as hydrodynamic tests were performed. The results showed the ability of the proposed pressure monitor tool to have control of the water pressure in a WDN with a simple, scalable, and economic system. The proposed system can be easily implemented in a real WDN by water utilities, thus improving the knowledge of pressure and increasing the efficiency level of the WDN management.

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