Friction factor and von Karman's k in open channels with bed-load

The assessment of the friction factor in open-channel flows with sediments is still an unsolved problem. For bed-load, various studies led to contrasting results, some finding that the friction factor is not affected by the sediment transport, whereas others observed an increase with the sediment concentration. Its effect was analysed in few studies only with gravel bed-load, and an empirical formula was proposed to predict the bed friction factor for pipe and open channel flows, yet with a limited physical meaning and a general deviation of open-channel data. Also the von Karman's k has been recognised to vary with sediment transport. In the framework of classical dimensional analysis, laboratory investigations are here extended to sand bed-load and new empirical formulae based on both original and literature data are proposed for the assessment of the bed friction factor and von Karman's k, thereby accounting for the main parameters which affect resistance.