An analytical approach to explain the Führböter equation

In dredging the main process to transport soil is slurry transport. The most well-known models to predict head losses are the models of Durand and Condolios which were presented in 1952, of Newitt et al. in 1955, Jufin and Lopatin in 1966, Wilson et al. in 1992 and Führböter in 1961. All models describe heterogeneous flow and some, namely those of Newitt et al. and Wilson et al., also apply to a stationary and sliding bed. The heterogeneous models are all empirical, based on the experiments carried out and contain one term for the excess hydraulic gradient losses. In 2013 Miedema and Ramsdell developed a new model based on energy considerations, containing a potential energy term and a kinetic energy term for uniform sands and gravels. An attempt is made to explain the Führböter model more physically based on the model of Miedema and Ramsdell. The use of the so-called S_kt factor is rejected based on the arguments presented. A set of equations and curves are derived for the so-called S_k factor of Führböter with mean, lower limit and upper limit curves, enabling the user to adapt the S_k curve depending on the pipe diameter and the liquid viscosity. The new S_k equations are based on physics and match the experiments of Führböter very well.