# 1.5: Approach of this Book

The book covers horizontal transport of settling slurries (Newtonian slurries). Pipelines under an angle with the horizontal and non-settling (non-Newtonian) slurries are not covered.

The book has the following approach:

1. Chapter 1 explains the context of slurry flow, based on flow regimes as identified in literature.

2. Chapter 2 gives definitions of the dimensionless numbers and other important parameters as used in the book. Definitions are the language of engineers and scientists and are thus essential for the understanding.

3. Chapter 3 deals with homogeneous Newtonian liquid flow through horizontal circular pipes. Equations and graphs are given to determine the Darcy Weisbach friction factor. The Swamee Jain (1976) equation for the Darcy Weisbach (Moody (1944)) friction factor is used in this book. Also the influence of the concentration of very fine particles on the liquid properties is discussed.

4. Chapter 4 explains the terminal settling velocity of particles, including hindered settling. In the theory derived, the Zanke (1977) equation for the settling velocity is used and the Richardson & Zaki (1954) approach for hindered settling is applied.

5. Chapter 5 shows the basics of the initiation of motion of particles and shells, which is important to understand the behavior of the interface between a bed and the liquid flow above the bed, especially for the stationary and sliding bed regimes. Initiation of motion is the start of sediment motion, but at higher flow velocities also erosion and/or sediment transport will occur. The basics of sediment transport as bed load and suspended load are discussed for open channel flow and pipe flow.

6. Chapter 6 gives an overview of the historical developments of models to predict head losses in slurry flow. The overview starts with the early history, followed by empirical and semi empirical models. The models are given, analyzed and discussed and issues of the models are addressed. The models for the Limit Deposit Velocity (LDV) are discussed, analyzed and compared. Conclusions are drawn regarding the behavior of the LDV related to the solids, liquid and flow parameters. A number of 2 layer models (2LM) and 3 layer models (3LM) based on physics are given and analyzed, as well as other physical models.

7. Chapter 7 describes the new Delft Head Loss & Limit Deposit Velocity (DHLLDV) Framework. The DHLLDV Framework is based on uniform sands or gravels and constant spatial volumetric concentration. This chapter starts with an overview of 8 flow regimes and 6 scenarios. The new models for the main flow regimes, the stationary bed regime without sheet flow and with sheet flow, the sliding bed regime, the heterogeneous regime, the homogeneous regime and the sliding flow regime, are derived and discussed. A new model for the Limit Deposit Velocity is derived, consisting of 5 particle size regions and a lower limit. Based on the LDV a method is shown to construct slip velocity or slip ratio curves from zero line speed to the LDV and above. Based on the slip ratio, the constant delivered volumetric concentration curves can be constructed. Knowing the slip ratio, the bed height for line speeds below the LDV can be determined. New equations are derived for this. The transition from the heterogeneous regime to the homogeneous regime requires special attention. First of all, this transition line speed gives a good indication of the operational line speed and allows to compare the DHLLDV Framework with many models from literature. Secondly the transition is not sharp, but depends on 3 velocities. The line speed where a particle still fits in the viscous sub layer, the transition line speed heterogeneous-homogeneous and the line speed where the lift force on a particle equals the submerged weight of the particle. Finally the grading of the Particle Size Distribution (PSD) is discussed. A method is given to construct resulting head loss, slip velocity and bed height curves for graded sands and gravels.

8. Chapter 8 summarizes the DHLLDV Framework. The essential equations are given, with reference to the original equations, to reproduce the DHLLDV Framework, accompanied with flow charts.

9. In chapter 9 the DHLLDV Framework is compared with other models from literature.

10. Chapter10showshowtoapplytheDHLLDVFrameworkonthehydraulictransportofacuttersuctiondredge.

11. Chapter 11 gives the journal and conference publications of the authors on which this book is based.

The DHLLDV Framework models have been verified and validated with numerous experimental data.

The results of experiments and calculations are shown in standard graphs showing Hydraulic Gradient versus Line Speed i(vls), the Relative Excess Hydraulic Gradient versus the Line Speed Erhg(vls) and the Relative Excess Hydraulic Gradient versus the Liquid Hydraulic Gradient (the clean water resistance) Erhg(il). The advantage of the Erhg(il) graph is that this type of graph is almost independent of the values of the spatial concentration Cvs and relative submerged density Rsd. The advantage of the im(vls) graph is that is clearly shows head losses versus flow and thus gives an indication of the required power and specific energy, combined with pump graphs. Most experimental data is shown in the Relative Excess Hydraulic Gradient versus the Liquid Hydraulic Gradient graph, Erhg(il).