*3.3. Physical Model of Hydromixture Transport*

The subject of the research was the transport of finely dispersed hydromixture from a reservoir to the settling tank in a pipeline of a total length of 632 m and a diameter equaling 200 mm. The total height difference between the inlet and the outlet length of the pipeline was 11 m.

We assumed that the flow of the tested hydromixture is fully developed, axiallysymmetrical and isothermal. The flowing medium consisted of a solid phase and water as a carrier liquid.

The calculations of the total pressure drop in the pipeline was carried out for the hydromixture transported under industrial conditions, i.e., with a solid phase concentration of Cm = 21.30% and a volumetric flow rate of Qv = 110 m3/h, which corresponds to a solid phase mass transport of 27 t/h. The results of the calculations performed for the base hydromixture were compared with the flow pressure drop values for hydromixtures with mass concentrations of 28.14%, 35.00%, 42.75% and 50.00%, to which the deflocculant additive was applied.

Based on the assumptions of the physical model, the pressure drop (Δp) of the hydromixture flow in the tested pipeline was calculated from the expression:

$$
\Delta \mathbf{p} = \frac{\rho\_{\rm m} \cdot \mathbf{U}\_s^2}{2} + \rho\_{\rm m} \cdot \mathbf{g} \cdot \Delta \mathbf{h} + \cdot \mathbf{p}\_{1-2} \tag{11}
$$

where ρ*<sup>m</sup>* is the density of the hydromixture, U*<sup>s</sup>* is the mean flow velocity, and Δh is the difference in level between the pump inlet and the pipeline outlet. <sup>Δ</sup>p1−<sup>2</sup> is the linear losses due to friction in pipeline sections, which were calculated from the Darcy–Weisbach equation as follows:

$$
\Delta \mathbf{p}\_{1-2} = \lambda \cdot \frac{\rho\_{\rm m} \cdot \mathbf{U}\_{\rm s}^2}{2} \cdot \frac{\mathbf{L}}{\mathbf{d}} \tag{12}
$$

where *λ* is the friction factor, *L* is the total length of the pipeline, and *d* is the pipeline diameter. The values of the friction factor *λ* were determined from the equation:

$$
\lambda = 4 \cdot f \tag{13}
$$
