# 8.5: The Sliding Bed Regime

Figure 8.5-1 shows the Erhg parameter as a function of the relative volumetric concentration (Cvr=Cvs/Cb) and the relative line speed (vls/vls,ldv,max) for the weight approach sliding bed friction (Miedema & Ramsdell (2014)) and a sliding bed friction factor μsf=0.4. The Erhg parameter is very close to the sliding friction coefficient μsf, especially for relative line speeds up to 1.5, the region where most probably the sliding bed will occur. So for the sliding bed regime the Erhg parameter is defined to be equal to the sliding friction coefficient μsf. Apparently the force equilibrium on the bed is not required to determine the hydraulic gradient. For determining the bed velocity and the slip, it still is.

$\ \mathrm{E}_{\mathrm{r h g}}=\frac{\mathrm{i}_{\mathrm{m}}-\mathrm{i}_{\mathrm{l}}}{\mathrm{R}_{\mathrm{s d}} \cdot \mathrm{C}_{\mathrm{v s}}}=\mu_{\mathrm{sf}}$

$\ \mathrm{i}_{\mathrm{m}}=\mathrm{i}_{\mathrm{l}}+\mathrm{R}_{\mathrm{s} \mathrm{d}} \cdot \mathrm{C}_{\mathrm{v s}} \cdot \mu_{\mathrm{s f}}$
$\ \Delta \mathrm{p}_{\mathrm{m}}=\Delta \mathrm{p}_{\mathrm{l}}+\rho_{\mathrm{l}} \cdot \mathrm{g} \cdot \Delta \mathrm{L} \cdot \mathrm{R}_{\mathrm{s d}} \cdot \mathrm{C}_{\mathrm{v s}} \cdot \mu_{\mathrm{s f}}$