 Dimensionless numbers Ar Archimedes number - Arp Archimedes number based on terminal settling velocity - Ba Bagnold number - Ct Cát number - D* The Bonneville parameter or dimensionless particle diameter - Fr Froude number - $$\ \widehat{\mathbf{F}} \mathbf{r}$$ Froude number squared - Frfl Froude number pipe flow - $$\ \widehat{\mathbf{F}} \mathbf{r}_{\mathbf{fl}}$$ Froude number pipe flow squared - Frp Froude number particle based on terminal settling velocity - $$\ \widehat{\mathbf{F}} \mathbf{r}_{\mathbf{p}}$$ Froude number particle based on terminal settling velocity squared - La Lắng number - P Rouse number - Re Reynolds number - Rep Particle Reynolds number based on terminal settling velocity - Re* Boundary Reynolds number - Refl Reynolds number pipe flow - Ri Richardson number - Stk Stokes number - Th Thủy number - $$\ \widehat{\mathbf{T}} \mathbf{h}$$ Thủy number cubed - Thls Thủy number based on line speed in pipe flow - Thfv Thủy number based on friction velocity in pipe flow - Thp Thủy number based on terminal settling velocity - θ Shields parameter - Symbols Cvs Volumetric spatial concentration - Cvt Volumetric transport (delivered) concentration - Cvr Relative volumetric concentration - Cvb Volumetric spatial concentration bed - Cx Durand drag coefficient - d Particle diameter m d15 Particle diameter 15% passing m d50 Particle diameter 50% passing m d85 Particle diameter 85% passing m Dp Pipe diameter m F Force N Fshear Shear force on bed N Fgravity Submerged gravity force on a particle N g Gravitational constant, 9.81 m/sec2 m/s2 ks The bed roughness (often a function of the particle diameter) m ks+ Roughness Reynolds number - l0 Characteristic dimension of flow m L Characteristic length of object or flow m m Mass of particle kg Qm Volume flow mixture through pipe m3/s Qs Volume flow solids through pipe m3/s Rsd Relative submerged density - r Coordinate perpendicular to the velocity m SG Specific gravity - Sm Specific gravity solids - Sm Specific gravity mixture - t0 Relaxation time - T Temperature C u Velocity of fluid m/s u0 Velocity of fluid m/s u* Friction velocity m/s v Characteristic velocity of object m/s vls Line speed m/s vsl Slip velocity m/s vt Terminal settling velocity m/s Vm Volume pipe segment m3 Vs Volume solids in pipe segment m3 x Length direction m y Distance to the wall m y+ Distance to the wall Reynolds number - β Hindered settling power (Richardson & Zaki) - β Diffusivity factor - δv Thickness of the viscous sub layer m δv+ Dimensionless thickness of viscous sub layer - $$\ \mathbf{\dot{\gamma}}$$ Velocity gradient 1/s κ Von Karman constant (about 0.4) - κC Concentration distribution coefficient - λl Darcy-Weisbach friction factor - λ Linear concentration according to Bagnold - $$\ \mathbf{\tau}_{\mathbf{1} \mathbf{2}}$$ Bed shear stress kPa νl Kinematic viscosity m2/s ρl Density of the liquid kg/m3 ρs Density of solids kg/m3 ρm Density of mixture kg/m3 ξ Slip ratio - μl Dynamic viscosity N·s/m2 ηl Dynamic viscosity N·s/m2 φ Angle of internal friction rad δ Angle of external friction rad