9.4: Nomenclature Comparisons

C_D

Particle drag coefficient

-

C_L

Lift coefficient

-

C_vt

Delivered (transport) volumetric concentration

-

C_vs

Spatial volumetric concentration

-

C_vb

Spatial volumetric concentration bed (1-n)

-

C_x

Durand & Condolios reversed particle Froude number

-

d

Particle diameter

m

d_m

Mean particle diameter Fuhrboter

m

d₅₀

Particle diameter with 50% passing

m

D_p

Pipe diameter

m

E_rhg

Relative excess hydraulic gradient

-

f_l

Fanning friction factor liquid

-

f_m

Fanning friction factor mixture

-

F_L

Lift force on particle

N

F_L

Durand & Condolios LDV Froude number

-

F_W

Submerged weight of particle

N

Fr

Froude number

-

g

Gravitational constant 9.81 m/s²

m/s²

i_l

Pure liquid hydraulic gradient

m/m

i_m

Mixture hydraulic gradient

m/m

K

Durand & Condolios constant

-

K₁

Newitt constant

-

ΔL

Pipe length

m

L_R

Lift force to submerged weight ratio

-

M

Power Wilson heterogeneous model

-

n

Porosity

-

Δp_l

Pressure loss liquid

kPa

Δp_m

Pressure loss mixture

kPa

R

Stratification ratio

-

Re

Reynolds number

-

R_sd

Relative submerged density

-

S_k

Fuhrboter particle coefficient

m/s

u_*

Friction velocity

-

v_ls

Line speed

m/s

v_ls,hh

Intersection velocity heterogeneous-homogeneous regimes

m/s

v_ls,ldv

Limit Deposit Velocity

m/s

v_min

Minimum hydraulic gradient line speed Jufin-Lopatin

m/s

v_sl

Slip velocity

m/s

v_t

Terminal settling velocity particle

m/s

α_δv=d

Influence factor thickness viscous sub layer

-

α_1a

Proportionality factor thickness viscous sub layer

-

α_1b

Offset factor thickness viscous sub layer

-

α_He=Ho

Influence factor intersection heterogeneous – homogeneous regimes

-

α_2a

Proportionality factor intersection heterogeneous – homogeneous regimes

-

α_2b

Offset factor intersection heterogeneous – homogeneous regimes

-

α_LR=1

Influence factor lift ratio equals 1

-

α_3a

Proportionality factor lift ratio equals 1

-

α_3b

Offset factor lift ratio equals 1

-

β

Richardson & Zaki hindered settling power

-

δ_v

Viscous sub layer thickness

m

δ_v,hh

Viscous sub layer thickness at intersection heterogeneous-homogeneous regimes

m

ε

Pipe wall roughness

-

κ_C

Concentration eccentricity factor

-

λ_l

Darcy Weisbach friction factor liquid

-

λ_m

Darcy Weisbach friction factor mixture

-

μ_sf

Sliding friction factor

-

ρ_l

Density liquid

ton/m³

ρ_s

Density solid

ton/m³

Kinematic viscosity liquid

m²/s

Φ

Durand & Condolios parameter

-

ψ

Durand & Condolios parameter

-

ψ*

Jufin-Lopatin particle Froude number

-

ζ

Fit function Fuhrboter

-

Ct

The Cát number (sand grains)

-

Th_fv

The Thủy number (water) based on friction velocity

-

La

The Lắng number (sediment)

-