2.5: Nomenclature
- Page ID
- 29273
Dimensionless numbers |
||
Ar |
Archimedes number |
- |
Ar_{p} |
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 |
- |
Fr_{fl} |
Froude number pipe flow |
- |
\(\ \widehat{\mathbf{F}} \mathbf{r}_{\mathbf{fl}}\) |
Froude number pipe flow squared |
- |
Fr_{p} |
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 |
- |
Re_{p} |
Particle Reynolds number based on terminal settling velocity |
- |
Re_{*} |
Boundary Reynolds number |
- |
Re_{fl} |
Reynolds number pipe flow |
- |
Ri |
Richardson number |
- |
Stk |
Stokes number |
- |
Th |
Thủy number |
- |
\(\ \widehat{\mathbf{T}} \mathbf{h}\) |
Thủy number cubed |
- |
Th_{ls} |
Thủy number based on line speed in pipe flow |
- |
Th_{fv} |
Thủy number based on friction velocity in pipe flow |
- |
Th_{p} |
Thủy number based on terminal settling velocity |
- |
θ |
Shields parameter |
- |
Symbols |
||
C_{vs} |
Volumetric spatial concentration |
- |
C_{vt} |
Volumetric transport (delivered) concentration |
- |
C_{vr} |
Relative volumetric concentration |
- |
C_{vb} |
Volumetric spatial concentration bed |
- |
C_{x} |
Durand drag coefficient |
- |
d |
Particle diameter |
m |
d_{15} |
Particle diameter 15% passing |
m |
d_{50} |
Particle diameter 50% passing |
m |
d_{85} |
Particle diameter 85% passing |
m |
D_{p} |
Pipe diameter |
m |
F |
Force |
N |
F_{shear} |
Shear force on bed |
N |
F_{gravity} |
Submerged gravity force on a particle |
N |
g |
Gravitational constant, 9.81 m/sec^{2} |
m/s^{2} |
k_{s} |
The bed roughness (often a function of the particle diameter) |
m |
k_{s}^{+} |
Roughness Reynolds number |
- |
l_{0} |
Characteristic dimension of flow |
m |
L |
Characteristic length of object or flow |
m |
m |
Mass of particle |
kg |
Q_{m} |
Volume flow mixture through pipe |
m^{3}/s |
Q_{s} |
Volume flow solids through pipe |
m^{3}/s |
R_{sd} |
Relative submerged density |
- |
r |
Coordinate perpendicular to the velocity |
m |
SG |
Specific gravity |
- |
S_{m} |
Specific gravity solids |
- |
S_{m} |
Specific gravity mixture |
- |
t_{0} |
Relaxation time |
- |
T |
Temperature |
C |
u |
Velocity of fluid |
m/s |
u_{0 } |
Velocity of fluid |
m/s |
u_{* } |
Friction velocity |
m/s |
v |
Characteristic velocity of object |
m/s |
v_{ls} |
Line speed |
m/s |
v_{sl} |
Slip velocity |
m/s |
v_{t } |
Terminal settling velocity |
m/s |
V_{m } |
Volume pipe segment |
m^{3} |
V_{s } |
Volume solids in pipe segment |
m^{3} |
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 |
δ_{v}^{+ } |
Dimensionless thickness of viscous sub layer |
- |
\(\ \mathbf{\dot{\gamma}}\) |
Velocity gradient |
1/s |
κ |
Von Karman constant (about 0.4) |
- |
κC |
Concentration distribution coefficient |
- |
λ_{l} |
Darcy-Weisbach friction factor |
- |
λ |
Linear concentration according to Bagnold |
- |
\(\ \mathbf{\tau}_{\mathbf{1} \mathbf{2}}\) |
Bed shear stress |
kPa |
ν_{l } |
Kinematic viscosity |
m^{2}/s |
ρ_{l } |
Density of the liquid |
kg/m^{3} |
ρ_{s } |
Density of solids |
kg/m^{3} |
ρ_{m } |
Density of mixture |
kg/m^{3} |
ξ |
Slip ratio |
- |
μ_{l } |
Dynamic viscosity |
N·s/m^{2} |
η_{l } |
Dynamic viscosity |
N·s/m^{2} |
φ |
Angle of internal friction |
rad |
δ |
Angle of external friction |
rad |