2.5: Nomenclature
- Page ID
- 29273
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)
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 |