6.14: Nomenclature Early History and Empirical and Semi-Empirical Models
- Page ID
- 31049
a |
Correction factor Jufin Lopatin |
- |
A |
Proportionality constant |
- |
b |
Correction factor Jufin Lopatin |
- |
CD |
Particle drag coefficient |
- |
Cms |
Spatial concentration by mass |
- |
Cv |
Volumetric concentration |
- |
Cvs |
Volumetric spatial concentration |
- |
Cvt |
Volumetric transport/delivered concentration |
- |
Cx |
Inverse particle Froude number squared according to Durand & Condolios Frp-2 |
- |
Cx,Gibert |
Inverse particle Froude number squared according to Gibert |
- |
d |
Particle diameter |
m |
d0 |
Average particle diameter Jufin Lopatin |
m |
d10 |
Particle diameter at which 10% by weight is smaller |
m |
d25 |
Particle diameter at which 25% by weight is smaller |
m |
d50 |
Particle diameter at which 50% by weight is smaller |
m |
d60 |
Particle diameter at which 60% by weight is smaller |
m |
dm |
Mean particle diameter |
m |
di |
Particle size fraction diameters |
m |
Dp |
Pipe diameter |
m |
Dp,H |
Hydraulic diameter pipe cross section above bed |
m |
Du |
Durand & Condolios constant (176-181) or (81-85) |
- |
Erhg |
Relative excess hydraulic gradient |
- |
fl |
Fanning friction factor liquid |
- |
fm |
Fanning friction factor mixture |
|
ELM |
Equivalent Liquid Model |
- |
FL, FL,m |
Durand & Condolios Limit Deposit Velocity coefficient |
- |
Frldv |
Flow Froude number at the Limit Deposit Velocity/critical velocity |
- |
Frfl |
Flow Froude number |
- |
Frp |
Particle Froude number 1/√Cx |
- |
g |
Gravitational constant |
9.81·m/s2 |
i |
Hydraulic gradient |
m.w.c./m |
im |
Hydraulic gradient mixture |
m.w.c./m |
iw,il |
Hydraulic gradient water/liquid |
- |
K |
Durand & Condolios constant (176-181) or (81-85) |
- |
K |
Constant others (Yagi, Babcock, etc.) |
- |
K |
Wilson proportionality constant |
- |
K |
Turian & Yuan constant |
- |
K1 |
Newitt coefficient for heterogeneous transport (1100) |
- |
K2 |
Newitt coefficient for sliding/moving bed (66) |
- |
K1-K10 |
Proportionality constants Thomas |
- |
L, ΔL |
Length of the pipeline |
m |
LDV |
Limit Deposit Velocity |
m/s |
LSDV |
Limit of Stationary Deposit Velocity |
m/s |
MHGV |
Minimum Hydraulic Gradient Velocity |
m/s |
Ncr |
Zandi & Govatos parameter for Limit Deposit Velocity |
- |
p |
Probability |
- |
per |
Relative excess pressure |
- |
Δp |
Head loss over a pipeline length ΔL |
kPa |
Δpm |
Head loss of mixture over a pipeline length ΔL |
kPa |
Δpl, Δpw |
Head loss of liquid/water over a pipeline length ΔL |
kPa |
PSD |
Particle Size Diagram/Distribution |
- |
Rsd |
Relative submerged density |
- |
Sk |
Solids effect factor Fuhrboter spatial concentration |
m/s |
Skt |
Solids effect factor Fuhrboter transport concentration |
m/s |
u* |
Friction velocity |
m/s |
vls |
Line speed |
m/s |
vls,ldv |
Limit Deposit Velocity (often called critical velocity) |
m/s |
vls,h-h |
Transition velocity heterogeneous vs. homogeneous according to Newitt |
m/s |
vls,MHGV |
Minimum Hydraulic Gradient Velocity |
m/s |
vmin |
Minimum gradient velocity |
m/s |
vt |
Terminal settling velocity of particles |
m/s |
vl |
Average liquid velocity |
m/s |
vp |
Average velocity particle |
m/s |
vs |
Average velocity solids |
m/s |
v50 |
50% stratification velocity Wilson |
m/s |
w |
Particle associated velocity |
m/s |
x |
Abscissa |
- |
y |
Ordinate |
- |
α |
Power in Yagi equation |
- |
α |
Darcy Weisbach friction factor constant |
- |
α |
Power of concentration in Turian & Yuan equation |
- |
α1 |
Darcy Weisbach friction factor power |
- |
α2 |
Darcy Weisbach friction factor power |
- |
β |
Power of Richardson & Zaki equation |
- |
β |
Power of Fanning friction factor liquid in Turian & Yuan equation |
- |
\(\ \boldsymbol\gamma\) |
Power of drag coefficient in Turian & Yuan equation |
- |
δ |
Power of Froude number in Turian & Yuan equation |
- |
ρl |
Liquid density |
ton/m3 |
ρw |
Density of water |
ton/m3 |
ρm |
Mixture density |
ton/m3 |
λl |
Darcy-Weisbach friction factor liquid to wall |
- |
μsf |
Friction coefficient for sliding bed (see also Srs) |
- |
μl |
Dynamic viscosity liquid |
Pa·s |
μm |
Dynamic viscosity mixture |
Pa·s |
Φ |
Durand relative excess pressure as ordinate in different graphs |
- |
ψ |
Durand abscissa, equations may differ due to historical development, later the relative submerged density has been added, sometimes the particle Froude number is omitted |
- |
ψ |
Particle shape coefficient, usually near 0.7 |
- |
ψ* |
Particle factor Jufin Lopatin |
- |
\(\ v_{\mathrm{w}}, v_{\mathrm{l}} \) |
Kinematic viscosity of water/liquid |
m2/s |
\(\ v_{\mathrm{m}} \) |
Kinematic viscosity of mixture with Thomas equation |
m2/s |
\(\ v_{\mathrm{r}} \) |
Relative kinematic viscosity \(\ v_{\mathrm{m}}/ v_{\mathrm{w}} \) |
- |
ξ |
Particle shape factor |
- |
ξ |
Slip ratio Yagi |
- |