6.14: Nomenclature Early History and Empirical and SemiEmpirical Models
 Page ID
 31049
a 
Correction factor Jufin Lopatin 
 
A 
Proportionality constant 
 
b 
Correction factor Jufin Lopatin 
 
C_{D} 
Particle drag coefficient 
 
C_{ms} 
Spatial concentration by mass 
 
C_{v} 
Volumetric concentration 
 
C_{vs} 
Volumetric spatial concentration 
 
C_{vt} 
Volumetric transport/delivered concentration 
 
C_{x} 
Inverse particle Froude number squared according to Durand & Condolios Fr_{p}^{2} 
 
C_{x,Gibert} 
Inverse particle Froude number squared according to Gibert 
 
d 
Particle diameter 
m 
d_{0} 
Average particle diameter Jufin Lopatin 
m 
d_{10} 
Particle diameter at which 10% by weight is smaller 
m 
d_{25} 
Particle diameter at which 25% by weight is smaller 
m 
d_{50} 
Particle diameter at which 50% by weight is smaller 
m 
d_{60} 
Particle diameter at which 60% by weight is smaller 
m 
d_{m} 
Mean particle diameter 
m 
d_{i} 
Particle size fraction diameters 
m 
D_{p} 
Pipe diameter 
m 
D_{p,H} 
Hydraulic diameter pipe cross section above bed 
m 
Du 
Durand & Condolios constant (176181) or (8185) 
 
E_{rhg} 
Relative excess hydraulic gradient 
 
f_{l} 
Fanning friction factor liquid 
 
f_{m} 
Fanning friction factor mixture 

ELM 
Equivalent Liquid Model 
 
F_{L}, F_{L,m} 
Durand & Condolios Limit Deposit Velocity coefficient 
 
Fr_{ldv} 
Flow Froude number at the Limit Deposit Velocity/critical velocity 
 
Fr_{fl} 
Flow Froude number 
 
Fr_{p} 
Particle Froude number 1/√C_{x} 
 
g 
Gravitational constant 
9.81·m/s^{2} 
i 
Hydraulic gradient 
m.w.c./m 
i_{m} 
Hydraulic gradient mixture 
m.w.c./m 
i_{w},i_{l} 
Hydraulic gradient water/liquid 
 
K 
Durand & Condolios constant (176181) or (8185) 
 
K 
Constant others (Yagi, Babcock, etc.) 
 
K 
Wilson proportionality constant 
 
K 
Turian & Yuan constant 
 
K_{1} 
Newitt coefficient for heterogeneous transport (1100) 
 
K_{2} 
Newitt coefficient for sliding/moving bed (66) 
 
K_{1}K_{10} 
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 
N_{cr} 
Zandi & Govatos parameter for Limit Deposit Velocity 
 
p 
Probability 
 
p_{er} 
Relative excess pressure 
 
Δp 
Head loss over a pipeline length ΔL 
kPa 
Δp_{m} 
Head loss of mixture over a pipeline length ΔL 
kPa 
Δp_{l}, Δp_{w} 
Head loss of liquid/water over a pipeline length ΔL 
kPa 
PSD 
Particle Size Diagram/Distribution 
 
R_{sd} 
Relative submerged density 
 
S_{k} 
Solids effect factor Fuhrboter spatial concentration 
m/s 
S_{kt} 
Solids effect factor Fuhrboter transport concentration 
m/s 
u_{*} 
Friction velocity 
m/s 
v_{ls} 
Line speed 
m/s 
v_{ls,ldv} 
Limit Deposit Velocity (often called critical velocity) 
m/s 
v_{ls,hh} 
Transition velocity heterogeneous vs. homogeneous according to Newitt 
m/s 
v_{ls,MHGV} 
Minimum Hydraulic Gradient Velocity 
m/s 
v_{min} 
Minimum gradient velocity 
m/s 
v_{t} 
Terminal settling velocity of particles 
m/s 
v_{l} 
Average liquid velocity 
m/s 
v_{p} 
Average velocity particle 
m/s 
v_{s} 
Average velocity solids 
m/s 
v_{50} 
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 
 
α_{1} 
Darcy Weisbach friction factor power 
 
α_{2 } 
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 
 
ρ_{l} 
Liquid density 
ton/m^{3} 
ρ_{w} 
Density of water 
ton/m^{3} 
ρ_{m} 
Mixture density 
ton/m^{3} 
λ_{l} 
DarcyWeisbach friction factor liquid to wall 
 
μ_{sf} 
Friction coefficient for sliding bed (see also S_{rs}) 
 
μ_{l} 
Dynamic viscosity liquid 
Pa·s 
μ_{m} 
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 
m^{2}/s 
\(\ v_{\mathrm{m}} \) 
Kinematic viscosity of mixture with Thomas equation 
m^{2}/s 
\(\ v_{\mathrm{r}} \) 
Relative kinematic viscosity \(\ v_{\mathrm{m}}/ v_{\mathrm{w}} \) 
 
ξ 
Particle shape factor 
 
ξ 
Slip ratio Yagi 
 