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6.14: Nomenclature Early History and Empirical and Semi-Empirical Models

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    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

    -

    This page titled 6.14: Nomenclature Early History and Empirical and Semi-Empirical Models is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Sape A. Miedema (TU Delft Open Textbooks) via source content that was edited to the style and standards of the LibreTexts platform.