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Engineering LibreTexts

2.5: Nomenclature

  • Page ID
    29273
  •  

    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

    Velocity of fluid

    m/s

    u

    Velocity of fluid

    m/s

    u

    Friction velocity

    m/s

    Characteristic velocity of object

    m/s

    vls 

    Line speed

    m/s

    vsl 

    Slip velocity

    m/s

    v

    Terminal settling velocity

    m/s

    V

    Volume pipe segment

    m3

    V

    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)

    -

    κ

    Concentration distribution coefficient

    -

    λl 

    Darcy-Weisbach friction factor

    -

    λ 

    Linear concentration according to Bagnold

    -

    \(\ \mathbf{\tau}_{\mathbf{1} \mathbf{2}}\) 

    Bed shear stress

    kPa

    ν

    Kinematic viscosity

    m2/s

    ρ

    Density of the liquid

    kg/m3

    ρ

    Density of solids

    kg/m3

    ρ

    Density of mixture

    kg/m3

    ξ 

    Slip ratio

    -

    μ

    Dynamic viscosity

    N·s/m2

    η

    Dynamic viscosity

    N·s/m2

    φ 

    Angle of internal friction

    rad

    δ 

    Angle of external friction

    rad