Sand trap
Diameter of smallest particle (1) d= 20 mm
Flow Particles density rs = 2400 kg/m3
Q= 500 m3/h Liquid density rL = 1000 kg/m3
Sand trap dimensions Liquid viscosity m= 0.001 Pa s
b= 3 m
h= 3 m Sand trap flow secttion
L= 6 m A= b*h
b= 3 m
h= 3 m
A= 9 m2
L vy
b Particle horizontal velocity
v= Q/A
vx Q= 0.138889
h A= 9.0 m²
vx = 0.015 m/s
Particle residence time
(1). The smallest particle that should be retained t= L/v
in sand trap L= 6 m
vx = 0.015 m/s
t= 388.8 s
Rev. cjc. 31.01.2014
Settling velocity of smallest particle
d= 20 mm
rs = 2400 kg/m3
rL = 1000 kg/m3
m= 0.001 Pa s
vy = Particle_Settling_velocity_d_rs_rL_mu
vy = #VALUE! m/s
Vertical distance travelled by the particle in
the time interval
H= v*t
vy = #VALUE! m/s
t= 388.8
H= #VALUE! m
H= #VALUE! mm
H
Velocidad de decantación
Velocidad de decantación de una esfera de diámetro d [mm], de un material de
densidad rs, en un fluido de densidad rL y viscosidad m [Pas]
v=
√ 4⋅g⋅d⋅( ρ s − ρ L )
3⋅C D⋅ρ L
v= ((4 *g *d *(rs - rL) / (3 * CD * rL))^0.5
v= ((4 *g *d *(rs - rL) / (3 * (Pipe_Slurry_DragCoefficient_CD_Re(Re)) * rL))^0.5
Re = v*d*r/m
CD = (Pipe_Slurry_DragCoefficient_CD_Re(Re)) [1]
La función es válida para numeros de Reynolds resultantes en el rango
0.0002 < Re < 1.000.000
Los límites están dados por el rango de validez del gráfico CD = CD(Re)
v= Pipe_Slurry_Vel_Decantacion_d_rs_rL_mu(d, rs, rL, m)
d= 2 mm
rs = 2400 kg/m3
rL = 1000 kg/m3
m= 0.001 Pa s
v= #VALUE! m/s
d d v v
mm mm m/s m/s mm/s
2 0.010 #VALUE! #VALUE!
50 0.050 #VALUE! #VALUE!
200 0.200 #VALUE! #VALUE!
500 0.5 0.063 #VALUE! #VALUE!
1000 1.0 0.137 #VALUE! #VALUE!
2000 2.0 0.255 #VALUE! #VALUE!
3000 3.0 0.361 #VALUE! #VALUE!
4000 4.0 0.420 #VALUE! #VALUE!
5000 5.0 0.473 #VALUE! #VALUE!
6000 6.0 0.521 #VALUE! #VALUE!
Velocidad de decantación de la partícula
d= 2 mm
rs = 2400 kg/m3
rL = 1000 kg/m3
m= 0.001 Pa s
vy = #VALUE! m/s
Function Slurry_Drag_Coefficient_CD_Re(Re)
f1 = (24 * Re ^ -1) ^ 10 + (21 * Re ^ -0.67) ^ 10 + (4 * Re ^ -0.33) ^ 10 + (0.4) ^ 10
f2 = ((0.148 * Re ^ 0.11) ^ -10 + (0.5) ^ -10) ^ -1
f3 = (1.57 * 10 ^ 8 * Re ^ -1.625) ^ 10
f4 = ((6 * 10 ^ -17 * Re ^ 2.63) ^ -10 + (0.2) ^ -10) ^ -1
CD = (1 / ((f1 + f2) ^ -1 + (f3) ^ -1) + f4) ^ 0.1
Slurry_Drag_Coefficient_CD_Re = CD
End Function
'Drag coefficient of flow around a sphere: Matching asymptotically the wide trend
'Jaber Almedeij
'Powder Technology 186 (2008) 218–223
'Available online at www.sciencedirect.com
'www.elsevier.com/locate/powtec
'For very small Reynolds numbers, Stokes proposed an analytical solution of drag coefficient by
'solving the general differential equation of Navier–Stokes
'
'CD = 24 / Re Eq.1
'
'The Stokes solution neglects the effects of inertia and is acceptable roughly for Re < 0.4,
'when the laminar boundary layer is not separated from the particle.
'Fig. 1. Drag coefficient for the wide range of Particle Reynolds numbers.
'Data shown in the figure obtained from Stokes regime by Eq. (1) and from experiments
'available in the literature [26,27].
'
Function Particle_Settling_velocity_d_rs_rL_mu(d, rs, rL, mu)
'v : Particle setting velocity in water [m/s]
'd : Particle diameter [microns]
'rs : Solid (particle) density kg/m3
'rL : Liquid density kg/m3
'mu : Liquid absolute viscosity [Pa]
d = d / 1000 / 1000 'm
g = 9.80665 'm/s2
DvStop = 1 / 100 / 100
vIncrement = 1 / 100
vasum = 1 / 100 / 100 'm/s
1000:
Re = vasum * d * rL / mu
vcalc = ((4 * g * d * (rs - rL)) / (3 * (Slurry_Drag_Coefficient_CD_Re(Re) * rL))) ^ 0.5
Dv = (vasum - vcalc)
If Abs(Dv) < DvStop Then
Particle_Settling_velocity_d_rs_rL_mu = vasum
Exit Function
Else: vasum = vcalc
End If
GoTo 1000
End Function
rag coefficient by
Microsoft Equation
3.0
[1] 'Drag coefficient of flow around a sphere: Matching asymptotically the wide trend
'Jaber Almedeij
'Powder Technology 186 (2008) 218–223
'Available online at www.sciencedirect.com
'www.elsevier.com/locate/powtec
