3
P gb 2
s a
l 1 2 d
t t
--=
+
^P h l (4)
Minimum required tangential velocity of the slurry at
the air core boundary is given by:
u
P2h 2^P
m
1 t =
-
i (5)
P1—P2 is the differential pressure
Hydrocyclone inlet feed velocity is always at higher
pressure, hence the entry flow velocity:
v u
2P
in
m
in 2 t =-
i (6)
The feed inlet diameter can be calculated through a
continuity equation at a defined throughput (Q), neglect-
ing friction losses at the inlet diameter:
d Q
cy rvin =(7)
The vortex finder diameter can be calculated through
the hydrocyclone diameter, minimum thickness and dcy
from Equation 7.
The dynamic behavior of the slurry boundary and air
interaction, relating surface tension of liquid in the slurry to
the strain rate of the liquid, leads to the potential thrust that
drives the slurry flow to the overflow of the hydrocyclone.
Considering the air impingement on the slurry boundary
and attributing the dynamic interaction with Griffith and
Rabinowicz’s equation [14] on liquid impingement, it is
possible to calculate the overflow slurry flow rate through
slurry diffusion in the air core. Salama and Venkatesh [15]
used this equation to calculate liquid impingement erosive
wear in oil well applications.
through the spigot opening. Previous researchers showed
that the axial position of the air core diameter depends on
the fluctuating operating conditions at the inlet [12]. The
major driving force for the separation of solid particles in
a hydrocyclone is the centrifugal force generated by the
rotational flow of slurry. Centrifugal force generated by
the incipient swirling motion drives the coarser particles to
the vortex free zone and are collected through the under-
flow. The forced vortex zone at the vicinity of the air core
transports the finer particles upward and they are collected
through the overflow. In this paper, low pressure required
to achieve the classification of the particles for a particu-
lar d50 size in the hydrocyclone and other operational and
geometrical parameters associated with the throughput to
be processed are calculated. Below is the schematic diagram
of the hydrodynamic representation for the pressure dis-
tribution considering the composite vortex flow inside the
hydrocyclone.
The differential pressure should be such that it should
generate potential thrust to carry the particles and fluid
along the forced vortex to the overflow of the hydrocyclone
[13]. Modelling the vortex equation:
P A P dr
dp
d dA dmg -+=c m (1)
As density is an explicit parameter assuming the change
is linear, density variation in the hydrocyclone can be given
by:
r a s
s a t t
t t
=+
-
b l (2)
Solving and integrating equation 1 and re-arranging
the terms we get:
P P2h r rdr dtdrD r g
s
s
s
1
t ta dl
--=
-
+^:##(3)
=Thickness of control volume
=Height of the control volume
=forced vortex radius, m
=tangential velocity, m/s
P =Static pressure, pa
ΔP =differential pressure, pa
δr
P P+ΔP
δl
air core
Forced
vortex
Free
vortex
Figure 2. Schematic diagram of pressure variation in composite vortex flow
Hydrcyclonewall
P gb 2
s a
l 1 2 d
t t
--=
+
^P h l (4)
Minimum required tangential velocity of the slurry at
the air core boundary is given by:
u
P2h 2^P
m
1 t =
-
i (5)
P1—P2 is the differential pressure
Hydrocyclone inlet feed velocity is always at higher
pressure, hence the entry flow velocity:
v u
2P
in
m
in 2 t =-
i (6)
The feed inlet diameter can be calculated through a
continuity equation at a defined throughput (Q), neglect-
ing friction losses at the inlet diameter:
d Q
cy rvin =(7)
The vortex finder diameter can be calculated through
the hydrocyclone diameter, minimum thickness and dcy
from Equation 7.
The dynamic behavior of the slurry boundary and air
interaction, relating surface tension of liquid in the slurry to
the strain rate of the liquid, leads to the potential thrust that
drives the slurry flow to the overflow of the hydrocyclone.
Considering the air impingement on the slurry boundary
and attributing the dynamic interaction with Griffith and
Rabinowicz’s equation [14] on liquid impingement, it is
possible to calculate the overflow slurry flow rate through
slurry diffusion in the air core. Salama and Venkatesh [15]
used this equation to calculate liquid impingement erosive
wear in oil well applications.
through the spigot opening. Previous researchers showed
that the axial position of the air core diameter depends on
the fluctuating operating conditions at the inlet [12]. The
major driving force for the separation of solid particles in
a hydrocyclone is the centrifugal force generated by the
rotational flow of slurry. Centrifugal force generated by
the incipient swirling motion drives the coarser particles to
the vortex free zone and are collected through the under-
flow. The forced vortex zone at the vicinity of the air core
transports the finer particles upward and they are collected
through the overflow. In this paper, low pressure required
to achieve the classification of the particles for a particu-
lar d50 size in the hydrocyclone and other operational and
geometrical parameters associated with the throughput to
be processed are calculated. Below is the schematic diagram
of the hydrodynamic representation for the pressure dis-
tribution considering the composite vortex flow inside the
hydrocyclone.
The differential pressure should be such that it should
generate potential thrust to carry the particles and fluid
along the forced vortex to the overflow of the hydrocyclone
[13]. Modelling the vortex equation:
P A P dr
dp
d dA dmg -+=c m (1)
As density is an explicit parameter assuming the change
is linear, density variation in the hydrocyclone can be given
by:
r a s
s a t t
t t
=+
-
b l (2)
Solving and integrating equation 1 and re-arranging
the terms we get:
P P2h r rdr dtdrD r g
s
s
s
1
t ta dl
--=
-
+^:##(3)
=Thickness of control volume
=Height of the control volume
=forced vortex radius, m
=tangential velocity, m/s
P =Static pressure, pa
ΔP =differential pressure, pa
δr
P P+ΔP
δl
air core
Forced
vortex
Free
vortex
Figure 2. Schematic diagram of pressure variation in composite vortex flow
Hydrcyclonewall