...
Lamella
...
Design
...
Program
...
The
...
lamella
...
are
...
the
...
plate
...
settlers
...
place
...
in
...
the
...
top
...
section
...
of
...
the
...
sedimentation
...
tank
...
that
...
help
...
floc
...
settle
...
out efficiently. 
Lamella Design Program Algorithm
The Lamella Design Program uses four constraints to determine design values, the critical velocity of 10 m/day, the upward velocity at the bottom of the tank, the minimum space between the lamella and the predetermined length of the sedimentation tank. All of these constraints come together to determine the length of the lamella. The minimum spacing between the lamella was determine via laboratory experiments, at spacing closer than 2 cm failure occured. The length of the sedimentation tank is set by the Sedimentation Program. The critical velocity is the rate at which a particle must fall to ensure that it settles out within the plate settlers. If the critical velocity is too large, flocs will not settle out, and will remain in the water sent through the distribution system. However, a small critical velocity comes at the expense of a large cross sectional tank area (so it is not practical to have an unnecessarily small critical velocity). The upward velocity at the bottom of the tank is important for sludge blanket formation, too high and the blanket will form too thin and will not capture particles, too slow and the blanket will either settle out instead of remaining suspended or the shear value in the blanket will be so high that flocs will get broken up in the blanket. Either of these issues would result in the sludge blanket being detrimental to the sedimentation process.
The program starts by determining the height needed for the launders above the lamella. This height needed for the launders is same as the depth of water needed above the lamella. This value is simply a function of leaving enough available headloss through the exit launder about the lamella to keep it properly submerged.
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To determine what the how long the lamella need to be, first the active length of the tank and the upward velocity under the lamella must be determined, but both of these values are dependent upon the length of the lamella. Therefore, an iterative loop of the following three equations was created to determine length of the lamella.
The active length of the tank is the total length of the sedimentation tank minus the inactive length of the sedimentation tank found below.
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efficiently. !Lamella.JPG! !lamella front view close up.PNG! h2. Lamella Design Program Algorithm The Lamella Design Program uses four constraints to determine design values, the critical velocity of 10 m/day, the upward velocity at the bottom of the tank, the minimum space between the lamella and the predetermined length of the sedimentation tank. All of these constraints come together to determine the length of the lamella. The minimum spacing between the lamella was determine via laboratory experiments, at spacing closer than 2 cm failure occured. The length of the sedimentation tank is set by the [Sedimentation Program|Sedimentation Tank Dimensions Design Program]. The critical velocity is the rate at which a particle must fall to ensure that it settles out within the plate settlers. If the critical velocity is too large, flocs will not settle out, and will remain in the water sent through the distribution system. However, a small critical velocity comes at the expense of a large cross sectional tank area (so it is not practical to have an unnecessarily small critical velocity). The upward velocity at the bottom of the tank is important for sludge blanket formation, too high and the blanket will form too thin and will not capture particles, too slow and the blanket will either settle out instead of remaining suspended or the shear value in the blanket will be so high that flocs will get broken up in the blanket. Either of these issues would result in the sludge blanket being detrimental to the sedimentation process. The program starts by determining the height needed for the launders above the lamella. This height needed for the launders is same as the depth of water needed above the lamella. This value is simply a function of leaving enough available headloss through the exit launder about the lamella to keep it properly submerged. {include:H.SedAbove} To determine what the how long the lamella need to be, first the active length of the tank and the upward velocity under the lamella must be determined, but both of these values are dependent upon the length of the lamella. Therefore, an iterative loop of the following three equations was created to determine length of the lamella. The active length of the tank is the total length of the sedimentation tank minus the inactive length of the sedimentation tank found below. {latex} \large $$ L.Inactive = L.SedPlate \cdot \cos (AN.SedPlate) + W.InletChannel + W.ExitChannel + 2 \cdot T.ChannelWall $$ {latex} \\ The upward velocity through the lamella: {latex} |
The upward velocity through the lamella:
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\large
$$
V.SedUpActiveBelow = {{Q.Sed} \over {W.Sed \cdot \left( {L.Sed - L.SedInactive} \right)}}
$$
{latex}
\\
Length of the Lamella:
{latex} |
Length of the Lamella:
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|---|
\large
$$
L.SedPlateEst = {{B.SedPlateMin \cdot \left( {{{V.SedUpActiveBelow} \over {V.SedCBod}} - 1} \right) + T.SedPlate} \over {\sin \left( {AN.SedPlate} \right) \cdot \cos \left( {AN.SedPlate} \right)}}
$$
{latex}
|
The
...
length
...
found
...
in
...
the
...
above
...
loop
...
is
...
an
...
estimated
...
length,
...
The
...
actual
...
lamella
...
length
...
is
...
dependent
...
on
...
the
...
length
...
of
...
the
...
plastic
...
sheeting
...
material
...
that
...
available.
...
Typically
...
this
...
sheeting
...
length
...
is
...
either
...
8
...
or
...
12
...
feet.
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|---|
} \large $$ L.SedPlate = {{L.SedPlateSheet} \over {floor\left( {{{L.SedPlateSheet} \over {L.SedPlateEst}}} \right)}} $$ {latex} |
From
...
this
...
number
...
the
...
actual
...
upward
...
velocity
...
(V.SedUpActiveBelow)
...
under
...
the
...
lamella
...
and
...
the
...
actual
...
space
...
needed
...
between
...
the
...
lamella
...
are
...
recalculated.
...
The
...
equation
...
for
...
V.SedUpActiveBelow
...
is
...
the
...
same
...
was
...
used
...
above.
...
The
...
perpendicular,
...
center
...
to
...
center,
...
space
...
between
...
lamella:
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|---|
} \large $$ B.SedPlate = {{L.SedPlate \cdot \sin \left( {AN.SedPlate} \right) \cdot \cos \left( {AN.SedPlate} \right) - T.SedPlate} \over {{{V.SedUpActiveBelow} \over {V.SedCBod}} - 1}} $$ {latex} |
Perpendicular
...
open
...
space
...
between
...
lamella
...
(does
...
not
...
include
...
material
...
thickness):
...
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|---|---|---|---|---|
|
...
The
...
horizontal
...
distance
...
between
...
lamella;
...
this
...
accounts
...
for
...
the
...
angle
...
of
...
the
...
lamella
...
in
...
the
...
tank:
| Latex |
|---|
} \large $$ B.SedPlateHorizontal = {{B.SedPlate} \over {\sin \left( {AN.SedPlate} \right)}} $$ {latex} |
Using
...
the
...
available
...
active
...
length
...
in
...
the
...
sedimentation
...
tank
...
and
...
the
...
known
...
length
...
of
...
the
...
lamella,
...
the
...
number
...
of
...
lamella
...
that
...
can
...
fit
...
in
...
the
...
tank
...
can
...
be
...
calculated
...
as
...
follows.
...
The
...
Number
...
of
...
Lamella:
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|---|
} \large $$ N.SedPlates = ceil\left( {{{L.SedActiveMax} \over {B.SedPlateHorizontal}}} \right) $$ {latex} |
The
...
vertical
...
height
...
taken
...
up
...
by
...
the
...
lamella
...
is
...
simply
...
a
...
function
...
of
...
the
...
lamella
...
length
...
and
...
angle.
| Latex |
|---|
} \large $$ H.SedPlate = L.SedPlate \cdot \cos \left( {AN.SedPlate} \right) $$ {latex} |
The
...
thickness
...
of
...
the
...
lamella
...
contributes
...
a
...
small
...
but
...
significant
...
dead
...
zone
...
to
...
the
...
tank.
...
Now
...
that
...
the
...
exact
...
number
...
of
...
lamella
...
has
...
been
...
calculated,
...
more
...
accurate
...
values
...
of
...
active
...
tank
...
length,
...
upward
...
velocity,
...
and
...
critical
...
velocity
...
can
...
be
...
found.
...
Calculations
...
for
...
these
...
values
...
are
...
shown
...
below.
...
Active
...
Length
...
of
...
the
...
Tank:
...
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|---|---|---|---|---|
|
...
The
...
Actual
...
Upward
...
Velocity
...
at
...
the
...
Bottom
...
of
...
the
...
Tank:
...
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|---|---|---|---|---|
|
...
The
...
Critical
...
Velocity
...
Up
...
through
...
the
...
Lamella:
...
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|---|---|---|---|---|
|
...
The
...
height
...
of
...
the
...
water
...
in
...
the
...
sedimentation
...
tank
...
can
...
now
...
be
...
determined.
...
The
...
inletchannel
...
and
...
the
...
lamella
...
and
...
launders
...
coexist
...
in
...
the
...
same
...
top
...
portion
...
the
...
tank.
...
Therefore
...
the
...
water
...
height
...
is
...
the
...
maximum
...
of
...
these
...
two
...
pieces
...
plus
...
space
...
needed
...
for
...
the
...
elements
...
in
...
the
...
bottom
...
of
...
the
...
tank,
...
which
...
include
...
the
...
inlet
...
manifold
...
and
...
drain.
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} \large $$ HW.Sed = \max \left( {\left( {Z.SedSlopes + H.SedFrameWall + H.SedBetween + 2 \cdot outerdiameter(ND.SedPlateFrame) + H.SedPlate + H.SedAbove} \right),\left( {H.SedManifoldPort + H.SedBetween + T.ChannelWall + H.InletChannel} \right)} \right) $$ {latex} where !Sed tank Water height.PNG! |
where
For tanks where there are more than one bay per tank, a wall is constructed to separate bays. This wall has height that comes up to the top of ledge that supports the lamella frame. This was done so that the wall can lend support to the center section of the lamella. The equation used is as follows.
| Latex |
|---|
For tanks where there are more than one bay per tank, a wall is constructed to separate bays. This wall has height that comes up to the top of ledge that supports the lamella frame. This was done so that the wall can lend support to the center section of the lamella. The equation used is as follows. {latex} \large $$ H.SedBayDivider = Z.SedSlopes + H.SedFrameWall $$ {latex} |
The
...
inlet
...
manifold
...
is
...
formed
...
by
...
laying
...
concrete
...
plates
...
next
...
to
...
each
...
other.
...
The
...
width
...
of
...
each
...
slope
...
plate
...
is
...
defined
...
by
...
the
...
user.
...
If
...
the
...
length
...
of
...
the
...
sedimentation
...
tank
...
is
...
not
...
equally
...
divided
...
by
...
the
...
width
...
of
...
the
...
plate,
...
there
...
is
...
a
...
leftover
...
space
...
that
...
needs
...
to
...
be
...
filled
...
by
...
a
...
fraction
...
of
...
a
...
plate.
...
This
...
is
...
used
...
for
...
construction
...
purposes.
...
More
...
details
...
of
...
about
...
the
...
inlet
...
manifold
...
can
...
be
...
found
...
on
...
the
...
...
...
...
...
.
...
It
...
should
...
be
...
noted
...
that
...
this
...
calculation
...
could
...
not
...
be
...
done
...
in
...
the
...
inlet
...
manifold
...
program
...
because
...
the
...
size
...
of
...
the
...
inlet
...
channel
...
was
...
needed,
...
and
...
the
...
inlet
...
channel
...
is
...
not
...
defined
...
until
...
after
...
the
...
inlet
...
manifold
...
program.
| Latex |
|---|
} \large $$ {\rm{W}}_{{\rm{SedSlopePlateRemaining}}} = L_{Sed} - N_{SedPorts} \cdot W_{SedSlopePlate} $$ {latex} |