Batch
Centrifugal Machine Capacity and Gravity Factor Calculation
The batch centrifugal
machines have
been using to handle
white and refined sugar massecuites as well as for affination of raw sugar in
the sugar refineries.
The batch machines were fully satisfying the
sugar industry requirements for high sugar quality such as: low color, no lumps
and low residual moisture content.
The purpose of this article is to evaluate
the batch centrifugal machine capacity and its gravity factor
Parameters to be required for calculation:
Basket Shell Internal Diameter in meters = D
Thickness of the massecuite in meters
= e (Generally “e” value taken 0.14D for theoretical and 0.12D for
practical)
Basket top plate angle to horizontal level in
Deg.= θ (Generally this value having 5deg.)
Height of the basket in meters= H
RPM of the basket (maximum RPM in
Cycle) = N
Time required for one cycle in
sec = T
Density of the massecuite in
gm/ml = S
Formulas for Calculation :
Volume of the massecuite per cycle in M3 (M3/cycle) = V = π e[ H(D-e) + e tanθ ((3D-4e)/6)]
No. of cycles per hour (cycle/hr) =C
=3600/T
Capacity of the machine
(Theoretically) (Q)
Q = C x V in M3/hr (M3/cycle x Cycle/hr)
=Q x S in
tons/hr
But in practically calculating the capacity
of machine takes the following considerations.
1. Take
1 to 2 empty cycles during in an hour (Depends on massecuite condition) so
consider one empty full cycle in total cycles per hour.
2. While
charging the massecuite is always purged, spelling out some molasses such that
creating space for further massecuite. This is called purging capacity. It is
10% more than theoretical capacity.
Capacity of the machine
(Practically) =Q
[(C-1) x V] x 1.1 in M3/hr
Q x S in tons/hr
Empty Basket Shell Radius in mtrs
= R = D/2
Basket Shell Radius with massecuite in
mtrs = r = R-e
Mean Equivalent Radius in mtrs = Rm = 2/3 [(R3 – r3) / (R2 – r2)]
Gravity
factor = G = Rm x 1119 x (N /
1000)2
Gravity factor (General
formula) = G = D x N2 / 1800
Explanation for gravity factor formula
Gravity Factor
= Centrifugal force / Gravitational force
= m x Rm x w2 / m x g.
Where Rm is M.E.R. and
w = angular velocity = 2 π
N /60 g = 9.8 m/sec2
Gravity Factor =[ Rm . X 1 X (2πN / 60 )2 ] /
9.8
= Rm x 1119 x (N / 1000)2
How you are converting that volume into kg/charge
Volume of the massecuite per cycle in M3 = = π e[ H(D-e) + e tanθ ((3D-4e)/6)]
No. of
cycles per hour =C =3600/T
Capacity of
the machine (Theoretically) = Q = C x V in M3/hr
=Q x S in tons/hr
&
Gravity factor = G = Rm x 1119 x (N / 1000)2
Explanation
for above given default example in calculator
|
Practical capacity |
Theoretical capacity |
||
|
Tanθ |
0.087 |
0.087 |
|
|
H(D-e) |
1.586 |
1.550 |
|
|
(3D-4e)/6) |
0.714 |
0.691 |
|
|
e tanθ ((3D-4e)/6) |
0.013 |
0.014 |
|
|
π e[ H(D-e) + e tanθ
((3D-4e)/6)] |
1.024 |
1.169 |
M3 /cycle |
|
V x Density x 1000
x1.1(10%extra for pratical capacity only)) |
1644.443 |
1706.586 |
Kgs/Cycle |
|
Capacity of the machine x
No. of cycles per hour |
31244.42 |
34131.72 |
Kgs/hr |
|
31.24 |
34.13 |
Ton/hr |
|
|
R = D/2 |
0.850 |
0.850 |
|
|
r = R-e |
0.646 |
0.612 |
|
|
Rm = 2/3 [(R3 – r3) / (R2 – r2)] |
0.753 |
0.737 |
|
|
Rm x 1119 x ( N / 1000)2 |
928.526 |
910.000 |
The calculations are very helpful.
HOW TO CALCULATE CENTRIFUGAL MACHINE SCREEN OPENING
It is very simple
1. Find the hole dia of the screen – i.e mesh size ex: 0.06 (60 micron) or 0.09
( 90 micron)
2. Find the no of holes per sq.cm.
3. Find the perforated area of the each segment of the screen and calculate
total area in sq.cm
Now we can find the screen opening area
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